// Giac integration test file: "0 Independent test suites\Apostol Problems.txt"
// "nock" means we do not check the antiderivative
I:=i;
lst:=[

// James Stewart - Calculus (1987)

// Section 7.1 - Integration by Parts
[x^n,x,1,x^(1+n)/(1+n)],
[exp(x),x,1,exp(x)],
[1/x,x,1,log(x)],
[a^x,x,1,a^x/log(a)],
[sin(x),x,1,-cos(x)],
[cos(x),x,1,sin(x)],
[sec(x)^2,x,2,tan(x)],
[csc(x)^2,x,2,-cot(x)],
[sec(x)*tan(x),x,2,sec(x)],
[cot(x)*csc(x),x,2,-csc(x)],
[sinh(x),x,1,cosh(x)],
[cosh(x),x,1,sinh(x)],
[tan(x),x,1,-log(cos(x))],
[cot(x),x,1,log(sin(x))],
[x*sin(x),x,2,-x*cos(x)+sin(x)],
[log(x),x,1,-x+x*log(x)],
[exp(x)*x^2,x,3,2*exp(x)-2*exp(x)*x+exp(x)*x^2],
[exp(x)*sin(x),x,1,-1/2*exp(x)*cos(x)+1/2*exp(x)*sin(x)],
[arctan(x),x,2,x*arctan(x)-1/2*log(1+x^2)],
[exp(2*x)*x,x,2,-1/4*exp(2*x)+1/2*exp(2*x)*x],
[x*cos(x),x,2,cos(x)+x*sin(x)],
[x*sin(4*x),x,2,-1/4*x*cos(4*x)+1/16*sin(4*x)],
[x*log(x),x,1,-1/4*x^2+1/2*x^2*log(x)],
[x^2*cos(3*x),x,3,2/9*x*cos(3*x)-2/27*sin(3*x)+1/3*x^2*sin(3*x)],
[x^2*sin(2*x),x,3,1/4*cos(2*x)-1/2*x^2*cos(2*x)+1/2*x*sin(2*x)],
[log(x)^2,x,2,2*x-2*x*log(x)+x*log(x)^2],
[arcsin(x),x,2,x*arcsin(x)+sqrt(1-x^2)],
[t*cos(t)*sin(t),t,3,-1/4*t+1/4*cos(t)*sin(t)+1/2*t*sin(t)^2],
[t*sec(t)^2,t,2,log(cos(t))+t*tan(t)],
[t^2*log(t),t,1,-1/9*t^3+1/3*t^3*log(t)],
[exp(t)*t^3,t,4,-6*exp(t)+6*exp(t)*t-3*exp(t)*t^2+exp(t)*t^3],
[exp(2*t)*sin(3*t),t,1,-3/13*exp(2*t)*cos(3*t)+2/13*exp(2*t)*sin(3*t)],
[cos(3*t)/exp(t),t,1,-1/10*cos(3*t)/exp(t)+3/10*sin(3*t)/exp(t)],
[y*sinh(y),y,2,y*cosh(y)-sinh(y)],
[y*cosh(a*y),y,2,-cosh(a*y)/a^2+y*sinh(a*y)/a],
[t/exp(t),t,2,(-1)/exp(t)-t/exp(t)],
[log(t)*sqrt(t),t,1,-4/9*t^(3/2)+2/3*t^(3/2)*log(t)],
[x*cos(2*x),x,2,1/4*cos(2*x)+1/2*x*sin(2*x)],
[x^2/exp(x),x,3,(-2)/exp(x)-2*x/exp(x)-x^2/exp(x)],
[arccos(x),x,2,x*arccos(x)-sqrt(1-x^2)],
[x*csc(x)^2,x,2,-x*cot(x)+log(sin(x))],
[cos(5*x)*sin(3*x),x,1,1/4*cos(2*x)-1/16*cos(8*x)],
[sin(2*x)*sin(4*x),x,1,1/4*sin(2*x)-1/12*sin(6*x)],
[cos(x)*log(sin(x)),x,2,-sin(x)+log(sin(x))*sin(x)],
[exp(x^2)*x^3,x,2,-1/2*exp(x^2)+1/2*exp(x^2)*x^2],
[exp(x)*(3+2*x),x,2,-2*exp(x)+exp(x)*(3+2*x)],
[5^x*x,x,2,-5^x/log(5)^2+5^x*x/log(5)],
[cos(log(x)),x,1,1/2*x*cos(log(x))+1/2*x*sin(log(x))],
[exp(sqrt(x)),x,3,-2*exp(sqrt(x))+2*exp(sqrt(x))*sqrt(x)],
[log(sqrt(x)),x,1,-1/2*x+x*log(sqrt(x))],
[sin(log(x)),x,1,-1/2*x*cos(log(x))+1/2*x*sin(log(x))],
[sin(sqrt(x)),x,3,2*sin(sqrt(x))-2*cos(sqrt(x))*sqrt(x)],
[x^5*cos(x^3),x,3,1/3*cos(x^3)+1/3*x^3*sin(x^3)],
[exp(x^2)*x^5,x,3,exp(x^2)-exp(x^2)*x^2+1/2*exp(x^2)*x^4],
[x*arctan(x),x,3,-1/2*x+1/2*arctan(x)+1/2*x^2*arctan(x)],
[x*cos(Pi*x),x,2,cos(Pi*x)/Pi^2+x*sin(Pi*x)/Pi],
[log(x)*sqrt(x),x,1,-4/9*x^(3/2)+2/3*x^(3/2)*log(x)],

// Section 7.2 - Trigonometric Integrals
[sin(3*x)^2,x,2,1/2*x-1/6*cos(3*x)*sin(3*x)],
[cos(x)^2,x,2,1/2*x+1/2*cos(x)*sin(x)],
[cos(x)^4,x,3,3/8*x+3/8*cos(x)*sin(x)+1/4*cos(x)^3*sin(x)],
[sin(x)^3,x,2,-cos(x)+1/3*cos(x)^3],
[cos(x)^4*sin(x)^3,x,3,-1/5*cos(x)^5+1/7*cos(x)^7],
[cos(x)^3*sin(x)^4,x,3,1/5*sin(x)^5-1/7*sin(x)^7],
[cos(x)^2*sin(x)^4,x,4,1/16*x+1/16*cos(x)*sin(x)-1/8*cos(x)^3*sin(x)-1/6*cos(x)^3*sin(x)^3],
[cos(x)^2*sin(x)^2,x,3,1/8*x+1/8*cos(x)*sin(x)-1/4*cos(x)^3*sin(x)],
[(1-sin(2*x))^2,x,1,3/2*x+cos(2*x)-1/4*cos(2*x)*sin(2*x)],
[cos(x)*sin(1/6*Pi+x),x,3,1/4*x-1/4*cos(1/6*Pi+2*x)],
[cos(x)^5*sin(x)^5,x,4,1/6*sin(x)^6-1/4*sin(x)^8+1/10*sin(x)^10],
[sin(x)^6,x,4,5/16*x-5/16*cos(x)*sin(x)-5/24*cos(x)*sin(x)^3-1/6*cos(x)*sin(x)^5],
[cos(x)^6,x,4,5/16*x+5/16*cos(x)*sin(x)+5/24*cos(x)^3*sin(x)+1/6*cos(x)^5*sin(x)],
[cos(2*x)^4*sin(2*x)^2,x,4,1/16*x+1/32*cos(2*x)*sin(2*x)+1/48*cos(2*x)^3*sin(2*x)-1/12*cos(2*x)^5*sin(2*x)],
[sin(x)^5,x,2,-cos(x)+2/3*cos(x)^3-1/5*cos(x)^5],
[cos(x)^4*sin(x)^4,x,5,3/128*x+3/128*cos(x)*sin(x)+1/64*cos(x)^3*sin(x)-1/16*cos(x)^5*sin(x)-1/8*cos(x)^5*sin(x)^3],
[sin(x)^3*sqrt(cos(x)),x,3,-2/3*cos(x)^(3/2)+2/7*cos(x)^(7/2)],
[cos(x)^3*sqrt(sin(x)),x,3,2/3*sin(x)^(3/2)-2/7*sin(x)^(7/2)],
[cos(sqrt(x))^2/sqrt(x),x,3,cos(sqrt(x))*sin(sqrt(x))+sqrt(x)],
[x*sin(x^2)^3,x,3,-1/2*cos(x^2)+1/6*cos(x^2)^3],
[cos(x)^2*tan(x)^3,x,3,1/2*cos(x)^2-log(cos(x))],
[cot(x)^5*sin(x)^2,x,4,-1/2*csc(x)^2-2*log(sin(x))+1/2*sin(x)^2],
[(1-sin(x))/cos(x),x,2,log(1+sin(x))],
[1/(1-sin(x)),x,1,cos(x)/(1-sin(x))],
[tan(x)^2,x,2,-x+tan(x)],
[tan(x)^4,x,3,x-tan(x)+1/3*tan(x)^3],
[sec(x)^4,x,2,tan(x)+1/3*tan(x)^3],
[sec(x)^6,x,2,tan(x)+2/3*tan(x)^3+1/5*tan(x)^5],
[sec(x)^2*tan(x)^4,x,2,1/5*tan(x)^5],
[sec(x)^4*tan(x)^2,x,3,1/3*tan(x)^3+1/5*tan(x)^5],
[sec(x)^3*tan(x),x,2,1/3*sec(x)^3],
[sec(x)^3*tan(x)^3,x,3,-1/3*sec(x)^3+1/5*sec(x)^5],
[tan(x)^5,x,3,-log(cos(x))-1/2*tan(x)^2+1/4*tan(x)^4],
[tan(x)^6,x,4,-x+tan(x)-1/3*tan(x)^3+1/5*tan(x)^5],
[sec(x)*tan(x)^5,x,3,sec(x)-2/3*sec(x)^3+1/5*sec(x)^5],
[sec(x)^3*tan(x)^5,x,3,1/3*sec(x)^3-2/5*sec(x)^5+1/7*sec(x)^7],
[sec(x)^6*tan(x),x,2,1/6*sec(x)^6],
[sec(x)^6*tan(x)^3,x,3,-1/6*sec(x)^6+1/8*sec(x)^8],
[sec(x)^2/cot(x),x,2,1/2*sec(x)^2],
[sec(x)*tan(x)^2,x,2,-1/2*arctanh(sin(x))+1/2*sec(x)*tan(x)],
[cot(x)^2,x,2,-x-cot(x)],
[cot(x)^3,x,2,-1/2*cot(x)^2-log(sin(x))],
[cot(x)^4*csc(x)^4,x,3,-1/5*cot(x)^5-1/7*cot(x)^7],
[cot(x)^3*csc(x)^4,x,3,1/4*csc(x)^4-1/6*csc(x)^6],
[csc(x),x,1,-arctanh(cos(x))],
[csc(x)^3,x,2,-1/2*arctanh(cos(x))-1/2*cot(x)*csc(x)],
[cos(x)^2/sin(x),x,3,-arctanh(cos(x))+cos(x)],
[1/sin(x)^4,x,2,-cot(x)-1/3*cot(x)^3],
[sin(2*x)*sin(5*x),x,1,1/6*sin(3*x)-1/14*sin(7*x)],
[cos(x)*sin(3*x),x,1,-1/4*cos(2*x)-1/8*cos(4*x)],
[cos(3*x)*cos(4*x),x,1,1/2*sin(x)+1/14*sin(7*x)],
[sin(3*x)*sin(6*x),x,1,1/6*sin(3*x)-1/18*sin(9*x)],
[cos(x)^5*sin(x),x,2,-1/6*cos(x)^6],
[cos(x)*cos(2*x)*cos(3*x),x,5,1/4*x+1/8*sin(2*x)+1/16*sin(4*x)+1/24*sin(6*x)],
[(1-tan(x)^2)/sec(x)^2,x,2,cos(x)*sin(x)],
[(cos(x)+sin(x))/sin(2*x),x,6,-1/2*arctanh(cos(x))+1/2*arctanh(sin(x))],
[sin(x)^2*tan(x),x,3,1/2*cos(x)^2-log(cos(x))],
[cos(x)^2*cot(x)^3,x,4,-1/2*csc(x)^2-2*log(sin(x))+1/2*sin(x)^2],
[sec(x)^3*tan(x),x,2,1/3*sec(x)^3],
[sec(x)^3*tan(x)^3,x,3,-1/3*sec(x)^3+1/5*sec(x)^5],

// Section 7.3 - Trigonometric Substitution
[sqrt(9-x^2)/x^2,x,2,-arcsin(1/3*x)-sqrt(9-x^2)/x],
[1/(x^2*sqrt(4+x^2)),x,1,-1/4*sqrt(4+x^2)/x],
[x/sqrt(4+x^2),x,1,sqrt(4+x^2)],
[1/sqrt(-a^2+x^2),x,2,arctanh(x/sqrt(-a^2+x^2))],
[x^3/(9+4*x^2)^(3/2),x,3,9/16/sqrt(9+4*x^2)+1/16*sqrt(9+4*x^2)],
[x/sqrt(3-2*x-x^2),x,3,arcsin(1/2*(-1-x))-sqrt(3-2*x-x^2)],
[1/(x^2*sqrt(1-x^2)),x,1,-sqrt(1-x^2)/x],
[x^3*sqrt(4-x^2),x,3,-4/3*(4-x^2)^(3/2)+1/5*(4-x^2)^(5/2)],
[x/sqrt(1-x^2),x,1,-sqrt(1-x^2)],
[x*sqrt(4-x^2),x,1,-1/3*(4-x^2)^(3/2)],
[sqrt(1-4*x^2),x,2,1/4*arcsin(2*x)+1/2*x*sqrt(1-4*x^2)],
[x^3/sqrt(4+x^2),x,3,1/3*(4+x^2)^(3/2)-4*sqrt(4+x^2)],
[1/sqrt(9+x^2),x,1,arcsinh(1/3*x)],
[sqrt(1+x^2),x,2,1/2*arcsinh(x)+1/2*x*sqrt(1+x^2)],
[1/(x^3*sqrt(-16+x^2)),x,4,1/128*arctan(1/4*sqrt(-16+x^2))+1/32*sqrt(-16+x^2)/x^2],
[sqrt(-a^2+x^2)/x^4,x,1,1/3*(-a^2+x^2)^(3/2)/(a^2*x^3)],
[sqrt(-4+9*x^2)/x,x,4,-2*arctan(1/2*sqrt(-4+9*x^2))+sqrt(-4+9*x^2)],
[1/(x^2*sqrt(-9+16*x^2)),x,1,1/9*sqrt(-9+16*x^2)/x],
[x^2/(a^2-x^2)^(3/2),x,3,-arctan(x/sqrt(a^2-x^2))+x/sqrt(a^2-x^2)],
[x^2/sqrt(5-x^2),x,2,5/2*arcsin(x/sqrt(5))-1/2*x*sqrt(5-x^2)],
[1/(x*sqrt(3+x^2)),x,3,-arctanh(sqrt(3+x^2)/sqrt(3))/sqrt(3)],
[x/(4+x^2)^(5/2),x,1,(-1/3)/(4+x^2)^(3/2)],
[x^3*sqrt(4-9*x^2),x,3,-4/243*(4-9*x^2)^(3/2)+1/405*(4-9*x^2)^(5/2)],
[x^2*sqrt(9-x^2),x,3,81/8*arcsin(1/3*x)-9/8*x*sqrt(9-x^2)+1/4*x^3*sqrt(9-x^2)],
[5*x*sqrt(1+x^2),x,2,5/3*(1+x^2)^(3/2)],
[1/(-25+4*x^2)^(3/2),x,1,-1/25*x/sqrt(-25+4*x^2)],
[sqrt(2*x-x^2),x,3,-1/2*arcsin(1-x)-1/2*(1-x)*sqrt(2*x-x^2)],
[1/sqrt(8+4*x+x^2),x,2,arcsinh(1/2*(2+x))],
[1/sqrt(-8+6*x+9*x^2),x,2,1/3*arctanh((1+3*x)/sqrt(-8+6*x+9*x^2))],
[x^2/sqrt(4*x-x^2),x,4,-6*arcsin(1-1/2*x)-3*sqrt(4*x-x^2)-1/2*x*sqrt(4*x-x^2)],
[1/(2+2*x+x^2)^2,x,3,1/2*(1+x)/(2+2*x+x^2)+1/2*arctan(1+x)],
[1/(5-4*x-x^2)^(5/2),x,2,1/27*(2+x)/(5-4*x-x^2)^(3/2)+2/243*(2+x)/sqrt(5-4*x-x^2)],
[exp(t)*sqrt(9-exp(2*t)),t,3,9/2*arcsin(1/3*exp(t))+1/2*exp(t)*sqrt(9-exp(2*t))],
[sqrt(-9+exp(2*t)),t,4,-3*arctan(1/3*sqrt(-9+exp(2*t)))+sqrt(-9+exp(2*t))],

// Section 7.4 - Integration of Rational Functions by Partial Fractions
[1/sqrt(a^2+x^2),x,2,arctanh(x/sqrt(a^2+x^2))],
[(5+x)/(-2+x+x^2),x,3,2*log(1-x)-log(2+x)],
[(x+x^3)/(-1+x),x,3,2*x+1/2*x^2+1/3*x^3+2*log(1-x)],
[(-1+2*x+x^2)/(-2*x+3*x^2+2*x^3),x,3,1/10*log(1-2*x)+1/2*log(x)-1/10*log(2+x)],
[(1+4*x-2*x^2+x^4)/(1-x-x^2+x^3),x,2,2/(1-x)+x+1/2*x^2+log(1-x)-log(1+x)],
[(4-x+2*x^2)/(4*x+x^3),x,6,-1/2*arctan(1/2*x)+log(x)+1/2*log(4+x^2)],
[(2-3*x+4*x^2)/(3-4*x+4*x^2),x,6,x+1/8*log(3-4*x+4*x^2)+1/4*arctan((1-2*x)/sqrt(2))/sqrt(2)],
[(1+x^2+x^3)/((-1+x)*x*(1+x^2)^3*(1+x+x^2)),x,14,1/8*(1+x)/(1+x^2)^2-3/8*(1-x)/(1+x^2)+3/16*x/(1+x^2)+7/16*arctan(x)+1/8*log(1-x)-log(x)+15/16*log(1+x^2)-1/2*log(1+x+x^2)-arctan((1+2*x)/sqrt(3))/sqrt(3)],
[(1-3*x+2*x^2-x^3)/(x*(1+x^2)^2),x,6,1/2*(-1-2*x)/(1+x^2)-2*arctan(x)+log(x)-1/2*log(1+x^2)],
[1/(1+x^2)^2,x,2,1/2*x/(1+x^2)+1/2*arctan(x)],
[1/((-1+x)*(2+x)),x,3,1/3*log(1-x)-1/3*log(2+x)],
[7/(-12+5*x+2*x^2),x,4,7/11*log(3-2*x)-7/11*log(4+x)],
[(-4+3*x+x^2)/((-1+2*x)^2*(3+2*x)),x,2,(-9/32)/(1-2*x)+41/128*log(1-2*x)-25/128*log(3+2*x)],
[(-x^2+x^3)/((-6+x)*(3+5*x)^3),x,3,(-12/1375)/(3+5*x)^2+201/15125/(3+5*x)+20/3993*log(6-x)+1493/499125*log(3+5*x)],
[1/(-x^3+x^4),x,3,1/2/x^2+1/x+log(1-x)-log(x)],
[(1-x-x^2+x^3+x^4)/(-x+x^3),x,4,x+1/2*x^2-log(x)+1/2*log(1-x^2)],
[(-2+x^2)/(x*(2+x^2)),x,3,-log(x)+log(2+x^2)],
[(2-4*x^2+x^3)/((1+x^2)*(2+x^2)),x,8,6*arctan(x)-1/2*log(1+x^2)+log(2+x^2)-5*arctan(x/sqrt(2))*sqrt(2)],
[(1+x^2+x^4)/((1+x^2)*(4+x^2)^2),x,6,-13/24*x/(4+x^2)+25/144*arctan(1/2*x)+1/9*arctan(x)],
[(1+16*x)/((5+x)^2*(-3+2*x)*(1+x+x^2)),x,6,(-79/273)/(5+x)+200/3211*log(3-2*x)+2731/24843*log(5+x)-481/5586*log(1+x+x^2)+451/2793*arctan((1+2*x)/sqrt(3))/sqrt(3)],
[x^4/(9+x^2)^3,x,3,-1/4*x^3/(9+x^2)^2-3/8*x/(9+x^2)+1/8*arctan(1/3*x)],
[19*x/((-1+x)^3*(3+5*x+4*x^2)^2),x,8,(-399/736)/(1-x)^2+(-1843/4416)/(1-x)+19/276*(39+44*x)/((1-x)^2*(3+5*x+4*x^2))+209/2304*log(1-x)-209/4608*log(3+5*x+4*x^2)+114437/52992*arctan((5+8*x)/sqrt(23))/sqrt(23)],
[(1+x^2+x^3)/(2*x^2+x^3+x^4),x,7,(-1/2)/x-1/4*log(x)+5/8*log(2+x+x^2)+1/4*arctan((1+2*x)/sqrt(7))/sqrt(7)],
[1/(-x^3+x^6),x,8,1/2/x^2+1/3*log(1-x)-1/6*log(1+x+x^2)-arctan((1+2*x)/sqrt(3))/sqrt(3)],
[x^2/(1+x),x,2,-x+1/2*x^2+log(1+x)],
[x/(-5+x),x,2,x+5*log(5-x)],
[(-1+4*x)/((-1+x)*(2+x)),x,2,log(1-x)+3*log(2+x)],
[1/((1+x)*(2+x)),x,3,log(1+x)-log(2+x)],
[(-5+6*x)/(3+2*x),x,2,3*x-7*log(3+2*x)],
[1/((a+x)*(b+x)),x,3,-log(a+x)/(a-b)+log(b+x)/(a-b)],
[(1+x^2)/(-x+x^2),x,3,x+2*log(1-x)-log(x)],
[(1-12*x+x^2+x^3)/(-12+x+x^2),x,5,1/2*x^2+1/7*log(3-x)-1/7*log(4+x)],
[(3+2*x)/(1+x)^2,x,2,(-1)/(1+x)+2*log(1+x)],
[1/(x*(1+x)*(3+2*x)),x,2,1/3*log(x)-log(1+x)+2/3*log(3+2*x)],
[(-3+5*x+6*x^2)/(-3*x+2*x^2+x^3),x,3,2*log(1-x)+log(x)+3*log(3+x)],
[x/(4+4*x+x^2),x,3,2/(2+x)+log(2+x)],
[1/((-1+x)^2*(4+x)),x,2,1/5/(1-x)-1/25*log(1-x)+1/25*log(4+x)],
[x^2/((-3+x)*(2+x)^2),x,2,4/5/(2+x)+9/25*log(3-x)+16/25*log(2+x)],
[(-2+3*x+5*x^2)/(2*x^2+x^3),x,3,1/x+2*log(x)+3*log(2+x)],
[(18-2*x-4*x^2)/(-6+x+4*x^2+x^3),x,2,log(1-x)-2*log(2+x)-3*log(3+x)],
[(2*x+x^2)/(4+3*x^2+x^3),x,1,1/3*log(4+3*x^2+x^3)],
[1/((-1+x)^2*x^2),x,2,1/(1-x)+(-1)/x-2*log(1-x)+2*log(x)],
[x^2/(1+x)^3,x,2,(-1/2)/(1+x)^2+2/(1+x)+log(1+x)],
[1/(-x^2+x^4),x,3,1/x-arctanh(x)],
[(-x+2*x^3)/(1-x^2+x^4),x,1,1/2*log(1-x^2+x^4)],
[x^3/(1+x^2),x,3,1/2*x^2-1/2*log(1+x^2)],
[(-1+x)/(2+2*x+x^2),x,4,-2*arctan(1+x)+1/2*log(2+2*x+x^2)],
[x/(1+x+x^2),x,4,1/2*log(1+x+x^2)-arctan((1+2*x)/sqrt(3))/sqrt(3)],
[(7+5*x+4*x^2)/(5+4*x+4*x^2),x,6,x+3/8*arctan(1/2+x)+1/8*log(5+4*x+4*x^2)],
[(5-4*x+3*x^2)/((-1+x)*(1+x^2)),x,5,-3*arctan(x)+2*log(1-x)+1/2*log(1+x^2)],
[(3+2*x)/(3*x+x^3),x,6,log(x)-1/2*log(3+x^2)+2*arctan(x/sqrt(3))/sqrt(3)],
[1/(-1+x^3),x,6,1/3*log(1-x)-1/6*log(1+x+x^2)-arctan((1+2*x)/sqrt(3))/sqrt(3)],
[x^3/(1+x^3),x,7,x-1/3*log(1+x)+1/6*log(1-x+x^2)+arctan((1-2*x)/sqrt(3))/sqrt(3)],
[(-1-2*x+x^2)/((-1+x)^2*(1+x^2)),x,5,1/(-1+x)+arctan(x)+log(1-x)-1/2*log(1+x^2)],
[x^4/(-1+x^4),x,4,x-1/2*arctan(x)-1/2*arctanh(x)],
[(-4+6*x-x^2+3*x^3)/((1+x^2)*(2+x^2)),x,6,-3*arctan(x)+3/2*log(1+x^2)+arctan(x/sqrt(2))*sqrt(2)],
[(1+x-2*x^2+x^3)/(4+5*x^2+x^4),x,7,-3/2*arctan(1/2*x)+arctan(x)+1/2*log(4+x^2)],
[(-3+x)/(4+2*x+x^2)^2,x,3,1/6*(-7-4*x)/(4+2*x+x^2)-2/3*arctan((1+x)/sqrt(3))/sqrt(3)],
[(1+x^4)/(x*(1+x^2)^2),x,3,1/(1+x^2)+log(x)],
[cos(x)*(-3+2*sin(x))/(2-3*sin(x)+sin(x)^2),x,2,log(2-3*sin(x)+sin(x)^2)],
[cos(x)^2*sin(x)/(5+cos(x)^2),x,3,-cos(x)+arctan(cos(x)/sqrt(5))*sqrt(5)],
[1/(-3+2*x+x^2),x,3,1/4*log(1-x)-1/4*log(3+x)],
[1/(-2*x+x^2),x,1,1/2*log(2-x)-1/2*log(x)],
[(1+2*x)/(-7+12*x+4*x^2),x,3,1/8*log(1-2*x)+3/8*log(7+2*x)],
[x/(-1+x+x^2),x,3,1/10*log(1+2*x-sqrt(5))*(5-sqrt(5))+1/10*log(1+2*x+sqrt(5))*(5+sqrt(5))],

// Section 7.5 - Rationalization Substitutions
[(-32+5*x-27*x^2+4*x^3)/(-70-299*x-286*x^2+50*x^3-13*x^4+30*x^5),x,6,-3146/80155*log(7-3*x)-334/323*log(1+2*x)+4822/4879*log(2+5*x)+11049/260015*log(5+x+x^2)+3988/13685*arctan((1+2*x)/sqrt(19))/sqrt(19)],
[(8-13*x^2-7*x^3+12*x^5)/(4-20*x+41*x^2-80*x^3+116*x^4-80*x^5+100*x^6),x,7,5828/9075/(2-5*x)+1/1452*(-313-502*x)/(1+2*x^2)-59096/99825*log(2-5*x)+2843/7986*log(1+2*x^2)-251/726*arctan(x*sqrt(2))/sqrt(2)+272/1331*arctan(x*sqrt(2))*sqrt(2)],
[sqrt(4+x)/x,x,3,-4*arctanh(1/2*sqrt(4+x))+2*sqrt(4+x)],
[1/((-1)/x^(1/3)+sqrt(x)),x,9,6/5*log(1-x^(1/6))-3/10*log(2+x^(1/6)+2*x^(1/3)+x^(1/6)*sqrt(5))*(1-sqrt(5))-3/10*log(2+x^(1/6)+2*x^(1/3)-x^(1/6)*sqrt(5))*(1+sqrt(5))+2*sqrt(x)+3/5*arctan((1+4*x^(1/6)-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2*(5-sqrt(5)))-3/5*arctan(1/2*(1+4*x^(1/6)+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*sqrt(2*(5+sqrt(5)))],
[1/(-4*cos(x)+3*sin(x)),x,2,-1/5*arctanh(1/5*(3*cos(x)+4*sin(x)))],
[1/(1+sqrt(x)),x,3,-2*log(1+sqrt(x))+2*sqrt(x)],
[1/(1+1/x^(1/3)),x,3,3*x^(1/3)-3/2*x^(2/3)+x-3*log(1+1/x^(1/3))-log(x)],
[sqrt(x)/(1+x),x,3,-2*arctan(sqrt(x))+2*sqrt(x)],
[1/(x*sqrt(1+x)),x,2,-2*arctanh(sqrt(1+x))],
[1/(-x^(1/3)+x),x,2,3/2*log(1-x^(2/3))],
[1/(x-sqrt(2+x)),x,4,4/3*log(2-sqrt(2+x))+2/3*log(1+sqrt(2+x))],
[x^2/sqrt(-1+x),x,2,4/3*(-1+x)^(3/2)+2/5*(-1+x)^(5/2)+2*sqrt(-1+x)],
[sqrt(-1+x)/(1+x),x,3,-2*arctan(sqrt(-1+x)/sqrt(2))*sqrt(2)+2*sqrt(-1+x)],
[1/sqrt(1+sqrt(x)),x,3,4/3*(1+sqrt(x))^(3/2)-4*sqrt(1+sqrt(x))],
[sqrt(x)/(x+x^2),x,3,2*arctan(sqrt(x))],
[(1+sqrt(x))/(-1+sqrt(x)),x,3,x+4*log(1-sqrt(x))+4*sqrt(x)],
[(1+1/x^(1/3))/(-1+1/x^(1/3)),x,4,-6*x^(1/3)-3*x^(2/3)-x-6*log(1-x^(1/3))],
[x^3/(1+x^2)^(1/3),x,3,-3/4*(1+x^2)^(2/3)+3/10*(1+x^2)^(5/3)],
[sqrt(x)/((-1)/x^(1/3)+sqrt(x)),x,10,6*x^(1/6)+x+6/5*log(1-x^(1/6))-3/10*log(2+x^(1/6)+2*x^(1/3)-x^(1/6)*sqrt(5))*(1-sqrt(5))-3/10*log(2+x^(1/6)+2*x^(1/3)+x^(1/6)*sqrt(5))*(1+sqrt(5))-3/5*arctan(1/2*(1+4*x^(1/6)+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*sqrt(2*(5-sqrt(5)))-3/5*arctan((1+4*x^(1/6)-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2*(5+sqrt(5)))],
[1/(1/x^(1/4)+sqrt(x)),x,9,4/3*log(1+x^(1/4))-2/3*log(1-x^(1/4)+sqrt(x))+4*arctan((1-2*x^(1/4))/sqrt(3))/sqrt(3)+2*sqrt(x)],
[1/(1/x^(1/3)+1/x^(1/4)),x,4,12*x^(1/12)-6*x^(1/6)+4*x^(1/4)-3*x^(1/3)+12/5*x^(5/12)+12/7*x^(7/12)-3/2*x^(2/3)+4/3*x^(3/4)-6/5*x^(5/6)+12/11*x^(11/12)-x+12/13*x^(13/12)-6/7*x^(7/6)+4/5*x^(5/4)-12*log(1+x^(1/12))-2*sqrt(x)],
[sqrt((1-x)/x),x,5,-arctan(sqrt(-1+1/x))+x*sqrt(-1+1/x)],
[cos(x)/(sin(x)+sin(x)^2),x,2,log(sin(x))-log(1+sin(x))],
[exp(2*x)/(2+3*exp(x)+exp(2*x)),x,4,-log(1+exp(x))+2*log(2+exp(x))],
[1/sqrt(1+exp(x)),x,3,-2*arctanh(sqrt(1+exp(x)))],
[sqrt(1-exp(x)),x,4,-2*arctanh(sqrt(1-exp(x)))+2*sqrt(1-exp(x))],
[1/(3-5*sin(x)),x,4,-1/4*log(cos(1/2*x)-3*sin(1/2*x))+1/4*log(3*cos(1/2*x)-sin(1/2*x))],
[1/(cos(x)+sin(x)),x,2,-arctanh((cos(x)-sin(x))/sqrt(2))/sqrt(2)],
[1/(1-cos(x)+sin(x)),x,2,-log(1+cot(1/2*x))],
[1/(4*cos(x)+3*sin(x)),x,2,-1/5*arctanh(1/5*(3*cos(x)-4*sin(x)))],
[1/(sin(x)+tan(x)),x,6,-1/2*arctanh(cos(x))+1/2*cot(x)*csc(x)-1/2*csc(x)^2],
[1/(2*sin(x)+sin(2*x)),x,4,1/4*log(tan(1/2*x))+1/8*tan(1/2*x)^2],
[sec(x)/(1+sin(x)),x,4,1/2*arctanh(sin(x))+(-1/2)/(1+sin(x))],
[1/(b*cos(x)+a*sin(x)),x,2,-arctanh((a*cos(x)-b*sin(x))/sqrt(a^2+b^2))/sqrt(a^2+b^2)],
[1/(b^2*cos(x)^2+a^2*sin(x)^2),x,2,arctan(a*tan(x)/b)/(a*b)],

// Section 7.6 - Strategy for Integration
[x/(-1+x^2),x,1,1/2*log(1-x^2)],
[sqrt(x)*(1+sqrt(x)),x,2,2/3*x^(3/2)+1/2*x^2],
[1/(1-cos(x)),x,1,-sin(x)/(1-cos(x))],
[sec(x)*tan(x)^2,x,2,-1/2*arctanh(sin(x))+1/2*sec(x)*tan(x)],
[sec(x)^3*tan(x)^3,x,3,-1/3*sec(x)^3+1/5*sec(x)^5],
[exp(sqrt(x)),x,3,-2*exp(sqrt(x))+2*exp(sqrt(x))*sqrt(x)],
[(1+x^5)/(-10*x-3*x^2+x^3),x,3,19*x+3/2*x^2+1/3*x^3+3126/35*log(5-x)-1/10*log(x)-31/14*log(2+x)],
[1/(x*sqrt(log(x))),x,2,2*sqrt(log(x))],
[(5+2*x)/(-3+x),x,2,2*x+11*log(3-x)],
[exp(exp(x)+x),x,2,exp(exp(x))],
[cos(x)^2*sin(x)^2,x,3,1/8*x+1/8*cos(x)*sin(x)-1/4*cos(x)^3*sin(x)],
[(-cos(x)+sin(x))/(cos(x)+sin(x)),x,1,-log(cos(x)+sin(x))],
[x/sqrt(1-x^2),x,1,-sqrt(1-x^2)],
[x^3*log(x),x,1,-1/16*x^4+1/4*x^4*log(x)],
[sqrt(-2+x)/(2+x),x,3,-4*arctan(1/2*sqrt(-2+x))+2*sqrt(-2+x)],
[x/(2+x)^2,x,2,2/(2+x)+log(2+x)],
[log(1+x^2),x,3,-2*x+2*arctan(x)+x*log(1+x^2)],
[sqrt(1+log(x))/(x*log(x)),x,"assume(x>1)",-2*arctanh(sqrt(1+log(x)))+2*sqrt(1+log(x))],
[(1+sqrt(x))^8,x,3,-2/9*(1+sqrt(x))^9+1/5*(1+sqrt(x))^10],
[sec(x)^4*tan(x)^3,x,3,-1/4*sec(x)^4+1/6*sec(x)^6],
[x/(2-2*x+x^2),x,4,-arctan(1-x)+1/2*log(2-2*x+x^2)],
[x*arcsin(x),x,3,-1/4*arcsin(x)+1/2*x^2*arcsin(x)+1/4*x*sqrt(1-x^2)],
[sqrt(9-x^2)/x,x,4,-3*arctanh(1/3*sqrt(9-x^2))+sqrt(9-x^2)],
[x/(2+3*x+x^2),x,3,-log(1+x)+2*log(2+x)],
[x^2*cosh(x),x,3,-2*x*cosh(x)+2*sinh(x)+x^2*sinh(x)],
[(1+x+x^3)/(4*x+2*x^2+x^4),x,1,1/4*log(4*x+2*x^2+x^4)],
[cos(x)/(1+sin(x)^2),x,2,arctan(sin(x))],
[cos(sqrt(x)),x,3,2*cos(sqrt(x))+2*sin(sqrt(x))*sqrt(x)],
[sin(Pi*x),x,1,-cos(Pi*x)/Pi],
[exp(2*x)/(1+exp(x)),x,3,exp(x)-log(1+exp(x))],
[exp(3*x)*cos(5*x),x,1,3/34*exp(3*x)*cos(5*x)+5/34*exp(3*x)*sin(5*x)],
[cos(3*x)*cos(5*x),x,1,1/4*sin(2*x)+1/16*sin(8*x)],
[1/(1+x+x^2+x^3),x,5,1/2*arctan(x)+1/2*log(1+x)-1/4*log(1+x^2)],
[x^2*log(1+x),x,3,-1/3*x+1/6*x^2-1/9*x^3+1/3*log(1+x)+1/3*x^3*log(1+x)],
[x^5/exp(x^3),x,2,(-1/3)/exp(x^3)-1/3*x^3/exp(x^3)],
[tan(4*x)^2,x,2,-x+1/4*tan(4*x)],
[1/sqrt(-5+12*x+9*x^2),x,2,1/3*arctanh((2+3*x)/sqrt(-5+12*x+9*x^2))],
[x^2*arctan(x),x,4,-1/6*x^2+1/3*x^3*arctan(x)+1/6*log(1+x^2)],
[(1-sqrt(x))/x^(1/3),x,2,3/2*x^(2/3)-6/7*x^(7/6)],
[1/((-1)/exp(x)+exp(x)),x,2,-arctanh(exp(x))],
[x/(10+2*x^2+x^4),x,3,1/6*arctan(1/3*(1+x^2))],
[1/(1/x^(1/3)+x),x,2,3/4*log(1+x^(4/3))],
[cos(x)^4*sin(x)^2,x,4,1/16*x+1/16*cos(x)*sin(x)+1/24*cos(x)^3*sin(x)-1/6*cos(x)^5*sin(x)],
[1/sqrt(5-4*x-x^2),x,2,-arcsin(1/3*(-2-x))],
[x/(1-x^2+sqrt(1-x^2)),x,3,-log(1+sqrt(1-x^2))],
[(1+cos(x))*csc(x),x,2,log(1-cos(x))],
[exp(x)/(-1+exp(2*x)),x,2,-arctanh(exp(x))],
[1/(-8+x^3),x,6,1/12*log(2-x)-1/24*log(4+2*x+x^2)-1/4*arctan((1+x)/sqrt(3))/sqrt(3)],
[x^5*cosh(x),x,6,-120*cosh(x)-60*x^2*cosh(x)-5*x^4*cosh(x)+120*x*sinh(x)+20*x^3*sinh(x)+x^5*sinh(x)],
[log(tan(x))/(cos(x)*sin(x)),x,1,1/2*log(tan(x))^2],
[-2*x+x^2+x^3,x,1,-x^2+1/3*x^3+1/4*x^4],
[(1+exp(x))/(1-exp(x)),x,3,x-2*log(1-exp(x))],
[x/((1+x^2)*(4+x^2)),x,4,1/6*log(1+x^2)-1/6*log(4+x^2)],
[1/(4-5*sin(x)),x,4,-1/3*log(cos(1/2*x)-2*sin(1/2*x))+1/3*log(2*cos(1/2*x)-sin(1/2*x))],
[x*(c+x)^(1/3),x,2,-3/4*c*(c+x)^(4/3)+3/7*(c+x)^(7/3)],
[exp(x^(1/3)),x,4,6*exp(x^(1/3))-6*exp(x^(1/3))*x^(1/3)+3*exp(x^(1/3))*x^(2/3)],
[1/(4+x+sqrt(1+x)),x,5,log(4+x+sqrt(1+x))-2*arctan((1+2*sqrt(1+x))/sqrt(11))/sqrt(11)],
[(1+x^3)/(-x^2+x^3),x,3,1/x+x+2*log(1-x)-log(x)],
[(-3+4*x+x^2)*sin(2*x),x,8,7/4*cos(2*x)-2*x*cos(2*x)-1/2*x^2*cos(2*x)+sin(2*x)+1/2*x*sin(2*x)],
[cos(cos(x))*sin(x),x,2,-sin(cos(x))],
[1/sqrt(16-x^2),x,1,arcsin(1/4*x)],
[x^3/(1+x)^10,x,2,1/9/(1+x)^9+(-3/8)/(1+x)^8+3/7/(1+x)^7+(-1/6)/(1+x)^6],
[cot(2*x)^3*csc(2*x)^3,x,3,1/6*csc(2*x)^3-1/10*csc(2*x)^5],
[(x+sin(x))^2,x,6,1/2*x+1/3*x^3-2*x*cos(x)+2*sin(x)-1/2*cos(x)*sin(x)],
[exp(arctan(x))/(1+x^2),x,1,exp(arctan(x))],
[1/(x*(1+x^4)),x,4,log(x)-1/4*log(1+x^4)],
[t^3/exp(2*t),t,4,(-3/8)/exp(2*t)-3/4*t/exp(2*t)-3/4*t^2/exp(2*t)-1/2*t^3/exp(2*t)],
[sqrt(t)/(1+t^(1/3)),t,7,-6*t^(1/6)-6/5*t^(5/6)+6/7*t^(7/6)+6*arctan(t^(1/6))+2*sqrt(t)],
[sin(x)*sin(2*x)*sin(3*x),x,5,-1/8*cos(2*x)-1/16*cos(4*x)+1/24*cos(6*x)],
[log(1/2*x),x,1,-x+x*log(1/2*x)],
[sqrt((1+x)/(1-x)),x,3,2*arctan(sqrt((1+x)/(1-x)))-(1-x)*sqrt((1+x)/(1-x))],
[x*log(x)/sqrt(-1+x^2),x,5,arctan(sqrt(-1+x^2))-sqrt(-1+x^2)+log(x)*sqrt(-1+x^2)],
[(a+x)/(a^2+x^2),x,3,arctan(x/a)+1/2*log(a^2+x^2)],
[sqrt(1+x-x^2),x,3,-5/8*arcsin((1-2*x)/sqrt(5))-1/4*(1-2*x)*sqrt(1+x-x^2)],
[x^4/(16+x^10),x,2,1/20*arctan(1/4*x^5)],
[(2+x)/(2+x+x^2),x,4,1/2*log(2+x+x^2)+3*arctan((1+2*x)/sqrt(7))/sqrt(7)],
[x*sec(x)*tan(x),x,2,-arctanh(sin(x))+x*sec(x)],
[x/(-a^4+x^4),x,2,-1/2*arctanh(x^2/a^2)/a^2],
[1/(sqrt(x)+sqrt(1+x)),x,3,-2/3*x^(3/2)+2/3*(1+x)^(3/2)],
[1/(1+(-1)/exp(x)+2*exp(x)),x,4,1/3*log(1-2*exp(x))-1/3*log(1+exp(x))],
[arctan(sqrt(x))/sqrt(x),x,2,-log(1+x)+2*arctan(sqrt(x))*sqrt(x)],
[log(1+x)/x^2,x,4,log(x)-log(1+x)-log(1+x)/x],
[1/(-exp(x)+exp(3*x)),x,3,exp(-x)-arctanh(exp(x))],
[(1+cos(x)^2)/(1-cos(x)^2),x,4,-x-2*cot(x)],

// Section 7.?
[1/(x*sqrt(-25+2*x)),x,2,2/5*arctan(1/5*sqrt(-25+2*x))],
[sin(2*x)/sqrt(9-cos(x)^4),x,5,-arcsin(1/3*cos(x)^2)],
[x^2/sqrt(5-4*x^2),x,2,5/16*arcsin(2*x/sqrt(5))-1/8*x*sqrt(5-4*x^2)],
[x^3*sin(x),x,4,6*x*cos(x)-x^3*cos(x)-6*sin(x)+3*x^2*sin(x)],
[x*sqrt(4+2*x+x^2),x,4,1/3*(4+2*x+x^2)^(3/2)-3/2*arcsinh((1+x)/sqrt(3))-1/2*(1+x)*sqrt(4+2*x+x^2)],
[x*(5+x^2)^8,x,1,1/18*(5+x^2)^9],
[cos(x)^2*sin(x)^5,x,3,-1/3*cos(x)^3+2/5*cos(x)^5-1/7*cos(x)^7],
[cos(4*x)/exp(3*x),x,1,-3/25*cos(4*x)/exp(3*x)+4/25*sin(4*x)/exp(3*x)],
[csc(1/2*x)^3,x,2,-arctanh(cos(1/2*x))-cot(1/2*x)*csc(1/2*x)],
[sqrt(-1+9*x^2)/x^2,x,3,3*arctanh(3*x/sqrt(-1+9*x^2))-sqrt(-1+9*x^2)/x],
[sqrt(4-3*x^2)/x,x,4,-2*arctanh(1/2*sqrt(4-3*x^2))+sqrt(4-3*x^2)],
[exp(3*x)*x^2,x,3,2/27*exp(3*x)-2/9*exp(3*x)*x+1/3*exp(3*x)*x^2],
[cos(x)*sin(x)/sqrt(1+sin(x)),x,3,2/3*(1+sin(x))^(3/2)-2*sqrt(1+sin(x))],
[x*arcsin(x^2),x,3,1/2*x^2*arcsin(x^2)+1/2*sqrt(1-x^4)],
[x^3*arcsin(x^2),x,5,-1/8*arcsin(x^2)+1/4*x^4*arcsin(x^2)+1/8*x^2*sqrt(1-x^4)],
[exp(x)*sech(exp(x)),x,2,arctan(sinh(exp(x)))],
[x^2*cos(3*x),x,3,2/9*x*cos(3*x)-2/27*sin(3*x)+1/3*x^2*sin(3*x)],
[sqrt(5-4*x-x^2),x,3,-9/2*arcsin(1/3*(-2-x))+1/2*(2+x)*sqrt(5-4*x-x^2)],
[x^5/(x^2+sqrt(2)),x,3,1/4*x^4+log(x^2+sqrt(2))-x^2/sqrt(2)],
[sec(x)^5,x,3,3/8*arctanh(sin(x))+3/8*sec(x)*tan(x)+1/4*sec(x)^3*tan(x)],
[sin(2*x)^6,x,4,5/16*x-5/32*cos(2*x)*sin(2*x)-5/48*cos(2*x)*sin(2*x)^3-1/12*cos(2*x)*sin(2*x)^5],
[cos(x)*log(sin(x))*sin(x)^2,x,4,-1/9*sin(x)^3+1/3*log(sin(x))*sin(x)^3],
[1/(exp(x)*(1+2*exp(x))),x,3,(-1)/exp(x)-2*x+2*log(1+2*exp(x))],
[sqrt(2+3*cos(x))*tan(x),x,4,2*arctanh(sqrt(2+3*cos(x))/sqrt(2))*sqrt(2)-2*sqrt(2+3*cos(x))],
[x/sqrt(-4*x+x^2),x,3,4*arctanh(x/sqrt(-4*x+x^2))+sqrt(-4*x+x^2)],
[cos(x)^5,x,2,sin(x)-2/3*sin(x)^3+1/5*sin(x)^5],
[x^4/exp(x),x,5,(-24)/exp(x)-24*x/exp(x)-12*x^2/exp(x)-4*x^3/exp(x)-x^4/exp(x)],
[x^4/sqrt(-2+x^10),x,3,1/5*arctanh(x^5/sqrt(-2+x^10))],
[exp(x)*cos(4+3*x),x,1,1/10*exp(x)*cos(4+3*x)+3/10*exp(x)*sin(4+3*x)],
[exp(x)*log(1+exp(x)),x,4,-exp(x)+(1+exp(x))*log(1+exp(x)),-exp(x)+log(1+exp(x))+exp(x)*log(1+exp(x))],
[x^2*arctan(x),x,4,-1/6*x^2+1/3*x^3*arctan(x)+1/6*log(1+x^2)],
[sqrt(-1+exp(2*x)),x,4,-arctan(sqrt(-1+exp(2*x)))+sqrt(-1+exp(2*x))],
[exp(sin(x))*sin(2*x),x,4,-2*exp(sin(x))+2*exp(sin(x))*sin(x)],
[x^2*sqrt(5-x^2),x,3,25/8*arcsin(x/sqrt(5))-5/8*x*sqrt(5-x^2)+1/4*x^3*sqrt(5-x^2)],
[x^2*(1+x^3)^4,x,1,1/15*(1+x^3)^5],
[cos(x)^3*sin(x)^3,x,3,1/4*sin(x)^4-1/6*sin(x)^6],
[sec(x)^4*tan(x)^2,x,3,1/3*tan(x)^3+1/5*tan(x)^5],
[x*sqrt(1+2*x),x,2,-1/6*(1+2*x)^(3/2)+1/10*(1+2*x)^(5/2)],
[sin(x)^4,x,3,3/8*x-3/8*cos(x)*sin(x)-1/4*cos(x)*sin(x)^3],
[tan(x)^3,x,2,log(cos(x))+1/2*tan(x)^2],
[x^5*sqrt(1+x^2),x,3,1/3*(1+x^2)^(3/2)-2/5*(1+x^2)^(5/2)+1/7*(1+x^2)^(7/2)]
]:;


res:=[]:;
S:=182; S:=size(lst);
failint:=[]; failsimp:=[]; nock:=[]; ass:=[];
print("Integration independent test suites, Steward "+S);
file:=fopen("intinds.tst");
T0:=time();
for j from 0 to S-1 do
  l:=eval(lst,1)[j]; 
  f:=l[0]; v:=l[1]; hyp:=l[2]; print(f);
  purge(unquote(v));
  if (type(hyp)==string) expr(hyp); // eval assumption
  print(j+1,f,v,hyp,about(unquote(v)));
  try { g:=integrate(f,unquote(v)); } catch(err){ g:="integrate(err)"; }
  s:=""+eval(g,1);
  h:=false;
  fail:=size(s.find("integrate("))>0 || hyp==x;
  if (fail) failint.append(j+1);
  if (hyp=="nock") nock.append(j+1);
  if (hyp.type==string && size(hyp.find("assume("))>0) ass.append(j+1);
  if (hyp!="nock" && !fail)  h:=simplify(diff(g,unquote(v))-f); else print("nock");
  purge(unquote(assumptions));
  fgh:=""+eval([j+1,f,g,h],1);
  if (eval(h,1)!=0) failsimp.append(j+1);
  print(fgh);
  //res.append([f,g,h]); print(res[size(res)-1]);
  fprint(file,"",fgh);
od:;
fprint(file,"","Time:",time()-T0,", tests: ",S,", integration failures: ",size(failint),failint,", simplification failures: ",size(failsimp),failsimp,", not cheked: ",size(nock),nock,", assumptions: ",size(ass),ass);
fclose(file);
print("Integration independent test suites, Steward ","tests: ",S,", integration failures: ",size(failint),failint,", simplification failures: ",size(failsimp),failsimp,", not cheked: ",size(nock),nock,", assumptions: ",size(ass),ass);
//res;
