1,1,19,0,0.073366," ","integrate(cot(x)**4,x)","x + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{3}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}}"," ",0,"x + cos(x)/sin(x) - cos(x)**3/(3*sin(x)**3)","A",0
2,1,14,0,0.108193," ","integrate(1/x**4/(x**2+1),x)","\operatorname{atan}{\left(x \right)} + \frac{3 x^{2} - 1}{3 x^{3}}"," ",0,"atan(x) + (3*x**2 - 1)/(3*x**3)","A",0
3,1,15,0,0.219822," ","integrate((x**2+x)/x**(1/2),x)","\frac{2 x^{\frac{5}{2}}}{5} + \frac{2 x^{\frac{3}{2}}}{3}"," ",0,"2*x**(5/2)/5 + 2*x**(3/2)/3","A",0
4,1,2,0,0.059976," ","integrate(cos(x),x)","\sin{\left(x \right)}"," ",0,"sin(x)","A",0
5,1,5,0,0.083899," ","integrate(exp(x**2)*x,x)","\frac{e^{x^{2}}}{2}"," ",0,"exp(x**2)/2","A",0
6,1,7,0,0.069590," ","integrate(sec(x)**2*tan(x),x)","\frac{1}{2 \cos^{2}{\left(x \right)}}"," ",0,"1/(2*cos(x)**2)","A",0
7,1,22,0,0.189556," ","integrate(x*(x**2+1)**(1/2),x)","\frac{x^{2} \sqrt{x^{2} + 1}}{3} + \frac{\sqrt{x^{2} + 1}}{3}"," ",0,"x**2*sqrt(x**2 + 1)/3 + sqrt(x**2 + 1)/3","B",0
8,1,15,0,0.299601," ","integrate(exp(x)*sin(x),x)","\frac{e^{x} \sin{\left(x \right)}}{2} - \frac{e^{x} \cos{\left(x \right)}}{2}"," ",0,"exp(x)*sin(x)/2 - exp(x)*cos(x)/2","A",0
9,1,8,0,0.070227," ","integrate(cos(x)*csc(x)**2/sin(x)**2,x)","- \frac{1}{3 \sin^{3}{\left(x \right)}}"," ",0,"-1/(3*sin(x)**3)","A",0
10,1,3,0,0.627870," ","integrate(sin(exp(x)),x)","\operatorname{Si}{\left(e^{x} \right)}"," ",0,"Si(exp(x))","A",0
11,1,2,0,0.603531," ","integrate(sin(y)/y,y)","\operatorname{Si}{\left(y \right)}"," ",0,"Si(y)","A",0
12,1,5,0,0.077732," ","integrate(exp(x)+sin(x),x)","e^{x} - \cos{\left(x \right)}"," ",0,"exp(x) - cos(x)","A",0
13,1,5,0,0.086222," ","integrate(exp(x**2)+2*exp(x**2)*x**2,x)","x e^{x^{2}}"," ",0,"x*exp(x**2)","A",0
14,1,20,0,0.093562," ","integrate((x+exp(x))**2,x)","\frac{x^{3}}{3} + \frac{\left(4 x - 4\right) e^{x}}{2} + \frac{e^{2 x}}{2}"," ",0,"x**3/3 + (4*x - 4)*exp(x)/2 + exp(2*x)/2","A",0
15,1,15,0,0.088316," ","integrate(2*exp(x)+exp(2*x)+x**2,x)","\frac{x^{3}}{3} + \frac{e^{2 x}}{2} + 2 e^{x}"," ",0,"x**3/3 + exp(2*x)/2 + 2*exp(x)","A",0
16,1,5,0,0.058973," ","integrate(cos(x)*sin(x),x)","\frac{\sin^{2}{\left(x \right)}}{2}"," ",0,"sin(x)**2/2","A",0
17,1,5,0,0.083941," ","integrate(exp(x**2)*x,x)","\frac{e^{x^{2}}}{2}"," ",0,"exp(x**2)/2","A",0
18,1,22,0,0.190713," ","integrate(x*(x**2+1)**(1/2),x)","\frac{x^{2} \sqrt{x^{2} + 1}}{3} + \frac{\sqrt{x^{2} + 1}}{3}"," ",0,"x**2*sqrt(x**2 + 1)/3 + sqrt(x**2 + 1)/3","B",0
19,1,5,0,0.077327," ","integrate(exp(x)/(1+exp(x)),x)","\log{\left(e^{x} + 1 \right)}"," ",0,"log(exp(x) + 1)","A",0
20,1,7,0,0.056185," ","integrate(x**(3/2),x)","\frac{2 x^{\frac{5}{2}}}{5}"," ",0,"2*x**(5/2)/5","A",0
21,1,7,0,0.122936," ","integrate(cos(3+2*x),x)","\frac{\sin{\left(2 x + 3 \right)}}{2}"," ",0,"sin(2*x + 3)/2","A",0
22,1,7,0,0.056042," ","integrate(2*exp(2*x)*y*z,x)","y z e^{2 x}"," ",0,"y*z*exp(2*x)","A",0
23,1,8,0,1.958662," ","integrate(exp(x)*cos(exp(x))**2*sin(exp(x)),x)","- \frac{\cos^{3}{\left(e^{x} \right)}}{3}"," ",0,"-cos(exp(x))**3/3","A",0
24,1,34,0,0.934382," ","integrate(x*(1+x)**(1/2),x)","\frac{2 x^{2} \sqrt{x + 1}}{5} + \frac{2 x \sqrt{x + 1}}{15} - \frac{4 \sqrt{x + 1}}{15}"," ",0,"2*x**2*sqrt(x + 1)/5 + 2*x*sqrt(x + 1)/15 - 4*sqrt(x + 1)/15","A",0
25,1,17,0,0.124334," ","integrate(1/(x**4-1),x)","\frac{\log{\left(x - 1 \right)}}{4} - \frac{\log{\left(x + 1 \right)}}{4} - \frac{\operatorname{atan}{\left(x \right)}}{2}"," ",0,"log(x - 1)/4 - log(x + 1)/4 - atan(x)/2","A",0
26,1,15,0,0.114136," ","integrate(exp(x)/(2+3*exp(2*x)),x)","\operatorname{RootSum} {\left(24 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + e^{x} \right)} \right)\right)}"," ",0,"RootSum(24*_z**2 + 1, Lambda(_i, _i*log(4*_i + exp(x))))","A",0
27,1,22,0,0.161707," ","integrate(exp(2*x)/(A+B*exp(4*x)),x)","\operatorname{RootSum} {\left(16 z^{2} A B + 1, \left( i \mapsto i \log{\left(4 i A + e^{2 x} \right)} \right)\right)}"," ",0,"RootSum(16*_z**2*A*B + 1, Lambda(_i, _i*log(4*_i*A + exp(2*x))))","A",0
28,1,8,0,0.093791," ","integrate(exp(1+x)/(1+exp(x)),x)","e \log{\left(e^{x} + 1 \right)}"," ",0,"E*log(exp(x) + 1)","A",0
29,1,10,0,0.090179," ","integrate((10*E)**x,x)","\frac{\left(10 e\right)^{x}}{1 + \log{\left(10 \right)}}"," ",0,"(10*E)**x/(1 + log(10))","A",0
30,1,15,0,0.598934," ","integrate(x**3*sin(x**2),x)","- \frac{x^{2} \cos{\left(x^{2} \right)}}{2} + \frac{\sin{\left(x^{2} \right)}}{2}"," ",0,"-x**2*cos(x**2)/2 + sin(x**2)/2","A",0
31,1,46,0,0.169051," ","integrate(x**7/(x**12+1),x)","- \frac{\log{\left(x^{4} + 1 \right)}}{12} + \frac{\log{\left(x^{8} - x^{4} + 1 \right)}}{24} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} - \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"-log(x**4 + 1)/12 + log(x**8 - x**4 + 1)/24 + sqrt(3)*atan(2*sqrt(3)*x**4/3 - sqrt(3)/3)/12","A",0
32,1,54,0,2.894914," ","integrate(x**(3*a)*sin(x**(2*a)),x)","\frac{x x^{5 a} \Gamma\left(\frac{5}{4} + \frac{1}{4 a}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{4} + \frac{1}{4 a} \\ \frac{3}{2}, \frac{9}{4} + \frac{1}{4 a} \end{matrix}\middle| {- \frac{x^{4 a}}{4}} \right)}}{4 a \Gamma\left(\frac{9}{4} + \frac{1}{4 a}\right)}"," ",0,"x*x**(5*a)*gamma(5/4 + 1/(4*a))*hyper((5/4 + 1/(4*a),), (3/2, 9/4 + 1/(4*a)), -x**(4*a)/4)/(4*a*gamma(9/4 + 1/(4*a)))","A",0
33,1,20,0,0.308074," ","integrate(cos(x**(1/2)),x)","2 \sqrt{x} \sin{\left(\sqrt{x} \right)} + 2 \cos{\left(\sqrt{x} \right)}"," ",0,"2*sqrt(x)*sin(sqrt(x)) + 2*cos(sqrt(x))","A",0
34,1,34,0,0.951147," ","integrate(x*(1+x)**(1/2),x)","\frac{2 x^{2} \sqrt{x + 1}}{5} + \frac{2 x \sqrt{x + 1}}{15} - \frac{4 \sqrt{x + 1}}{15}"," ",0,"2*x**2*sqrt(x + 1)/5 + 2*x*sqrt(x + 1)/15 - 4*sqrt(x + 1)/15","A",0
35,0,0,0,0.000000," ","integrate(1/(x**(1/3)+x**(1/2)),x)","\int \frac{1}{\sqrt[3]{x} + \sqrt{x}}\, dx"," ",0,"Integral(1/(x**(1/3) + sqrt(x)), x)","F",0
36,0,0,0,0.000000," ","integrate(((1+x)/(3+2*x))**(1/2),x)","\int \sqrt{\frac{x + 1}{2 x + 3}}\, dx"," ",0,"Integral(sqrt((x + 1)/(2*x + 3)), x)","F",0
37,1,105,0,2.138752," ","integrate(x**4/(-x**2+1)**(5/2),x)","\frac{3 x^{4} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} + \frac{4 x^{3} \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} - \frac{6 x^{2} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} - \frac{3 x \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} + \frac{3 \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3}"," ",0,"3*x**4*asin(x)/(3*x**4 - 6*x**2 + 3) + 4*x**3*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) - 6*x**2*asin(x)/(3*x**4 - 6*x**2 + 3) - 3*x*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) + 3*asin(x)/(3*x**4 - 6*x**2 + 3)","B",0
38,1,190,0,8.746231," ","integrate(x**(1/2)*(1+x)**(5/2),x)","\begin{cases} - \frac{5 \operatorname{acosh}{\left(\sqrt{x + 1} \right)}}{64} + \frac{\left(x + 1\right)^{\frac{9}{2}}}{4 \sqrt{x}} - \frac{7 \left(x + 1\right)^{\frac{7}{2}}}{24 \sqrt{x}} - \frac{\left(x + 1\right)^{\frac{5}{2}}}{96 \sqrt{x}} - \frac{5 \left(x + 1\right)^{\frac{3}{2}}}{192 \sqrt{x}} + \frac{5 \sqrt{x + 1}}{64 \sqrt{x}} & \text{for}\: \left|{x + 1}\right| > 1 \\\frac{5 i \operatorname{asin}{\left(\sqrt{x + 1} \right)}}{64} - \frac{i \left(x + 1\right)^{\frac{9}{2}}}{4 \sqrt{- x}} + \frac{7 i \left(x + 1\right)^{\frac{7}{2}}}{24 \sqrt{- x}} + \frac{i \left(x + 1\right)^{\frac{5}{2}}}{96 \sqrt{- x}} + \frac{5 i \left(x + 1\right)^{\frac{3}{2}}}{192 \sqrt{- x}} - \frac{5 i \sqrt{x + 1}}{64 \sqrt{- x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*acosh(sqrt(x + 1))/64 + (x + 1)**(9/2)/(4*sqrt(x)) - 7*(x + 1)**(7/2)/(24*sqrt(x)) - (x + 1)**(5/2)/(96*sqrt(x)) - 5*(x + 1)**(3/2)/(192*sqrt(x)) + 5*sqrt(x + 1)/(64*sqrt(x)), Abs(x + 1) > 1), (5*I*asin(sqrt(x + 1))/64 - I*(x + 1)**(9/2)/(4*sqrt(-x)) + 7*I*(x + 1)**(7/2)/(24*sqrt(-x)) + I*(x + 1)**(5/2)/(96*sqrt(-x)) + 5*I*(x + 1)**(3/2)/(192*sqrt(-x)) - 5*I*sqrt(x + 1)/(64*sqrt(-x)), True))","A",0
39,1,105,0,2.154583," ","integrate(x**4/(-x**2+1)**(5/2),x)","\frac{3 x^{4} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} + \frac{4 x^{3} \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} - \frac{6 x^{2} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} - \frac{3 x \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} + \frac{3 \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3}"," ",0,"3*x**4*asin(x)/(3*x**4 - 6*x**2 + 3) + 4*x**3*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) - 6*x**2*asin(x)/(3*x**4 - 6*x**2 + 3) - 3*x*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) + 3*asin(x)/(3*x**4 - 6*x**2 + 3)","B",0
40,0,0,0,0.000000," ","integrate((-B**2*y**2+A**2+B**2)**(1/2)/(-y**2+1),y)","- \int \frac{\sqrt{A^{2} - B^{2} y^{2} + B^{2}}}{y^{2} - 1}\, dy"," ",0,"-Integral(sqrt(A**2 - B**2*y**2 + B**2)/(y**2 - 1), y)","F",0
41,1,10,0,0.062278," ","integrate(sin(x)**2,x)","\frac{x}{2} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}"," ",0,"x/2 - sin(x)*cos(x)/2","A",0
42,0,0,0,0.000000," ","integrate((A**2+B**2*sin(x)**2)**(1/2)/sin(x),x)","\int \frac{\sqrt{A^{2} + B^{2} \sin^{2}{\left(x \right)}}}{\sin{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(A**2 + B**2*sin(x)**2)/sin(x), x)","F",0
43,1,3,0,0.191539," ","integrate(1/(1+cos(x)),x)","\tan{\left(\frac{x}{2} \right)}"," ",0,"tan(x/2)","A",0
44,1,5,0,0.078044," ","integrate(exp(x)*x,x)","\left(x - 1\right) e^{x}"," ",0,"(x - 1)*exp(x)","A",0
45,1,5,0,0.087153," ","integrate(exp(x)*x/(1+x)**2,x)","\frac{e^{x}}{x + 1}"," ",0,"exp(x)/(x + 1)","A",0
46,1,5,0,0.087213," ","integrate(exp(x**2)*(2*x**2+1),x)","x e^{x^{2}}"," ",0,"x*exp(x**2)","A",0
47,1,8,0,0.197038," ","integrate(exp(x**2),x)","\frac{\sqrt{\pi} \operatorname{erfi}{\left(x \right)}}{2}"," ",0,"sqrt(pi)*erfi(x)/2","A",0
48,1,2,0,0.710801," ","integrate(exp(x)/x,x)","\operatorname{Ei}{\left(x \right)}"," ",0,"Ei(x)","A",0
49,1,41,0,0.133295," ","integrate(x/(x**3+1),x)","- \frac{\log{\left(x + 1 \right)}}{3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-log(x + 1)/3 + log(x**2 - x + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
50,1,83,0,0.250640," ","integrate(1/(x**6-1),x)","\frac{\log{\left(x - 1 \right)}}{6} - \frac{\log{\left(x + 1 \right)}}{6} + \frac{\log{\left(x^{2} - x + 1 \right)}}{12} - \frac{\log{\left(x^{2} + x + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"log(x - 1)/6 - log(x + 1)/6 + log(x**2 - x + 1)/12 - log(x**2 + x + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/6","B",0
51,1,70,0,0.304120," ","integrate(1/(A**4-A**2*B**2+(-A**2+B**2)*x**2),x)","- \frac{\log{\left(- \frac{A^{3}}{\left(A - B\right) \left(A + B\right)} + \frac{A B^{2}}{\left(A - B\right) \left(A + B\right)} + x \right)}}{2 A \left(A - B\right) \left(A + B\right)} + \frac{\log{\left(\frac{A^{3}}{\left(A - B\right) \left(A + B\right)} - \frac{A B^{2}}{\left(A - B\right) \left(A + B\right)} + x \right)}}{2 A \left(A - B\right) \left(A + B\right)}"," ",0,"-log(-A**3/((A - B)*(A + B)) + A*B**2/((A - B)*(A + B)) + x)/(2*A*(A - B)*(A + B)) + log(A**3/((A - B)*(A + B)) - A*B**2/((A - B)*(A + B)) + x)/(2*A*(A - B)*(A + B))","B",0
52,1,12,0,0.088525," ","integrate(x*ln(x),x)","\frac{x^{2} \log{\left(x \right)}}{2} - \frac{x^{2}}{4}"," ",0,"x**2*log(x)/2 - x**2/4","A",0
53,1,32,0,0.340551," ","integrate(x**2*asin(x),x)","\frac{x^{3} \operatorname{asin}{\left(x \right)}}{3} + \frac{x^{2} \sqrt{1 - x^{2}}}{9} + \frac{2 \sqrt{1 - x^{2}}}{9}"," ",0,"x**3*asin(x)/3 + x**2*sqrt(1 - x**2)/9 + 2*sqrt(1 - x**2)/9","A",0
54,1,5,0,0.076549," ","integrate(1/(x**2+2*x+1),x)","- \frac{1}{x + 1}"," ",0,"-1/(x + 1)","A",0
55,1,5,0,0.088097," ","integrate(ln(x)/(1+ln(x))**2,x)","\frac{x}{\log{\left(x \right)} + 1}"," ",0,"x/(log(x) + 1)","A",0
56,1,15,0,0.137546," ","integrate(1/x/(1+ln(x)**2),x)","\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}"," ",0,"RootSum(4*_z**2 + 1, Lambda(_i, _i*log(2*_i + log(x))))","B",0
57,1,2,0,0.447997," ","integrate(1/ln(x),x)","\operatorname{li}{\left(x \right)}"," ",0,"li(x)","A",0
58,1,15,0,0.180528," ","integrate(x*(cos(x)+sin(x)),x)","x \sin{\left(x \right)} - x \cos{\left(x \right)} + \sin{\left(x \right)} + \cos{\left(x \right)}"," ",0,"x*sin(x) - x*cos(x) + sin(x) + cos(x)","A",0
59,1,8,0,0.084892," ","integrate((x+exp(x))/exp(x),x)","x + \left(- x - 1\right) e^{- x}"," ",0,"x + (-x - 1)*exp(-x)","A",0
60,1,26,0,0.094699," ","integrate((1+exp(x))**2*x,x)","\frac{x^{2}}{2} + \frac{\left(2 x - 1\right) e^{2 x}}{4} + \frac{\left(8 x - 8\right) e^{x}}{4}"," ",0,"x**2/2 + (2*x - 1)*exp(2*x)/4 + (8*x - 8)*exp(x)/4","A",0
61,1,7,0,0.174788," ","integrate(x*cos(x),x)","x \sin{\left(x \right)} + \cos{\left(x \right)}"," ",0,"x*sin(x) + cos(x)","A",0
62,1,20,0,0.308015," ","integrate(cos(x**(1/2)),x)","2 \sqrt{x} \sin{\left(\sqrt{x} \right)} + 2 \cos{\left(\sqrt{x} \right)}"," ",0,"2*sqrt(x)*sin(sqrt(x)) + 2*cos(sqrt(x))","A",0
63,1,7,0,0.174771," ","integrate(x*cos(x),x)","x \sin{\left(x \right)} + \cos{\left(x \right)}"," ",0,"x*sin(x) + cos(x)","A",0
64,1,22,0,0.102109," ","integrate(x*ln(x)**2,x)","\frac{x^{2} \log{\left(x \right)}^{2}}{2} - \frac{x^{2} \log{\left(x \right)}}{2} + \frac{x^{2}}{4}"," ",0,"x**2*log(x)**2/2 - x**2*log(x)/2 + x**2/4","A",0
65,1,8,0,0.569751," ","integrate(cos(x)*(1+sin(x)**3),x)","\frac{\sin^{4}{\left(x \right)}}{4} + \sin{\left(x \right)}"," ",0,"sin(x)**4/4 + sin(x)","A",0
66,1,15,0,0.141005," ","integrate(1/x/(1+ln(x)**2),x)","\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}"," ",0,"RootSum(4*_z**2 + 1, Lambda(_i, _i*log(2*_i + log(x))))","B",0
67,1,3,0,0.410200," ","integrate(1/(1+asin(x)**2)/(-x**2+1)**(1/2),x)","\operatorname{atan}{\left(\operatorname{asin}{\left(x \right)} \right)}"," ",0,"atan(asin(x))","A",0
68,1,12,0,0.150354," ","integrate(sin(x)/(cos(x)+sin(x)),x)","\frac{x}{2} - \frac{\log{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{2}"," ",0,"x/2 - log(sin(x) + cos(x))/2","A",0
69,0,0,0,0.000000," ","integrate(-(A**2+B**2*(-y**2+1))**(1/2)/(-y**2+1),y)","\int \frac{\sqrt{A^{2} - B^{2} y^{2} + B^{2}}}{\left(y - 1\right) \left(y + 1\right)}\, dy"," ",0,"Integral(sqrt(A**2 - B**2*y**2 + B**2)/((y - 1)*(y + 1)), y)","F",0
70,-1,0,0,0.000000," ","integrate((-A**2-B**2)*cos(z)**2/B/(1-(A**2+B**2)*sin(z)**2/B**2),z)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,1,422,0,1.926542," ","integrate((-A**2-B**2)/B/(w**2+1)**2/(1-(A**2+B**2)*w**2/B**2/(w**2+1)),w)","\left(A^{2} B + B^{3}\right) \left(- \frac{A \log{\left(w + \frac{- \frac{A^{9}}{B \left(A^{2} + B^{2}\right)^{3}} - \frac{A^{7} B}{\left(A^{2} + B^{2}\right)^{3}} + \frac{A^{5} B^{3}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{A^{5}}{B \left(A^{2} + B^{2}\right)} + \frac{A^{3} B^{5}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{A B^{3}}{A^{2} + B^{2}}}{A^{2}} \right)}}{2 B \left(A^{2} + B^{2}\right)} + \frac{A \log{\left(w + \frac{\frac{A^{9}}{B \left(A^{2} + B^{2}\right)^{3}} + \frac{A^{7} B}{\left(A^{2} + B^{2}\right)^{3}} - \frac{A^{5} B^{3}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{A^{5}}{B \left(A^{2} + B^{2}\right)} - \frac{A^{3} B^{5}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{A B^{3}}{A^{2} + B^{2}}}{A^{2}} \right)}}{2 B \left(A^{2} + B^{2}\right)} + \frac{i \log{\left(w + \frac{- \frac{i A^{6} B^{2}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{i A^{4} B^{4}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{i A^{4}}{A^{2} + B^{2}} + \frac{i A^{2} B^{6}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{i B^{8}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{i B^{4}}{A^{2} + B^{2}}}{A^{2}} \right)}}{2 \left(A^{2} + B^{2}\right)} - \frac{i \log{\left(w + \frac{\frac{i A^{6} B^{2}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{i A^{4} B^{4}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{i A^{4}}{A^{2} + B^{2}} - \frac{i A^{2} B^{6}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{i B^{8}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{i B^{4}}{A^{2} + B^{2}}}{A^{2}} \right)}}{2 \left(A^{2} + B^{2}\right)}\right)"," ",0,"(A**2*B + B**3)*(-A*log(w + (-A**9/(B*(A**2 + B**2)**3) - A**7*B/(A**2 + B**2)**3 + A**5*B**3/(A**2 + B**2)**3 + A**5/(B*(A**2 + B**2)) + A**3*B**5/(A**2 + B**2)**3 + A*B**3/(A**2 + B**2))/A**2)/(2*B*(A**2 + B**2)) + A*log(w + (A**9/(B*(A**2 + B**2)**3) + A**7*B/(A**2 + B**2)**3 - A**5*B**3/(A**2 + B**2)**3 - A**5/(B*(A**2 + B**2)) - A**3*B**5/(A**2 + B**2)**3 - A*B**3/(A**2 + B**2))/A**2)/(2*B*(A**2 + B**2)) + I*log(w + (-I*A**6*B**2/(A**2 + B**2)**3 - I*A**4*B**4/(A**2 + B**2)**3 - I*A**4/(A**2 + B**2) + I*A**2*B**6/(A**2 + B**2)**3 + I*B**8/(A**2 + B**2)**3 - I*B**4/(A**2 + B**2))/A**2)/(2*(A**2 + B**2)) - I*log(w + (I*A**6*B**2/(A**2 + B**2)**3 + I*A**4*B**4/(A**2 + B**2)**3 + I*A**4/(A**2 + B**2) - I*A**2*B**6/(A**2 + B**2)**3 - I*B**8/(A**2 + B**2)**3 + I*B**4/(A**2 + B**2))/A**2)/(2*(A**2 + B**2)))","C",0
72,1,422,0,1.896821," ","integrate(-B*(A**2+B**2)/(w**2+1)/(-A**2*w**2+B**2),w)","\left(A^{2} B + B^{3}\right) \left(- \frac{A \log{\left(w + \frac{- \frac{A^{9}}{B \left(A^{2} + B^{2}\right)^{3}} - \frac{A^{7} B}{\left(A^{2} + B^{2}\right)^{3}} + \frac{A^{5} B^{3}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{A^{5}}{B \left(A^{2} + B^{2}\right)} + \frac{A^{3} B^{5}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{A B^{3}}{A^{2} + B^{2}}}{A^{2}} \right)}}{2 B \left(A^{2} + B^{2}\right)} + \frac{A \log{\left(w + \frac{\frac{A^{9}}{B \left(A^{2} + B^{2}\right)^{3}} + \frac{A^{7} B}{\left(A^{2} + B^{2}\right)^{3}} - \frac{A^{5} B^{3}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{A^{5}}{B \left(A^{2} + B^{2}\right)} - \frac{A^{3} B^{5}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{A B^{3}}{A^{2} + B^{2}}}{A^{2}} \right)}}{2 B \left(A^{2} + B^{2}\right)} + \frac{i \log{\left(w + \frac{- \frac{i A^{6} B^{2}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{i A^{4} B^{4}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{i A^{4}}{A^{2} + B^{2}} + \frac{i A^{2} B^{6}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{i B^{8}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{i B^{4}}{A^{2} + B^{2}}}{A^{2}} \right)}}{2 \left(A^{2} + B^{2}\right)} - \frac{i \log{\left(w + \frac{\frac{i A^{6} B^{2}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{i A^{4} B^{4}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{i A^{4}}{A^{2} + B^{2}} - \frac{i A^{2} B^{6}}{\left(A^{2} + B^{2}\right)^{3}} - \frac{i B^{8}}{\left(A^{2} + B^{2}\right)^{3}} + \frac{i B^{4}}{A^{2} + B^{2}}}{A^{2}} \right)}}{2 \left(A^{2} + B^{2}\right)}\right)"," ",0,"(A**2*B + B**3)*(-A*log(w + (-A**9/(B*(A**2 + B**2)**3) - A**7*B/(A**2 + B**2)**3 + A**5*B**3/(A**2 + B**2)**3 + A**5/(B*(A**2 + B**2)) + A**3*B**5/(A**2 + B**2)**3 + A*B**3/(A**2 + B**2))/A**2)/(2*B*(A**2 + B**2)) + A*log(w + (A**9/(B*(A**2 + B**2)**3) + A**7*B/(A**2 + B**2)**3 - A**5*B**3/(A**2 + B**2)**3 - A**5/(B*(A**2 + B**2)) - A**3*B**5/(A**2 + B**2)**3 - A*B**3/(A**2 + B**2))/A**2)/(2*B*(A**2 + B**2)) + I*log(w + (-I*A**6*B**2/(A**2 + B**2)**3 - I*A**4*B**4/(A**2 + B**2)**3 - I*A**4/(A**2 + B**2) + I*A**2*B**6/(A**2 + B**2)**3 + I*B**8/(A**2 + B**2)**3 - I*B**4/(A**2 + B**2))/A**2)/(2*(A**2 + B**2)) - I*log(w + (I*A**6*B**2/(A**2 + B**2)**3 + I*A**4*B**4/(A**2 + B**2)**3 + I*A**4/(A**2 + B**2) - I*A**2*B**6/(A**2 + B**2)**3 - I*B**8/(A**2 + B**2)**3 + I*B**4/(A**2 + B**2))/A**2)/(2*(A**2 + B**2)))","C",0
73,1,105,0,2.069513," ","integrate(x**4/(-x**2+1)**(5/2),x)","\frac{3 x^{4} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} + \frac{4 x^{3} \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} - \frac{6 x^{2} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} - \frac{3 x \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} + \frac{3 \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3}"," ",0,"3*x**4*asin(x)/(3*x**4 - 6*x**2 + 3) + 4*x**3*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) - 6*x**2*asin(x)/(3*x**4 - 6*x**2 + 3) - 3*x*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) + 3*asin(x)/(3*x**4 - 6*x**2 + 3)","B",0
74,1,19,0,0.065211," ","integrate(sin(y)**4/cos(y)**4,y)","y + \frac{\sin^{3}{\left(y \right)}}{3 \cos^{3}{\left(y \right)}} - \frac{\sin{\left(y \right)}}{\cos{\left(y \right)}}"," ",0,"y + sin(y)**3/(3*cos(y)**3) - sin(y)/cos(y)","A",0
75,1,8,0,0.086358," ","integrate(z**4/(z**2+1),z)","\frac{z^{3}}{3} - z + \operatorname{atan}{\left(z \right)}"," ",0,"z**3/3 - z + atan(z)","A",0
76,1,5,0,0.086574," ","integrate(exp(x**2)*(2*x**2+1),x)","x e^{x^{2}}"," ",0,"x*exp(x**2)","A",0
77,1,20,0,0.120183," ","integrate(exp(x**2)*(2*x**6+5*x**4+x**3+4*x**2+1)/(x**2+1)**2,x)","\frac{\left(2 x^{3} + 2 x + 1\right) e^{x^{2}}}{2 x^{2} + 2}"," ",0,"(2*x**3 + 2*x + 1)*exp(x**2)/(2*x**2 + 2)","A",0
78,1,7,0,0.075441," ","integrate(exp(-1-x),x)","- e^{- x - 1}"," ",0,"-exp(-x - 1)","A",0
79,1,19,0,0.095297," ","integrate((1/x+x)*ln(x),x)","\frac{x^{2} \log{\left(x \right)}}{2} - \frac{x^{2}}{4} + \frac{\log{\left(x \right)}^{2}}{2}"," ",0,"x**2*log(x)/2 - x**2/4 + log(x)**2/2","A",0
80,1,5,0,0.092305," ","integrate(x/(x**4+1),x)","\frac{\operatorname{atan}{\left(x^{2} \right)}}{2}"," ",0,"atan(x**2)/2","A",0
81,1,10,0,0.094932," ","integrate(x**5/(x**4+1),x)","\frac{x^{2}}{2} - \frac{\operatorname{atan}{\left(x^{2} \right)}}{2}"," ",0,"x**2/2 - atan(x**2)/2","A",0
82,1,36,0,0.389228," ","integrate(1/(1+tan(x)**2),x)","\frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} + \frac{x}{2 \tan^{2}{\left(x \right)} + 2} + \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2}"," ",0,"x*tan(x)**2/(2*tan(x)**2 + 2) + x/(2*tan(x)**2 + 2) + tan(x)/(2*tan(x)**2 + 2)","B",0
83,1,105,0,2.086098," ","integrate(x**4/(-x**2+1)**(5/2),x)","\frac{3 x^{4} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} + \frac{4 x^{3} \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} - \frac{6 x^{2} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} - \frac{3 x \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} + \frac{3 \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3}"," ",0,"3*x**4*asin(x)/(3*x**4 - 6*x**2 + 3) + 4*x**3*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) - 6*x**2*asin(x)/(3*x**4 - 6*x**2 + 3) - 3*x*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) + 3*asin(x)/(3*x**4 - 6*x**2 + 3)","B",0
84,1,34,0,0.513987," ","integrate(-x**2/(-x**2+1)**(3/2),x)","\frac{x^{2} \operatorname{asin}{\left(x \right)}}{x^{2} - 1} + \frac{x \sqrt{1 - x^{2}}}{x^{2} - 1} - \frac{\operatorname{asin}{\left(x \right)}}{x^{2} - 1}"," ",0,"x**2*asin(x)/(x**2 - 1) + x*sqrt(1 - x**2)/(x**2 - 1) - asin(x)/(x**2 - 1)","B",0
85,1,15,0,0.297173," ","integrate(exp(x)*sin(x),x)","\frac{e^{x} \sin{\left(x \right)}}{2} - \frac{e^{x} \cos{\left(x \right)}}{2}"," ",0,"exp(x)*sin(x)/2 - exp(x)*cos(x)/2","A",0
86,1,2,0,0.055094," ","integrate(1/x,x)","\log{\left(x \right)}"," ",0,"log(x)","A",0
87,0,0,0,0.000000," ","integrate(sec(2*t)/(1+sec(t)**2+3*tan(t)),t)","\int \frac{\sec{\left(2 t \right)}}{3 \tan{\left(t \right)} + \sec^{2}{\left(t \right)} + 1}\, dt"," ",0,"Integral(sec(2*t)/(3*tan(t) + sec(t)**2 + 1), t)","F",0
88,1,10,0,0.066219," ","integrate(1/sec(x)**2,x)","\frac{x}{2} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}"," ",0,"x/2 + sin(x)*cos(x)/2","A",0
89,1,14,0,0.215438," ","integrate((x**2+1)/x**(1/2),x)","\frac{2 x^{\frac{5}{2}}}{5} + 2 \sqrt{x}"," ",0,"2*x**(5/2)/5 + 2*sqrt(x)","A",0
90,0,0,0,0.000000," ","integrate(x/(x**2+2*x+5)**(1/2),x)","\int \frac{x}{\sqrt{x^{2} + 2 x + 5}}\, dx"," ",0,"Integral(x/sqrt(x**2 + 2*x + 5), x)","F",0
91,1,5,0,0.062056," ","integrate(cos(x)*sin(x)**2,x)","\frac{\sin^{3}{\left(x \right)}}{3}"," ",0,"sin(x)**3/3","A",0
92,1,5,0,0.077765," ","integrate(exp(x)/(1+exp(x)),x)","\log{\left(e^{x} + 1 \right)}"," ",0,"log(exp(x) + 1)","A",0
93,1,8,0,0.087692," ","integrate(exp(2*x)/(1+exp(x)),x)","e^{x} - \log{\left(e^{x} + 1 \right)}"," ",0,"exp(x) - log(exp(x) + 1)","A",0
94,1,7,0,0.336981," ","integrate(1/(1-cos(x)),x)","- \frac{1}{\tan{\left(\frac{x}{2} \right)}}"," ",0,"-1/tan(x/2)","A",0
95,1,7,0,0.068507," ","integrate(sec(x)**2*tan(x),x)","\frac{1}{2 \cos^{2}{\left(x \right)}}"," ",0,"1/(2*cos(x)**2)","A",0
96,1,12,0,0.086416," ","integrate(x*ln(x),x)","\frac{x^{2} \log{\left(x \right)}}{2} - \frac{x^{2}}{4}"," ",0,"x**2*log(x)/2 - x**2/4","A",0
97,1,5,0,0.058740," ","integrate(cos(x)*sin(x),x)","\frac{\sin^{2}{\left(x \right)}}{2}"," ",0,"sin(x)**2/2","A",0
98,0,0,0,0.000000," ","integrate((1+x)/(-x**2+2*x)**(1/2),x)","\int \frac{x + 1}{\sqrt{- x \left(x - 2\right)}}\, dx"," ",0,"Integral((x + 1)/sqrt(-x*(x - 2)), x)","F",0
99,1,15,0,0.116148," ","integrate(2*exp(x)/(2+3*exp(2*x)),x)","\operatorname{RootSum} {\left(6 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + e^{x} \right)} \right)\right)}"," ",0,"RootSum(6*_z**2 + 1, Lambda(_i, _i*log(2*_i + exp(x))))","A",0
100,1,105,0,2.141564," ","integrate(x**4/(-x**2+1)**(5/2),x)","\frac{3 x^{4} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} + \frac{4 x^{3} \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} - \frac{6 x^{2} \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3} - \frac{3 x \sqrt{1 - x^{2}}}{3 x^{4} - 6 x^{2} + 3} + \frac{3 \operatorname{asin}{\left(x \right)}}{3 x^{4} - 6 x^{2} + 3}"," ",0,"3*x**4*asin(x)/(3*x**4 - 6*x**2 + 3) + 4*x**3*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) - 6*x**2*asin(x)/(3*x**4 - 6*x**2 + 3) - 3*x*sqrt(1 - x**2)/(3*x**4 - 6*x**2 + 3) + 3*asin(x)/(3*x**4 - 6*x**2 + 3)","B",0
101,1,24,0,0.122416," ","integrate(exp(6*x)/(1+exp(4*x)),x)","\frac{e^{2 x}}{2} + \operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(- 4 i + e^{2 x} \right)} \right)\right)}"," ",0,"exp(2*x)/2 + RootSum(16*_z**2 + 1, Lambda(_i, _i*log(-4*_i + exp(2*x))))","A",0
102,1,31,0,0.137478," ","integrate(ln(3*x**2+2),x)","x \log{\left(3 x^{2} + 2 \right)} - 2 x + \frac{2 \sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{2} \right)}}{3}"," ",0,"x*log(3*x**2 + 2) - 2*x + 2*sqrt(6)*atan(sqrt(6)*x/2)/3","A",0
103,1,15,0,0.055431," ","integrate(1/r/(2*H*r**2-a**2)**(1/2),x)","\frac{x}{r \sqrt{2 H r^{2} - a^{2}}}"," ",0,"x/(r*sqrt(2*H*r**2 - a**2))","A",0
104,1,19,0,0.057401," ","integrate(1/r/(2*H*r**2-a**2-e**2)**(1/2),x)","\frac{x}{r \sqrt{2 H r^{2} - a^{2} - e^{2}}}"," ",0,"x/(r*sqrt(2*H*r**2 - a**2 - e**2))","A",0
105,1,22,0,0.057923," ","integrate(1/r/(-2*K*r**4+2*H*r**2-a**2)**(1/2),x)","\frac{x}{r \sqrt{2 H r^{2} - 2 K r^{4} - a^{2}}}"," ",0,"x/(r*sqrt(2*H*r**2 - 2*K*r**4 - a**2))","A",0
106,1,26,0,0.059923," ","integrate(1/r/(-2*K*r**4+2*H*r**2-a**2-e**2)**(1/2),x)","\frac{x}{r \sqrt{2 H r^{2} - 2 K r^{4} - a^{2} - e^{2}}}"," ",0,"x/(r*sqrt(2*H*r**2 - 2*K*r**4 - a**2 - e**2))","A",0
107,1,20,0,0.057120," ","integrate(1/r/(2*H*r**2-2*K*r-a**2)**(1/2),x)","\frac{x}{r \sqrt{2 H r^{2} - 2 K r - a^{2}}}"," ",0,"x/(r*sqrt(2*H*r**2 - 2*K*r - a**2))","A",0
108,1,24,0,0.059206," ","integrate(1/r/(2*H*r**2-2*K*r-a**2-e**2)**(1/2),x)","\frac{x}{r \sqrt{2 H r^{2} - 2 K r - a^{2} - e^{2}}}"," ",0,"x/(r*sqrt(2*H*r**2 - 2*K*r - a**2 - e**2))","A",0
109,1,17,0,0.054936," ","integrate(r/(2*E*r**2-a**2)**(1/2),x)","\frac{r x}{\sqrt{- a^{2} + 2 e r^{2}}}"," ",0,"r*x/sqrt(-a**2 + 2*E*r**2)","A",0
110,1,20,0,0.056759," ","integrate(r/(2*E*r**2-a**2-e**2)**(1/2),x)","\frac{r x}{\sqrt{- a^{2} - e^{2} + 2 e r^{2}}}"," ",0,"r*x/sqrt(-a**2 - e**2 + 2*E*r**2)","A",0
111,1,24,0,0.058237," ","integrate(r/(-2*K*r**4+2*E*r**2-a**2)**(1/2),x)","\frac{r x}{\sqrt{- 2 K r^{4} - a^{2} + 2 e r^{2}}}"," ",0,"r*x/sqrt(-2*K*r**4 - a**2 + 2*E*r**2)","A",0
112,1,27,0,0.057997," ","integrate(r/(-2*K*r**4+2*E*r**2-a**2-e**2)**(1/2),x)","\frac{r x}{\sqrt{- 2 K r^{4} - a^{2} - e^{2} + 2 e r^{2}}}"," ",0,"r*x/sqrt(-2*K*r**4 - a**2 - e**2 + 2*E*r**2)","A",0
113,1,24,0,0.058784," ","integrate(r/(2*H*r**2-2*K*r-a**2-e**2)**(1/2),x)","\frac{r x}{\sqrt{2 H r^{2} - 2 K r - a^{2} - e^{2}}}"," ",0,"r*x/sqrt(2*H*r**2 - 2*K*r - a**2 - e**2)","A",0
