1,1,20,0,0.144415," ","integrate(1/(-b**2*x**2+a**2),x)","- \frac{\frac{\log{\left(- \frac{a}{b} + x \right)}}{2} - \frac{\log{\left(\frac{a}{b} + x \right)}}{2}}{a b}"," ",0,"-(log(-a/b + x)/2 - log(a/b + x)/2)/(a*b)","B",0
2,1,26,0,0.140503," ","integrate(1/(b**2*x**2+a**2),x)","\frac{- \frac{i \log{\left(- \frac{i a}{b} + x \right)}}{2} + \frac{i \log{\left(\frac{i a}{b} + x \right)}}{2}}{a b}"," ",0,"(-I*log(-I*a/b + x)/2 + I*log(I*a/b + x)/2)/(a*b)","C",0
3,1,29,0,0.113209," ","integrate(sec(2*a*x),x)","\begin{cases} \frac{- \frac{\log{\left(\sin{\left(2 a x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(2 a x \right)} + 1 \right)}}{2}}{2 a} & \text{for}\: 2 a \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-log(sin(2*a*x) - 1)/2 + log(sin(2*a*x) + 1)/2)/(2*a), Ne(2*a, 0)), (x, True))","A",0
4,1,22,0,0.110965," ","integrate(1/4/sin(1/3*x),x)","\frac{3 \log{\left(\cos{\left(\frac{x}{3} \right)} - 1 \right)}}{8} - \frac{3 \log{\left(\cos{\left(\frac{x}{3} \right)} + 1 \right)}}{8}"," ",0,"3*log(cos(x/3) - 1)/8 - 3*log(cos(x/3) + 1)/8","B",0
5,1,22,0,0.218309," ","integrate(-1/cos(1/4*pi+2*x),x)","\frac{\log{\left(\tan{\left(x + \frac{\pi}{8} \right)} - 1 \right)}}{2} - \frac{\log{\left(\tan{\left(x + \frac{\pi}{8} \right)} + 1 \right)}}{2}"," ",0,"log(tan(x + pi/8) - 1)/2 - log(tan(x + pi/8) + 1)/2","A",0
6,1,3,0,0.067594," ","integrate(sec(x)*tan(x),x)","\frac{1}{\cos{\left(x \right)}}"," ",0,"1/cos(x)","A",0
7,1,5,0,0.070228," ","integrate(cot(x)*csc(x),x)","- \frac{1}{\sin{\left(x \right)}}"," ",0,"-1/sin(x)","A",0
8,1,7,0,0.793439," ","integrate(tan(x)/sin(2*x),x)","\frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)}}"," ",0,"sin(x)/(2*cos(x))","B",0
9,1,3,0,0.204936," ","integrate(1/(1+cos(x)),x)","\tan{\left(\frac{x}{2} \right)}"," ",0,"tan(x/2)","A",0
10,1,7,0,0.344094," ","integrate(1/(1-cos(x)),x)","- \frac{1}{\tan{\left(\frac{x}{2} \right)}}"," ",0,"-1/tan(x/2)","A",0
11,1,15,0,0.371295," ","integrate(sin(x)/(a-b*cos(x)),x)","\begin{cases} \frac{\log{\left(- \frac{a}{b} + \cos{\left(x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\- \frac{\cos{\left(x \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(-a/b + cos(x))/b, Ne(b, 0)), (-cos(x)/a, True))","A",0
12,1,31,0,0.707473," ","integrate(cos(x)/(a**2+b**2*sin(x)**2),x)","\begin{cases} \frac{\tilde{\infty}}{\sin{\left(x \right)}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{b^{2} \sin{\left(x \right)}} & \text{for}\: a = 0 \\\frac{\sin{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \\\frac{\operatorname{atan}{\left(\frac{b \sin{\left(x \right)}}{a} \right)}}{a b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sin(x), Eq(a, 0) & Eq(b, 0)), (-1/(b**2*sin(x)), Eq(a, 0)), (sin(x)/a**2, Eq(b, 0)), (atan(b*sin(x)/a)/(a*b), True))","A",0
13,1,44,0,0.727612," ","integrate(cos(x)/(a**2-b**2*sin(x)**2),x)","\begin{cases} \frac{\tilde{\infty}}{\sin{\left(x \right)}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{1}{b^{2} \sin{\left(x \right)}} & \text{for}\: a = 0 \\\frac{\sin{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \\- \frac{\log{\left(- \frac{a}{b} + \sin{\left(x \right)} \right)}}{2 a b} + \frac{\log{\left(\frac{a}{b} + \sin{\left(x \right)} \right)}}{2 a b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sin(x), Eq(a, 0) & Eq(b, 0)), (1/(b**2*sin(x)), Eq(a, 0)), (sin(x)/a**2, Eq(b, 0)), (-log(-a/b + sin(x))/(2*a*b) + log(a/b + sin(x))/(2*a*b), True))","A",0
14,1,32,0,2.977129," ","integrate(sin(2*x)/(a**2+b**2*sin(x)**2),x)","2 \left(\begin{cases} - \frac{\cos^{2}{\left(x \right)}}{2 a^{2}} & \text{for}\: b^{2} = 0 \\\frac{\log{\left(a^{2} + b^{2} \sin^{2}{\left(x \right)} \right)}}{2 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"2*Piecewise((-cos(x)**2/(2*a**2), Eq(b**2, 0)), (log(a**2 + b**2*sin(x)**2)/(2*b**2), True))","A",0
15,1,34,0,3.323250," ","integrate(sin(2*x)/(a**2-b**2*sin(x)**2),x)","2 \left(\begin{cases} - \frac{\cos^{2}{\left(x \right)}}{2 a^{2}} & \text{for}\: b^{2} = 0 \\- \frac{\log{\left(a^{2} - b^{2} \sin^{2}{\left(x \right)} \right)}}{2 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"2*Piecewise((-cos(x)**2/(2*a**2), Eq(b**2, 0)), (-log(a**2 - b**2*sin(x)**2)/(2*b**2), True))","A",0
16,1,34,0,2.997179," ","integrate(sin(2*x)/(a**2+b**2*cos(x)**2),x)","2 \left(\begin{cases} - \frac{\cos^{2}{\left(x \right)}}{2 a^{2}} & \text{for}\: b^{2} = 0 \\- \frac{\log{\left(a^{2} + b^{2} \cos^{2}{\left(x \right)} \right)}}{2 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"2*Piecewise((-cos(x)**2/(2*a**2), Eq(b**2, 0)), (-log(a**2 + b**2*cos(x)**2)/(2*b**2), True))","A",0
17,1,32,0,3.216955," ","integrate(sin(2*x)/(a**2-b**2*cos(x)**2),x)","2 \left(\begin{cases} - \frac{\cos^{2}{\left(x \right)}}{2 a^{2}} & \text{for}\: b^{2} = 0 \\\frac{\log{\left(a^{2} - b^{2} \cos^{2}{\left(x \right)} \right)}}{2 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"2*Piecewise((-cos(x)**2/(2*a**2), Eq(b**2, 0)), (log(a**2 - b**2*cos(x)**2)/(2*b**2), True))","A",0
18,1,61,0,0.679978," ","integrate(1/(4-cos(x)**2),x)","\frac{\sqrt{3} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{6} + \frac{\sqrt{3} \left(\operatorname{atan}{\left(\sqrt{3} \tan{\left(\frac{x}{2} \right)} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{6}"," ",0,"sqrt(3)*(atan(sqrt(3)*tan(x/2)/3) + pi*floor((x/2 - pi/2)/pi))/6 + sqrt(3)*(atan(sqrt(3)*tan(x/2)) + pi*floor((x/2 - pi/2)/pi))/6","A",0
19,1,15,0,0.107823," ","integrate(exp(x)/(-1+exp(2*x)),x)","\frac{\log{\left(e^{x} - 1 \right)}}{2} - \frac{\log{\left(e^{x} + 1 \right)}}{2}"," ",0,"log(exp(x) - 1)/2 - log(exp(x) + 1)/2","B",0
20,1,3,0,0.098215," ","integrate(1/x/ln(x),x)","\log{\left(\log{\left(x \right)} \right)}"," ",0,"log(log(x))","A",0
21,1,15,0,0.140743," ","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
22,1,7,0,0.099994," ","integrate(1/x/(1-ln(x)),x)","- \log{\left(\log{\left(x \right)} - 1 \right)}"," ",0,"-log(log(x) - 1)","A",0
23,1,7,0,0.106769," ","integrate(1/x/(1+ln(x/a)),x)","\log{\left(\log{\left(\frac{x}{a} \right)} + 1 \right)}"," ",0,"log(log(x/a) + 1)","A",0
24,1,22,0,0.416224," ","integrate((1+x-x**(1/2))**2/x**2,x)","- 4 \sqrt{x} + x + 3 \log{\left(x \right)} - \frac{1}{x} + \frac{4}{\sqrt{x}}"," ",0,"-4*sqrt(x) + x + 3*log(x) - 1/x + 4/sqrt(x)","A",0
25,1,31,0,7.857330," ","integrate((2-x**(2/3))*(x+x**(1/2))/x**(3/2),x)","- \frac{6 x^{\frac{7}{6}}}{7} - \frac{3 x^{\frac{2}{3}}}{2} + 4 \sqrt{x} + 4 \log{\left(\sqrt{x} \right)}"," ",0,"-6*x**(7/6)/7 - 3*x**(2/3)/2 + 4*sqrt(x) + 4*log(sqrt(x))","A",0
26,1,8,0,0.080180," ","integrate((-1+2*x)/(3+2*x),x)","x - 2 \log{\left(2 x + 3 \right)}"," ",0,"x - 2*log(2*x + 3)","A",0
27,1,42,0,0.118326," ","integrate((-5+2*x)/(3*x**2-2),x)","\left(\frac{1}{3} - \frac{5 \sqrt{6}}{12}\right) \log{\left(x - \frac{\sqrt{6}}{3} \right)} + \left(\frac{1}{3} + \frac{5 \sqrt{6}}{12}\right) \log{\left(x + \frac{\sqrt{6}}{3} \right)}"," ",0,"(1/3 - 5*sqrt(6)/12)*log(x - sqrt(6)/3) + (1/3 + 5*sqrt(6)/12)*log(x + sqrt(6)/3)","A",0
28,1,27,0,0.116194," ","integrate((-5+2*x)/(3*x**2+2),x)","\frac{\log{\left(x^{2} + \frac{2}{3} \right)}}{3} - \frac{5 \sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{2} \right)}}{6}"," ",0,"log(x**2 + 2/3)/3 - 5*sqrt(6)*atan(sqrt(6)*x/2)/6","A",0
29,1,22,0,0.548101," ","integrate(sin(1/4*x)*sin(x),x)","- \frac{16 \sin{\left(\frac{x}{4} \right)} \cos{\left(x \right)}}{15} + \frac{4 \sin{\left(x \right)} \cos{\left(\frac{x}{4} \right)}}{15}"," ",0,"-16*sin(x/4)*cos(x)/15 + 4*sin(x)*cos(x/4)/15","A",0
30,1,26,0,0.549021," ","integrate(cos(3*x)*cos(4*x),x)","- \frac{3 \sin{\left(3 x \right)} \cos{\left(4 x \right)}}{7} + \frac{4 \sin{\left(4 x \right)} \cos{\left(3 x \right)}}{7}"," ",0,"-3*sin(3*x)*cos(4*x)/7 + 4*sin(4*x)*cos(3*x)/7","B",0
31,1,138,0,1.538217," ","integrate(-tan(x)*tan(a-x),x)","- \left(\begin{cases} \frac{2 x \tan{\left(a \right)}}{2 \tan^{2}{\left(a \right)} + 2} - \frac{2 \log{\left(\tan{\left(x \right)} + \frac{1}{\tan{\left(a \right)}} \right)}}{2 \tan^{2}{\left(a \right)} + 2} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2 \tan^{2}{\left(a \right)} + 2} & \text{for}\: a \neq 0 \\\frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2} & \text{otherwise} \end{cases}\right) \tan{\left(a \right)} + \begin{cases} - \frac{2 x \tan{\left(a \right)}}{2 \tan^{3}{\left(a \right)} + 2 \tan{\left(a \right)}} + \frac{2 \log{\left(\tan{\left(x \right)} + \frac{1}{\tan{\left(a \right)}} \right)}}{2 \tan^{3}{\left(a \right)} + 2 \tan{\left(a \right)}} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(a \right)}}{2 \tan^{3}{\left(a \right)} + 2 \tan{\left(a \right)}} & \text{for}\: a \neq 0 \\- x + \tan{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((2*x*tan(a)/(2*tan(a)**2 + 2) - 2*log(tan(x) + 1/tan(a))/(2*tan(a)**2 + 2) + log(tan(x)**2 + 1)/(2*tan(a)**2 + 2), Ne(a, 0)), (log(tan(x)**2 + 1)/2, True))*tan(a) + Piecewise((-2*x*tan(a)/(2*tan(a)**3 + 2*tan(a)) + 2*log(tan(x) + 1/tan(a))/(2*tan(a)**3 + 2*tan(a)) + log(tan(x)**2 + 1)*tan(a)**2/(2*tan(a)**3 + 2*tan(a)), Ne(a, 0)), (-x + tan(x), True))","B",0
32,1,10,0,0.064710," ","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
33,1,10,0,0.062462," ","integrate(cos(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
34,1,7,0,0.064348," ","integrate(cos(x)**3*sin(x),x)","- \frac{\cos^{4}{\left(x \right)}}{4}"," ",0,"-cos(x)**4/4","A",0
35,1,15,0,0.089836," ","integrate(cos(x)**3/sin(x)**4,x)","- \frac{1 - 3 \sin^{2}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}}"," ",0,"-(1 - 3*sin(x)**2)/(3*sin(x)**3)","A",0
36,1,12,0,0.073889," ","integrate(1/cos(x)**2/sin(x)**2,x)","- \frac{2 \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}}"," ",0,"-2*cos(2*x)/sin(2*x)","B",0
37,1,19,0,0.074344," ","integrate(cot(3/4*x)**2,x)","- x - \frac{4 \cos{\left(\frac{3 x}{4} \right)}}{3 \sin{\left(\frac{3 x}{4} \right)}}"," ",0,"-x - 4*cos(3*x/4)/(3*sin(3*x/4))","A",0
38,1,17,0,0.152243," ","integrate((1+tan(2*x))**2,x)","\frac{\log{\left(\tan^{2}{\left(2 x \right)} + 1 \right)}}{2} + \frac{\tan{\left(2 x \right)}}{2}"," ",0,"log(tan(2*x)**2 + 1)/2 + tan(2*x)/2","A",0
39,1,10,0,0.371418," ","integrate((-cot(x)+tan(x))**2,x)","- 4 x + \tan{\left(x \right)} - \frac{1}{\tan{\left(x \right)}}"," ",0,"-4*x + tan(x) - 1/tan(x)","A",0
40,1,10,0,1.377461," ","integrate((-sec(x)+tan(x))**2,x)","- x + 2 \tan{\left(x \right)} - 2 \sec{\left(x \right)}"," ",0,"-x + 2*tan(x) - 2*sec(x)","A",0
41,1,29,0,0.536839," ","integrate(sin(x)/(1+sin(x)),x)","\frac{x \tan{\left(\frac{x}{2} \right)}}{\tan{\left(\frac{x}{2} \right)} + 1} + \frac{x}{\tan{\left(\frac{x}{2} \right)} + 1} + \frac{2}{\tan{\left(\frac{x}{2} \right)} + 1}"," ",0,"x*tan(x/2)/(tan(x/2) + 1) + x/(tan(x/2) + 1) + 2/(tan(x/2) + 1)","B",0
42,1,8,0,0.485497," ","integrate(cos(x)/(1-cos(x)),x)","- x - \frac{1}{\tan{\left(\frac{x}{2} \right)}}"," ",0,"-x - 1/tan(x/2)","A",0
43,1,19,0,0.116825," ","integrate((-1+exp(1/2*x))**3/exp(1/2*x),x)","3 x - 6 e^{\frac{x}{2}} + e^{x} + 2 e^{- \frac{x}{2}}"," ",0,"3*x - 6*exp(x/2) + exp(x) + 2*exp(-x/2)","A",0
44,1,12,0,0.104003," ","integrate(1/(x**2-6*x+5),x)","\frac{\log{\left(x - 5 \right)}}{4} - \frac{\log{\left(x - 1 \right)}}{4}"," ",0,"log(x - 5)/4 - log(x - 1)/4","A",0
45,1,10,0,0.112975," ","integrate(x**2/(x**6-6*x**3+13),x)","\frac{\operatorname{atan}{\left(\frac{x^{3}}{2} - \frac{3}{2} \right)}}{6}"," ",0,"atan(x**3/2 - 3/2)/6","A",0
46,1,42,0,0.117166," ","integrate((2+x)/(x**2-4*x-1),x)","\left(\frac{1}{2} - \frac{2 \sqrt{5}}{5}\right) \log{\left(x - 2 + \sqrt{5} \right)} + \left(\frac{1}{2} + \frac{2 \sqrt{5}}{5}\right) \log{\left(x - \sqrt{5} - 2 \right)}"," ",0,"(1/2 - 2*sqrt(5)/5)*log(x - 2 + sqrt(5)) + (1/2 + 2*sqrt(5)/5)*log(x - sqrt(5) - 2)","A",0
47,1,29,0,0.136906," ","integrate(1/(1+(1+x)**(1/3)),x)","\frac{3 \left(x + 1\right)^{\frac{2}{3}}}{2} - 3 \sqrt[3]{x + 1} + 3 \log{\left(\sqrt[3]{x + 1} + 1 \right)}"," ",0,"3*(x + 1)**(2/3)/2 - 3*(x + 1)**(1/3) + 3*log((x + 1)**(1/3) + 1)","A",0
48,1,94,0,1.323886," ","integrate(1/(a*x+b)/x**(1/2),x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 \sqrt{x}}{b} & \text{for}\: a = 0 \\- \frac{2}{a \sqrt{x}} & \text{for}\: b = 0 \\- \frac{i \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a \sqrt{b} \sqrt{\frac{1}{a}}} + \frac{i \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + \sqrt{x} \right)}}{a \sqrt{b} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*sqrt(x)/b, Eq(a, 0)), (-2/(a*sqrt(x)), Eq(b, 0)), (-I*log(-I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a*sqrt(b)*sqrt(1/a)) + I*log(I*sqrt(b)*sqrt(1/a) + sqrt(x))/(a*sqrt(b)*sqrt(1/a)), True))","A",0
49,1,37,0,0.632543," ","integrate(x**3*(x**2+1)**(1/2),x)","\frac{x^{4} \sqrt{x^{2} + 1}}{5} + \frac{x^{2} \sqrt{x^{2} + 1}}{15} - \frac{2 \sqrt{x^{2} + 1}}{15}"," ",0,"x**4*sqrt(x**2 + 1)/5 + x**2*sqrt(x**2 + 1)/15 - 2*sqrt(x**2 + 1)/15","A",0
50,1,29,0,1.074875," ","integrate(x/(a**4-x**4)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{x^{2}}{a^{2}} \right)}}{2} & \text{for}\: \left|{\frac{x^{4}}{a^{4}}}\right| > 1 \\\frac{\operatorname{asin}{\left(\frac{x^{2}}{a^{2}} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(x**2/a**2)/2, Abs(x**4/a**4) > 1), (asin(x**2/a**2)/2, True))","A",0
51,1,22,0,1.067961," ","integrate(1/x/(-a**2+x**2)**(1/2),x)","\begin{cases} \frac{i \operatorname{acosh}{\left(\frac{a}{x} \right)}}{a} & \text{for}\: \left|{\frac{a^{2}}{x^{2}}}\right| > 1 \\- \frac{\operatorname{asin}{\left(\frac{a}{x} \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*acosh(a/x)/a, Abs(a**2/x**2) > 1), (-asin(a/x)/a, True))","A",0
52,1,22,0,1.090753," ","integrate(1/x/(a**2-x**2)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{a}{x} \right)}}{a} & \text{for}\: \left|{\frac{a^{2}}{x^{2}}}\right| > 1 \\\frac{i \operatorname{asin}{\left(\frac{a}{x} \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(a/x)/a, Abs(a**2/x**2) > 1), (I*asin(a/x)/a, True))","A",0
53,1,7,0,1.041905," ","integrate(1/x/(a**2+x**2)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{a}{x} \right)}}{a}"," ",0,"-asinh(a/x)/a","A",0
54,0,0,0,0.000000," ","integrate(1/(-x**2+x+2)**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} + x + 2}}\, dx"," ",0,"Integral(1/sqrt(-x**2 + x + 2), x)","F",0
55,0,0,0,0.000000," ","integrate(1/(3*x**2-4*x+5)**(1/2),x)","\int \frac{1}{\sqrt{3 x^{2} - 4 x + 5}}\, dx"," ",0,"Integral(1/sqrt(3*x**2 - 4*x + 5), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(-x**2+x)**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} + x}}\, dx"," ",0,"Integral(1/sqrt(-x**2 + x), x)","F",0
57,0,0,0,0.000000," ","integrate((1+2*x)/(-x**2+x+2)**(1/2),x)","\int \frac{2 x + 1}{\sqrt{- \left(x - 2\right) \left(x + 1\right)}}\, dx"," ",0,"Integral((2*x + 1)/sqrt(-(x - 2)*(x + 1)), x)","F",0
58,0,0,0,0.000000," ","integrate(1/x/(-x**2+x+2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(x - 2\right) \left(x + 1\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(-(x - 2)*(x + 1))), x)","F",0
59,0,0,0,0.000000," ","integrate(1/(-2+x)/(-x**2+x+2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x - 2\right) \left(x + 1\right)} \left(x - 2\right)}\, dx"," ",0,"Integral(1/(sqrt(-(x - 2)*(x + 1))*(x - 2)), x)","F",0
60,1,22,0,0.820792," ","integrate((2+3*sin(x))/(1-cos(x))/sin(x),x)","\log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - \frac{3}{\tan{\left(\frac{x}{2} \right)}} - \frac{1}{2 \tan^{2}{\left(\frac{x}{2} \right)}}"," ",0,"log(tan(x/2)) - 3/tan(x/2) - 1/(2*tan(x/2)**2)","A",0
61,0,0,0,0.000000," ","integrate(1/(2+3*cos(x)**2),x)","\int \frac{1}{3 \cos^{2}{\left(x \right)} + 2}\, dx"," ",0,"Integral(1/(3*cos(x)**2 + 2), x)","F",0
62,1,27,0,1.480047," ","integrate((1-tan(x))/sin(2*x),x)","\frac{\log{\left(\cos{\left(2 x \right)} - 1 \right)}}{4} - \frac{\log{\left(\cos{\left(2 x \right)} + 1 \right)}}{4} - \frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)}}"," ",0,"log(cos(2*x) - 1)/4 - log(cos(2*x) + 1)/4 - sin(x)/(2*cos(x))","B",0
63,1,15,0,0.165859," ","integrate((1+tan(x)**2)/(1-tan(x)**2),x)","- \frac{\log{\left(\tan{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{2}"," ",0,"-log(tan(x) - 1)/2 + log(tan(x) + 1)/2","A",0
64,-1,0,0,0.000000," ","integrate((a**2-4*cos(x)**2)**(3/4)*sin(2*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,1,17,0,2.286815," ","integrate(sin(2*x)/(a**2-4*sin(x)**2)**(1/3),x)","- \frac{3 \left(a^{2} - 4 \sin^{2}{\left(x \right)}\right)^{\frac{2}{3}}}{8}"," ",0,"-3*(a**2 - 4*sin(x)**2)**(2/3)/8","A",0
66,0,0,0,0.000000," ","integrate(1/(-1+a**(2*x))**(1/2),x)","\int \frac{1}{\sqrt{a^{2 x} - 1}}\, dx"," ",0,"Integral(1/sqrt(a**(2*x) - 1), x)","F",0
67,1,7,0,0.736528," ","integrate(exp(1/2*x)/(-1+exp(x))**(1/2),x)","2 \operatorname{acosh}{\left(e^{\frac{x}{2}} \right)}"," ",0,"2*acosh(exp(x/2))","A",0
68,1,15,0,1.786768," ","integrate(atan(x)**n/(x**2+1),x)","\begin{cases} \frac{\operatorname{atan}^{n + 1}{\left(x \right)}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left(\operatorname{atan}{\left(x \right)} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((atan(x)**(n + 1)/(n + 1), Ne(n, -1)), (log(atan(x)), True))","A",0
69,0,0,0,0.000000," ","integrate(asin(x/a)**(3/2)/(a**2-x**2)**(1/2),x)","\int \frac{\operatorname{asin}^{\frac{3}{2}}{\left(\frac{x}{a} \right)}}{\sqrt{- \left(- a + x\right) \left(a + x\right)}}\, dx"," ",0,"Integral(asin(x/a)**(3/2)/sqrt(-(-a + x)*(a + x)), x)","F",0
70,1,7,0,2.682744," ","integrate(1/acos(x)**3/(-x**2+1)**(1/2),x)","\frac{1}{2 \operatorname{acos}^{2}{\left(x \right)}}"," ",0,"1/(2*acos(x)**2)","A",0
71,1,22,0,0.105461," ","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
72,1,15,0,0.102533," ","integrate(ln(x)/x**5,x)","- \frac{\log{\left(x \right)}}{4 x^{4}} - \frac{1}{16 x^{4}}"," ",0,"-log(x)/(4*x**4) - 1/(16*x**4)","A",0
73,1,26,0,0.132495," ","integrate(x**2*ln((-1+x)/x),x)","\frac{x^{3} \log{\left(\frac{x - 1}{x} \right)}}{3} - \frac{x^{2}}{6} - \frac{x}{3} - \frac{\log{\left(x - 1 \right)}}{3}"," ",0,"x**3*log((x - 1)/x)/3 - x**2/6 - x/3 - log(x - 1)/3","A",0
74,1,17,0,0.068106," ","integrate(cos(x)**5,x)","\frac{\sin^{5}{\left(x \right)}}{5} - \frac{2 \sin^{3}{\left(x \right)}}{3} + \sin{\left(x \right)}"," ",0,"sin(x)**5/5 - 2*sin(x)**3/3 + sin(x)","A",0
75,1,31,0,0.065076," ","integrate(cos(x)**4*sin(x)**2,x)","\frac{x}{16} - \frac{\sin{\left(x \right)} \cos^{5}{\left(x \right)}}{6} + \frac{\sin{\left(x \right)} \cos^{3}{\left(x \right)}}{24} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{16}"," ",0,"x/16 - sin(x)*cos(x)**5/6 + sin(x)*cos(x)**3/24 + sin(x)*cos(x)/16","A",0
76,1,46,0,0.153195," ","integrate(1/sin(x)**5,x)","\frac{3 \cos^{3}{\left(x \right)} - 5 \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 8} + \frac{3 \log{\left(\cos{\left(x \right)} - 1 \right)}}{16} - \frac{3 \log{\left(\cos{\left(x \right)} + 1 \right)}}{16}"," ",0,"(3*cos(x)**3 - 5*cos(x))/(8*cos(x)**4 - 16*cos(x)**2 + 8) + 3*log(cos(x) - 1)/16 - 3*log(cos(x) + 1)/16","A",0
77,1,17,0,0.457869," ","integrate(sin(x)/exp(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
78,1,26,0,0.327654," ","integrate(exp(2*x)*sin(3*x),x)","\frac{2 e^{2 x} \sin{\left(3 x \right)}}{13} - \frac{3 e^{2 x} \cos{\left(3 x \right)}}{13}"," ",0,"2*exp(2*x)*sin(3*x)/13 - 3*exp(2*x)*cos(3*x)/13","A",0
79,1,107,0,1.058307," ","integrate(a**x*cos(x),x)","\begin{cases} \frac{i x e^{- i x} \sin{\left(x \right)}}{2} + \frac{x e^{- i x} \cos{\left(x \right)}}{2} + \frac{i e^{- i x} \cos{\left(x \right)}}{2} & \text{for}\: a = e^{- i} \\- \frac{i x e^{i x} \sin{\left(x \right)}}{2} + \frac{x e^{i x} \cos{\left(x \right)}}{2} - \frac{i e^{i x} \cos{\left(x \right)}}{2} & \text{for}\: a = e^{i} \\\frac{a^{x} \log{\left(a \right)} \cos{\left(x \right)}}{\log{\left(a \right)}^{2} + 1} + \frac{a^{x} \sin{\left(x \right)}}{\log{\left(a \right)}^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x*exp(-I*x)*sin(x)/2 + x*exp(-I*x)*cos(x)/2 + I*exp(-I*x)*cos(x)/2, Eq(a, exp(-I))), (-I*x*exp(I*x)*sin(x)/2 + x*exp(I*x)*cos(x)/2 - I*exp(I*x)*cos(x)/2, Eq(a, exp(I))), (a**x*log(a)*cos(x)/(log(a)**2 + 1) + a**x*sin(x)/(log(a)**2 + 1), True))","A",0
80,1,15,0,0.399942," ","integrate(cos(ln(x)),x)","\frac{x \sin{\left(\log{\left(x \right)} \right)}}{2} + \frac{x \cos{\left(\log{\left(x \right)} \right)}}{2}"," ",0,"x*sin(log(x))/2 + x*cos(log(x))/2","A",0
81,1,15,0,20.571018," ","integrate(ln(cos(x))*sec(x)**2,x)","- x + \log{\left(\cos{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}"," ",0,"-x + log(cos(x))*tan(x) + sin(x)/cos(x)","A",0
82,1,19,0,0.181016," ","integrate(x*tan(x)**2,x)","- \frac{x^{2}}{2} + x \tan{\left(x \right)} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2}"," ",0,"-x**2/2 + x*tan(x) - log(tan(x)**2 + 1)/2","A",0
83,1,22,0,1.976186," ","integrate(asin(x)/x**2,x)","\begin{cases} - \operatorname{acosh}{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\i \operatorname{asin}{\left(\frac{1}{x} \right)} & \text{otherwise} \end{cases} - \frac{\operatorname{asin}{\left(x \right)}}{x}"," ",0,"Piecewise((-acosh(1/x), 1/Abs(x**2) > 1), (I*asin(1/x), True)) - asin(x)/x","A",0
84,1,22,0,0.203233," ","integrate(asin(x)**2,x)","x \operatorname{asin}^{2}{\left(x \right)} - 2 x + 2 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}"," ",0,"x*asin(x)**2 - 2*x + 2*sqrt(1 - x**2)*asin(x)","A",0
85,1,19,0,0.394667," ","integrate(x**2*atan(x)/(x**2+1),x)","x \operatorname{atan}{\left(x \right)} - \frac{\log{\left(x^{2} + 1 \right)}}{2} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{2}"," ",0,"x*atan(x) - log(x**2 + 1)/2 - atan(x)**2/2","A",0
86,0,0,0,0.000000," ","integrate(acos((x/(1+x))**(1/2)),x)","\int \operatorname{acos}{\left(\sqrt{\frac{x}{x + 1}} \right)}\, dx"," ",0,"Integral(acos(sqrt(x/(x + 1))), x)","F",0
87,1,22,0,0.063672," ","integrate((3*x**2+2*x)**3,x)","\frac{27 x^{7}}{7} + 9 x^{6} + \frac{36 x^{5}}{5} + 2 x^{4}"," ",0,"27*x**7/7 + 9*x**6 + 36*x**5/5 + 2*x**4","A",0
88,1,34,0,0.068295," ","integrate((-1+x)*(3*x**2+2*x-1)**2,x)","\frac{3 x^{6}}{2} + \frac{3 x^{5}}{5} - \frac{7 x^{4}}{2} - \frac{2 x^{3}}{3} + \frac{5 x^{2}}{2} - x"," ",0,"3*x**6/2 + 3*x**5/5 - 7*x**4/2 - 2*x**3/3 + 5*x**2/2 - x","A",0
89,1,75,0,60.373017," ","integrate(x**(-1+k)*(a+b*x**k)**n,x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge k = 0 \wedge n = -1 \\\frac{a^{n} x^{k}}{k} & \text{for}\: b = 0 \\\left(a + b\right)^{n} \log{\left(x \right)} & \text{for}\: k = 0 \\\frac{\log{\left(\frac{a}{b} + x^{k} \right)}}{b k} & \text{for}\: n = -1 \\\frac{a \left(a + b x^{k}\right)^{n}}{b k n + b k} + \frac{b x^{k} \left(a + b x^{k}\right)^{n}}{b k n + b k} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(k, 0) & Eq(n, -1)), (a**n*x**k/k, Eq(b, 0)), ((a + b)**n*log(x), Eq(k, 0)), (log(a/b + x**k)/(b*k), Eq(n, -1)), (a*(a + b*x**k)**n/(b*k*n + b*k) + b*x**k*(a + b*x**k)**n/(b*k*n + b*k), True))","A",0
90,1,20,0,0.078505," ","integrate(x**3/(1+2*x),x)","\frac{x^{3}}{6} - \frac{x^{2}}{8} + \frac{x}{8} - \frac{\log{\left(2 x + 1 \right)}}{16}"," ",0,"x**3/6 - x**2/8 + x/8 - log(2*x + 1)/16","A",0
91,1,34,0,0.102336," ","integrate(x**6/(3*x**2+2),x)","\frac{x^{5}}{15} - \frac{2 x^{3}}{27} + \frac{4 x}{27} - \frac{4 \sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{2} \right)}}{81}"," ",0,"x**5/15 - 2*x**3/27 + 4*x/27 - 4*sqrt(6)*atan(sqrt(6)*x/2)/81","A",0
92,1,14,0,0.109679," ","integrate(1/(3*x**2-7*x+2),x)","\frac{\log{\left(x - 2 \right)}}{5} - \frac{\log{\left(x - \frac{1}{3} \right)}}{5}"," ",0,"log(x - 2)/5 - log(x - 1/3)/5","A",0
93,1,36,0,0.116149," ","integrate((-1+3*x)/(x**2-x+1),x)","\frac{3 \log{\left(x^{2} - x + 1 \right)}}{2} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"3*log(x**2 - x + 1)/2 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
94,1,22,0,0.111833," ","integrate(x**2/(x**2+2*x+5),x)","x - \log{\left(x^{2} + 2 x + 5 \right)} - \frac{3 \operatorname{atan}{\left(\frac{x}{2} + \frac{1}{2} \right)}}{2}"," ",0,"x - log(x**2 + 2*x + 5) - 3*atan(x/2 + 1/2)/2","A",0
95,1,46,0,0.121460," ","integrate((6*x**4-5*x**3+4*x**2)/(2*x**2-x+1),x)","x^{3} - \frac{x^{2}}{2} + \frac{\log{\left(x^{2} - \frac{x}{2} + \frac{1}{2} \right)}}{4} + \frac{\sqrt{7} \operatorname{atan}{\left(\frac{4 \sqrt{7} x}{7} - \frac{\sqrt{7}}{7} \right)}}{14}"," ",0,"x**3 - x**2/2 + log(x**2 - x/2 + 1/2)/4 + sqrt(7)*atan(4*sqrt(7)*x/7 - sqrt(7)/7)/14","A",0
96,1,17,0,0.139317," ","integrate((x**2+x-1)/(x**3+x**2-6*x),x)","\frac{\log{\left(x \right)}}{6} + \frac{\log{\left(x - 2 \right)}}{2} + \frac{\log{\left(x + 3 \right)}}{3}"," ",0,"log(x)/6 + log(x - 2)/2 + log(x + 3)/3","A",0
97,1,26,0,0.258960," ","integrate((11*a**2-7*a*x+5*x**2)/(-6*a**3+11*a**2*x-6*a*x**2+x**3),x)","\frac{35 \log{\left(- 3 a + x \right)}}{2} - 17 \log{\left(- 2 a + x \right)} + \frac{9 \log{\left(- a + x \right)}}{2}"," ",0,"35*log(-3*a + x)/2 - 17*log(-2*a + x) + 9*log(-a + x)/2","A",0
98,1,29,0,0.186664," ","integrate((x**2-x+2)/(x**4-5*x**2+4),x)","\frac{\log{\left(x - 2 \right)}}{3} - \frac{\log{\left(x - 1 \right)}}{3} + \frac{2 \log{\left(x + 1 \right)}}{3} - \frac{2 \log{\left(x + 2 \right)}}{3}"," ",0,"log(x - 2)/3 - log(x - 1)/3 + 2*log(x + 1)/3 - 2*log(x + 2)/3","A",0
99,1,60,0,0.583175," ","integrate((2*x**2-5)/(x**4-5*x**2+6),x)","\frac{\sqrt{2} \log{\left(x - \sqrt{2} \right)}}{4} - \frac{\sqrt{2} \log{\left(x + \sqrt{2} \right)}}{4} + \frac{\sqrt{3} \log{\left(x - \sqrt{3} \right)}}{6} - \frac{\sqrt{3} \log{\left(x + \sqrt{3} \right)}}{6}"," ",0,"sqrt(2)*log(x - sqrt(2))/4 - sqrt(2)*log(x + sqrt(2))/4 + sqrt(3)*log(x - sqrt(3))/6 - sqrt(3)*log(x + sqrt(3))/6","A",0
100,1,26,0,0.186970," ","integrate(1/(-4+x)/(-3+x)/(-2+x)/(-1+x),x)","\frac{\log{\left(x - 4 \right)}}{6} - \frac{\log{\left(x - 3 \right)}}{2} + \frac{\log{\left(x - 2 \right)}}{2} - \frac{\log{\left(x - 1 \right)}}{6}"," ",0,"log(x - 4)/6 - log(x - 3)/2 + log(x - 2)/2 - log(x - 1)/6","A",0
101,1,17,0,0.095637," ","integrate((x**2+1)/(-1+x)**3,x)","\frac{1 - 2 x}{x^{2} - 2 x + 1} + \log{\left(x - 1 \right)}"," ",0,"(1 - 2*x)/(x**2 - 2*x + 1) + log(x - 1)","A",0
102,1,31,0,0.090355," ","integrate(x**5/(3+x)**2,x)","\frac{x^{4}}{4} - 2 x^{3} + \frac{27 x^{2}}{2} - 108 x + 405 \log{\left(x + 3 \right)} + \frac{243}{x + 3}"," ",0,"x**4/4 - 2*x**3 + 27*x**2/2 - 108*x + 405*log(x + 3) + 243/(x + 3)","A",0
103,1,31,0,0.142081," ","integrate((5*x**3-2)/(x**4-8*x**3+18*x**2-27),x)","\frac{955 - 407 x}{16 x^{2} - 96 x + 144} + \frac{313 \log{\left(x - 3 \right)}}{64} + \frac{7 \log{\left(x + 1 \right)}}{64}"," ",0,"(955 - 407*x)/(16*x**2 - 96*x + 144) + 313*log(x - 3)/64 + 7*log(x + 1)/64","A",0
104,1,26,0,0.146205," ","integrate((x**3-6*x**2+3*x-9)/(3+x)**2/(4+x)**2,x)","\frac{280 x + 939}{x^{2} + 7 x + 12} + 264 \log{\left(x + 3 \right)} - 263 \log{\left(x + 4 \right)}"," ",0,"(280*x + 939)/(x**2 + 7*x + 12) + 264*log(x + 3) - 263*log(x + 4)","A",0
105,1,32,0,0.159391," ","integrate((x**3+x**2+2)/x/(x**2-1)**2,x)","\frac{- x - 3}{2 x^{2} - 2} + 2 \log{\left(x \right)} - \frac{3 \log{\left(x - 1 \right)}}{4} - \frac{5 \log{\left(x + 1 \right)}}{4}"," ",0,"(-x - 3)/(2*x**2 - 2) + 2*log(x) - 3*log(x - 1)/4 - 5*log(x + 1)/4","A",0
106,1,37,0,0.174927," ","integrate(1/(x**6-x**5-x**4+x**3),x)","2 \log{\left(x \right)} - \frac{7 \log{\left(x - 1 \right)}}{4} - \frac{\log{\left(x + 1 \right)}}{4} + \frac{- 3 x^{2} + x + 1}{2 x^{3} - 2 x^{2}}"," ",0,"2*log(x) - 7*log(x - 1)/4 - log(x + 1)/4 + (-3*x**2 + x + 1)/(2*x**3 - 2*x**2)","A",0
107,1,22,0,0.127509," ","integrate((x**4+1)/(x**3-x**2+x-1),x)","\frac{x^{2}}{2} + x + \log{\left(x - 1 \right)} - \frac{\log{\left(x^{2} + 1 \right)}}{2} - \operatorname{atan}{\left(x \right)}"," ",0,"x**2/2 + x + log(x - 1) - log(x**2 + 1)/2 - atan(x)","A",0
108,1,22,0,0.189934," ","integrate(1/x/(1+x)/(x**2+1),x)","\log{\left(x \right)} - \frac{\log{\left(x + 1 \right)}}{2} - \frac{\log{\left(x^{2} + 1 \right)}}{4} - \frac{\operatorname{atan}{\left(x \right)}}{2}"," ",0,"log(x) - log(x + 1)/2 - log(x**2 + 1)/4 - atan(x)/2","A",0
109,1,29,0,0.156777," ","integrate(x**2/(x**4+x**2-2),x)","\frac{\log{\left(x - 1 \right)}}{6} - \frac{\log{\left(x + 1 \right)}}{6} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{3}"," ",0,"log(x - 1)/6 - log(x + 1)/6 + sqrt(2)*atan(sqrt(2)*x/2)/3","A",0
110,1,39,0,0.162395," ","integrate((x**3+4*x**2+6*x)/(x**4+2*x**3+3*x**2+4*x+2),x)","- \frac{\log{\left(x + 1 \right)}}{3} + \frac{2 \log{\left(x^{2} + 2 \right)}}{3} + \frac{4 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{3} + \frac{1}{x + 1}"," ",0,"-log(x + 1)/3 + 2*log(x**2 + 2)/3 + 4*sqrt(2)*atan(sqrt(2)*x/2)/3 + 1/(x + 1)","A",0
111,1,37,0,0.220415," ","integrate(x/(1+x)/(1+2*x)**2/(x**2+1),x)","\frac{16 \log{\left(x + \frac{1}{2} \right)}}{25} - \frac{\log{\left(x + 1 \right)}}{2} - \frac{7 \log{\left(x^{2} + 1 \right)}}{100} + \frac{\operatorname{atan}{\left(x \right)}}{50} + \frac{2}{10 x + 5}"," ",0,"16*log(x + 1/2)/25 - log(x + 1)/2 - 7*log(x**2 + 1)/100 + atan(x)/50 + 2/(10*x + 5)","A",0
112,1,36,0,0.175267," ","integrate((3*x**2+x-2)/(-1+x)**3/(x**2+1),x)","\frac{4 - 5 x}{2 x^{2} - 4 x + 2} - \frac{3 \log{\left(x - 1 \right)}}{2} + \frac{3 \log{\left(x^{2} + 1 \right)}}{4} - \operatorname{atan}{\left(x \right)}"," ",0,"(4 - 5*x)/(2*x**2 - 4*x + 2) - 3*log(x - 1)/2 + 3*log(x**2 + 1)/4 - atan(x)","A",0
113,1,70,0,0.207785," ","integrate(1/(x**4+x**2+1),x)","- \frac{\log{\left(x^{2} - x + 1 \right)}}{4} + \frac{\log{\left(x^{2} + x + 1 \right)}}{4} + \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**2 - x + 1)/4 + log(x**2 + x + 1)/4 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/6","A",0
114,1,306,0,0.590979," ","integrate((2*x**3+3)/(x**5-9*x),x)","- \frac{\log{\left(x \right)}}{3} + \left(\frac{1}{12} + \frac{\sqrt{3} i}{6}\right) \log{\left(x + \frac{17413}{11544} - \frac{943 \sqrt{3} i}{5772} + \frac{1368 \left(\frac{1}{12} + \frac{\sqrt{3} i}{6}\right)^{3}}{481} + \frac{4158 \left(\frac{1}{12} + \frac{\sqrt{3} i}{6}\right)^{2}}{481} - \frac{108000 \left(\frac{1}{12} + \frac{\sqrt{3} i}{6}\right)^{4}}{481} \right)} + \left(\frac{1}{12} - \frac{\sqrt{3} i}{6}\right) \log{\left(x + \frac{17413}{11544} - \frac{108000 \left(\frac{1}{12} - \frac{\sqrt{3} i}{6}\right)^{4}}{481} + \frac{4158 \left(\frac{1}{12} - \frac{\sqrt{3} i}{6}\right)^{2}}{481} + \frac{1368 \left(\frac{1}{12} - \frac{\sqrt{3} i}{6}\right)^{3}}{481} + \frac{943 \sqrt{3} i}{5772} \right)} + \left(\frac{1}{12} - \frac{\sqrt{3}}{6}\right) \log{\left(x - \frac{108000 \left(\frac{1}{12} - \frac{\sqrt{3}}{6}\right)^{4}}{481} + \frac{1368 \left(\frac{1}{12} - \frac{\sqrt{3}}{6}\right)^{3}}{481} + \frac{943 \sqrt{3}}{5772} + \frac{4158 \left(\frac{1}{12} - \frac{\sqrt{3}}{6}\right)^{2}}{481} + \frac{17413}{11544} \right)} + \left(\frac{1}{12} + \frac{\sqrt{3}}{6}\right) \log{\left(x - \frac{108000 \left(\frac{1}{12} + \frac{\sqrt{3}}{6}\right)^{4}}{481} - \frac{943 \sqrt{3}}{5772} + \frac{1368 \left(\frac{1}{12} + \frac{\sqrt{3}}{6}\right)^{3}}{481} + \frac{4158 \left(\frac{1}{12} + \frac{\sqrt{3}}{6}\right)^{2}}{481} + \frac{17413}{11544} \right)}"," ",0,"-log(x)/3 + (1/12 + sqrt(3)*I/6)*log(x + 17413/11544 - 943*sqrt(3)*I/5772 + 1368*(1/12 + sqrt(3)*I/6)**3/481 + 4158*(1/12 + sqrt(3)*I/6)**2/481 - 108000*(1/12 + sqrt(3)*I/6)**4/481) + (1/12 - sqrt(3)*I/6)*log(x + 17413/11544 - 108000*(1/12 - sqrt(3)*I/6)**4/481 + 4158*(1/12 - sqrt(3)*I/6)**2/481 + 1368*(1/12 - sqrt(3)*I/6)**3/481 + 943*sqrt(3)*I/5772) + (1/12 - sqrt(3)/6)*log(x - 108000*(1/12 - sqrt(3)/6)**4/481 + 1368*(1/12 - sqrt(3)/6)**3/481 + 943*sqrt(3)/5772 + 4158*(1/12 - sqrt(3)/6)**2/481 + 17413/11544) + (1/12 + sqrt(3)/6)*log(x - 108000*(1/12 + sqrt(3)/6)**4/481 - 943*sqrt(3)/5772 + 1368*(1/12 + sqrt(3)/6)**3/481 + 4158*(1/12 + sqrt(3)/6)**2/481 + 17413/11544)","C",0
115,1,46,0,0.196212," ","integrate((5*x**3+8*x-20)/(-4+x)**3/(x**2-4*x+8),x)","\frac{81 - 41 x}{4 x^{2} - 32 x + 64} - \frac{45 \log{\left(x - 4 \right)}}{16} + \frac{45 \log{\left(x^{2} - 4 x + 8 \right)}}{32} + \frac{3 \operatorname{atan}{\left(\frac{x}{2} - 1 \right)}}{16}"," ",0,"(81 - 41*x)/(4*x**2 - 32*x + 64) - 45*log(x - 4)/16 + 45*log(x**2 - 4*x + 8)/32 + 3*atan(x/2 - 1)/16","A",0
116,1,44,0,0.435069," ","integrate(1/(x**2+1)/(x**2+2)/(x**2+3)/(x**2+4),x)","- \frac{\operatorname{atan}{\left(\frac{x}{2} \right)}}{12} + \frac{\operatorname{atan}{\left(x \right)}}{6} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{6}"," ",0,"-atan(x/2)/12 + atan(x)/6 - sqrt(2)*atan(sqrt(2)*x/2)/4 + sqrt(3)*atan(sqrt(3)*x/3)/6","A",0
117,1,32,0,0.190552," ","integrate(x/(x**2+1)/(x**2+2)/(x**2+3)/(x**2+4),x)","\frac{\log{\left(x^{2} + 1 \right)}}{12} - \frac{\log{\left(x^{2} + 2 \right)}}{4} + \frac{\log{\left(x^{2} + 3 \right)}}{4} - \frac{\log{\left(x^{2} + 4 \right)}}{12}"," ",0,"log(x**2 + 1)/12 - log(x**2 + 2)/4 + log(x**2 + 3)/4 - log(x**2 + 4)/12","A",0
118,1,73,0,0.136106," ","integrate(1/(a**3+x**3),x)","\frac{\frac{\log{\left(a + x \right)}}{3} + \left(- \frac{1}{6} - \frac{\sqrt{3} i}{6}\right) \log{\left(3 a \left(- \frac{1}{6} - \frac{\sqrt{3} i}{6}\right) + x \right)} + \left(- \frac{1}{6} + \frac{\sqrt{3} i}{6}\right) \log{\left(3 a \left(- \frac{1}{6} + \frac{\sqrt{3} i}{6}\right) + x \right)}}{a^{2}}"," ",0,"(log(a + x)/3 + (-1/6 - sqrt(3)*I/6)*log(3*a*(-1/6 - sqrt(3)*I/6) + x) + (-1/6 + sqrt(3)*I/6)*log(3*a*(-1/6 + sqrt(3)*I/6) + x))/a**2","C",0
119,1,71,0,0.134542," ","integrate(x/(a**3+x**3),x)","\frac{- \frac{\log{\left(a + x \right)}}{3} + \left(\frac{1}{6} - \frac{\sqrt{3} i}{6}\right) \log{\left(9 a \left(\frac{1}{6} - \frac{\sqrt{3} i}{6}\right)^{2} + x \right)} + \left(\frac{1}{6} + \frac{\sqrt{3} i}{6}\right) \log{\left(9 a \left(\frac{1}{6} + \frac{\sqrt{3} i}{6}\right)^{2} + x \right)}}{a}"," ",0,"(-log(a + x)/3 + (1/6 - sqrt(3)*I/6)*log(9*a*(1/6 - sqrt(3)*I/6)**2 + x) + (1/6 + sqrt(3)*I/6)*log(9*a*(1/6 + sqrt(3)*I/6)**2 + x))/a","C",0
120,1,8,0,0.103980," ","integrate(x**2/(a**3+x**3),x)","\frac{\log{\left(a^{3} + x^{3} \right)}}{3}"," ",0,"log(a**3 + x**3)/3","A",0
121,1,19,0,0.212960," ","integrate(1/x/(a**3+x**3),x)","\frac{\log{\left(x \right)}}{a^{3}} - \frac{\log{\left(a^{3} + x^{3} \right)}}{3 a^{3}}"," ",0,"log(x)/a**3 - log(a**3 + x**3)/(3*a**3)","A",0
122,1,83,0,0.173977," ","integrate(1/x**2/(a**3+x**3),x)","- \frac{1}{a^{3} x} + \frac{\frac{\log{\left(a + x \right)}}{3} + \left(- \frac{1}{6} - \frac{\sqrt{3} i}{6}\right) \log{\left(9 a \left(- \frac{1}{6} - \frac{\sqrt{3} i}{6}\right)^{2} + x \right)} + \left(- \frac{1}{6} + \frac{\sqrt{3} i}{6}\right) \log{\left(9 a \left(- \frac{1}{6} + \frac{\sqrt{3} i}{6}\right)^{2} + x \right)}}{a^{4}}"," ",0,"-1/(a**3*x) + (log(a + x)/3 + (-1/6 - sqrt(3)*I/6)*log(9*a*(-1/6 - sqrt(3)*I/6)**2 + x) + (-1/6 + sqrt(3)*I/6)*log(9*a*(-1/6 + sqrt(3)*I/6)**2 + x))/a**4","C",0
123,1,80,0,0.200270," ","integrate(1/x**3/(a**3+x**3),x)","- \frac{1}{2 a^{3} x^{2}} + \frac{- \frac{\log{\left(a + x \right)}}{3} + \left(\frac{1}{6} - \frac{\sqrt{3} i}{6}\right) \log{\left(- 3 a \left(\frac{1}{6} - \frac{\sqrt{3} i}{6}\right) + x \right)} + \left(\frac{1}{6} + \frac{\sqrt{3} i}{6}\right) \log{\left(- 3 a \left(\frac{1}{6} + \frac{\sqrt{3} i}{6}\right) + x \right)}}{a^{5}}"," ",0,"-1/(2*a**3*x**2) + (-log(a + x)/3 + (1/6 - sqrt(3)*I/6)*log(-3*a*(1/6 - sqrt(3)*I/6) + x) + (1/6 + sqrt(3)*I/6)*log(-3*a*(1/6 + sqrt(3)*I/6) + x))/a**5","C",0
124,1,29,0,0.267138," ","integrate(1/x**4/(a**3+x**3),x)","- \frac{1}{3 a^{3} x^{3}} - \frac{\log{\left(x \right)}}{a^{6}} + \frac{\log{\left(a^{3} + x^{3} \right)}}{3 a^{6}}"," ",0,"-1/(3*a**3*x**3) - log(x)/a**6 + log(a**3 + x**3)/(3*a**6)","A",0
125,1,90,0,0.219469," ","integrate(1/x**5/(a**3+x**3),x)","\frac{- a^{3} + 4 x^{3}}{4 a^{6} x^{4}} + \frac{- \frac{\log{\left(a + x \right)}}{3} + \left(\frac{1}{6} - \frac{\sqrt{3} i}{6}\right) \log{\left(9 a \left(\frac{1}{6} - \frac{\sqrt{3} i}{6}\right)^{2} + x \right)} + \left(\frac{1}{6} + \frac{\sqrt{3} i}{6}\right) \log{\left(9 a \left(\frac{1}{6} + \frac{\sqrt{3} i}{6}\right)^{2} + x \right)}}{a^{7}}"," ",0,"(-a**3 + 4*x**3)/(4*a**6*x**4) + (-log(a + x)/3 + (1/6 - sqrt(3)*I/6)*log(9*a*(1/6 - sqrt(3)*I/6)**2 + x) + (1/6 + sqrt(3)*I/6)*log(9*a*(1/6 + sqrt(3)*I/6)**2 + x))/a**7","C",0
126,1,92,0,2.971006," ","integrate(1/(x**m)/(a**3+x**3),x)","- \frac{m x x^{- m} \Phi\left(\frac{x^{3} e^{i \pi}}{a^{3}}, 1, \frac{1}{3} - \frac{m}{3}\right) \Gamma\left(\frac{1}{3} - \frac{m}{3}\right)}{9 a^{3} \Gamma\left(\frac{4}{3} - \frac{m}{3}\right)} + \frac{x x^{- m} \Phi\left(\frac{x^{3} e^{i \pi}}{a^{3}}, 1, \frac{1}{3} - \frac{m}{3}\right) \Gamma\left(\frac{1}{3} - \frac{m}{3}\right)}{9 a^{3} \Gamma\left(\frac{4}{3} - \frac{m}{3}\right)}"," ",0,"-m*x*x**(-m)*lerchphi(x**3*exp_polar(I*pi)/a**3, 1, 1/3 - m/3)*gamma(1/3 - m/3)/(9*a**3*gamma(4/3 - m/3)) + x*x**(-m)*lerchphi(x**3*exp_polar(I*pi)/a**3, 1, 1/3 - m/3)*gamma(1/3 - m/3)/(9*a**3*gamma(4/3 - m/3))","C",0
127,1,37,0,0.151976," ","integrate(1/(a**4-x**4),x)","- \frac{\frac{\log{\left(- a + x \right)}}{4} - \frac{\log{\left(a + x \right)}}{4} + \frac{i \log{\left(- i a + x \right)}}{4} - \frac{i \log{\left(i a + x \right)}}{4}}{a^{3}}"," ",0,"-(log(-a + x)/4 - log(a + x)/4 + I*log(-I*a + x)/4 - I*log(I*a + x)/4)/a**3","C",0
128,1,24,0,0.154980," ","integrate(x/(a**4-x**4),x)","- \frac{\frac{\log{\left(- a^{2} + x^{2} \right)}}{4} - \frac{\log{\left(a^{2} + x^{2} \right)}}{4}}{a^{2}}"," ",0,"-(log(-a**2 + x**2)/4 - log(a**2 + x**2)/4)/a**2","A",0
129,1,19,0,0.252476," ","integrate(1/x/(a**4-x**4),x)","\frac{\log{\left(x \right)}}{a^{4}} - \frac{\log{\left(- a^{4} + x^{4} \right)}}{4 a^{4}}"," ",0,"log(x)/a**4 - log(-a**4 + x**4)/(4*a**4)","A",0
130,1,44,0,0.204475," ","integrate(1/x**2/(a**4-x**4),x)","- \frac{1}{a^{4} x} - \frac{\frac{\log{\left(- a + x \right)}}{4} - \frac{\log{\left(a + x \right)}}{4} - \frac{i \log{\left(- i a + x \right)}}{4} + \frac{i \log{\left(i a + x \right)}}{4}}{a^{5}}"," ",0,"-1/(a**4*x) - (log(-a + x)/4 - log(a + x)/4 - I*log(-I*a + x)/4 + I*log(I*a + x)/4)/a**5","C",0
131,1,34,0,0.222576," ","integrate(1/x**3/(a**4-x**4),x)","- \frac{1}{2 a^{4} x^{2}} - \frac{\frac{\log{\left(- a^{2} + x^{2} \right)}}{4} - \frac{\log{\left(a^{2} + x^{2} \right)}}{4}}{a^{6}}"," ",0,"-1/(2*a**4*x**2) - (log(-a**2 + x**2)/4 - log(a**2 + x**2)/4)/a**6","A",0
132,1,48,0,0.226277," ","integrate(1/x**4/(a**4-x**4),x)","- \frac{1}{3 a^{4} x^{3}} - \frac{\frac{\log{\left(- a + x \right)}}{4} - \frac{\log{\left(a + x \right)}}{4} + \frac{i \log{\left(- i a + x \right)}}{4} - \frac{i \log{\left(i a + x \right)}}{4}}{a^{7}}"," ",0,"-1/(3*a**4*x**3) - (log(-a + x)/4 - log(a + x)/4 + I*log(-I*a + x)/4 - I*log(I*a + x)/4)/a**7","C",0
133,1,95,0,1.007295," ","integrate(1/(x**m)/(a**4-x**4),x)","- \frac{m x x^{- m} \Phi\left(\frac{x^{4} e^{2 i \pi}}{a^{4}}, 1, \frac{1}{4} - \frac{m}{4}\right) \Gamma\left(\frac{1}{4} - \frac{m}{4}\right)}{16 a^{4} \Gamma\left(\frac{5}{4} - \frac{m}{4}\right)} + \frac{x x^{- m} \Phi\left(\frac{x^{4} e^{2 i \pi}}{a^{4}}, 1, \frac{1}{4} - \frac{m}{4}\right) \Gamma\left(\frac{1}{4} - \frac{m}{4}\right)}{16 a^{4} \Gamma\left(\frac{5}{4} - \frac{m}{4}\right)}"," ",0,"-m*x*x**(-m)*lerchphi(x**4*exp_polar(2*I*pi)/a**4, 1, 1/4 - m/4)*gamma(1/4 - m/4)/(16*a**4*gamma(5/4 - m/4)) + x*x**(-m)*lerchphi(x**4*exp_polar(2*I*pi)/a**4, 1, 1/4 - m/4)*gamma(1/4 - m/4)/(16*a**4*gamma(5/4 - m/4))","C",0
134,1,29,0,0.145366," ","integrate(x/(a**4+x**4),x)","\frac{- \frac{i \log{\left(- i a^{2} + x^{2} \right)}}{4} + \frac{i \log{\left(i a^{2} + x^{2} \right)}}{4}}{a^{2}}"," ",0,"(-I*log(-I*a**2 + x**2)/4 + I*log(I*a**2 + x**2)/4)/a**2","C",0
135,1,19,0,0.139804," ","integrate(x**2/(a**4+x**4),x)","\frac{\operatorname{RootSum} {\left(256 t^{4} + 1, \left( t \mapsto t \log{\left(64 t^{3} a + x \right)} \right)\right)}}{a}"," ",0,"RootSum(256*_t**4 + 1, Lambda(_t, _t*log(64*_t**3*a + x)))/a","A",0
136,1,39,0,0.151560," ","integrate(1/(a**5+x**5),x)","\frac{\frac{\log{\left(a + x \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t a + x \right)} \right)\right)}}{a^{4}}"," ",0,"(log(a + x)/5 + RootSum(625*_t**4 + 125*_t**3 + 25*_t**2 + 5*_t + 1, Lambda(_t, _t*log(5*_t*a + x))))/a**4","A",0
137,1,41,0,0.138903," ","integrate(x/(a**5+x**5),x)","\frac{- \frac{\log{\left(a + x \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} - 125 t^{3} + 25 t^{2} - 5 t + 1, \left( t \mapsto t \log{\left(- 125 t^{3} a + x \right)} \right)\right)}}{a^{3}}"," ",0,"(-log(a + x)/5 + RootSum(625*_t**4 - 125*_t**3 + 25*_t**2 - 5*_t + 1, Lambda(_t, _t*log(-125*_t**3*a + x))))/a**3","A",0
138,1,41,0,0.153678," ","integrate(x**2/(a**5+x**5),x)","\frac{\frac{\log{\left(a + x \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(25 t^{2} a + x \right)} \right)\right)}}{a^{2}}"," ",0,"(log(a + x)/5 + RootSum(625*_t**4 + 125*_t**3 + 25*_t**2 + 5*_t + 1, Lambda(_t, _t*log(25*_t**2*a + x))))/a**2","A",0
139,1,39,0,0.150549," ","integrate(x**3/(a**5+x**5),x)","\frac{- \frac{\log{\left(a + x \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} - 125 t^{3} + 25 t^{2} - 5 t + 1, \left( t \mapsto t \log{\left(625 t^{4} a + x \right)} \right)\right)}}{a}"," ",0,"(-log(a + x)/5 + RootSum(625*_t**4 - 125*_t**3 + 25*_t**2 - 5*_t + 1, Lambda(_t, _t*log(625*_t**4*a + x))))/a","A",0
140,1,8,0,0.116435," ","integrate(x**4/(a**5+x**5),x)","\frac{\log{\left(a^{5} + x^{5} \right)}}{5}"," ",0,"log(a**5 + x**5)/5","A",0
141,1,19,0,0.263955," ","integrate(1/x/(a**5+x**5),x)","\frac{\log{\left(x \right)}}{a^{5}} - \frac{\log{\left(a^{5} + x^{5} \right)}}{5 a^{5}}"," ",0,"log(x)/a**5 - log(a**5 + x**5)/(5*a**5)","A",0
142,1,48,0,0.193787," ","integrate(1/x**2/(a**5+x**5),x)","- \frac{1}{a^{5} x} + \frac{\frac{\log{\left(a + x \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(625 t^{4} a + x \right)} \right)\right)}}{a^{6}}"," ",0,"-1/(a**5*x) + (log(a + x)/5 + RootSum(625*_t**4 + 125*_t**3 + 25*_t**2 + 5*_t + 1, Lambda(_t, _t*log(625*_t**4*a + x))))/a**6","A",0
143,1,51,0,0.221980," ","integrate(1/x**3/(a**5+x**5),x)","- \frac{1}{2 a^{5} x^{2}} + \frac{- \frac{\log{\left(a + x \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} - 125 t^{3} + 25 t^{2} - 5 t + 1, \left( t \mapsto t \log{\left(25 t^{2} a + x \right)} \right)\right)}}{a^{7}}"," ",0,"-1/(2*a**5*x**2) + (-log(a + x)/5 + RootSum(625*_t**4 - 125*_t**3 + 25*_t**2 - 5*_t + 1, Lambda(_t, _t*log(25*_t**2*a + x))))/a**7","A",0
144,1,51,0,0.218750," ","integrate(1/x**4/(a**5+x**5),x)","- \frac{1}{3 a^{5} x^{3}} + \frac{\frac{\log{\left(a + x \right)}}{5} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(125 t^{3} a + x \right)} \right)\right)}}{a^{8}}"," ",0,"-1/(3*a**5*x**3) + (log(a + x)/5 + RootSum(625*_t**4 + 125*_t**3 + 25*_t**2 + 5*_t + 1, Lambda(_t, _t*log(125*_t**3*a + x))))/a**8","A",0
145,1,92,0,24.441240," ","integrate(1/(x**m)/(a**5+x**5),x)","- \frac{m x x^{- m} \Phi\left(\frac{x^{5} e^{i \pi}}{a^{5}}, 1, \frac{1}{5} - \frac{m}{5}\right) \Gamma\left(\frac{1}{5} - \frac{m}{5}\right)}{25 a^{5} \Gamma\left(\frac{6}{5} - \frac{m}{5}\right)} + \frac{x x^{- m} \Phi\left(\frac{x^{5} e^{i \pi}}{a^{5}}, 1, \frac{1}{5} - \frac{m}{5}\right) \Gamma\left(\frac{1}{5} - \frac{m}{5}\right)}{25 a^{5} \Gamma\left(\frac{6}{5} - \frac{m}{5}\right)}"," ",0,"-m*x*x**(-m)*lerchphi(x**5*exp_polar(I*pi)/a**5, 1, 1/5 - m/5)*gamma(1/5 - m/5)/(25*a**5*gamma(6/5 - m/5)) + x*x**(-m)*lerchphi(x**5*exp_polar(I*pi)/a**5, 1, 1/5 - m/5)*gamma(1/5 - m/5)/(25*a**5*gamma(6/5 - m/5))","C",0
146,1,8,0,0.129387," ","integrate((x**4+1)/(x**6+1),x)","\operatorname{atan}{\left(x \right)} + \frac{\operatorname{atan}{\left(x^{3} \right)}}{3}"," ",0,"atan(x) + atan(x**3)/3","A",0
147,1,63,0,0.175460," ","integrate(1/(x**2+3*x+5)**3,x)","\frac{12 x^{3} + 54 x^{2} + 136 x + 123}{242 x^{4} + 1452 x^{3} + 4598 x^{2} + 7260 x + 6050} + \frac{12 \sqrt{11} \operatorname{atan}{\left(\frac{2 \sqrt{11} x}{11} + \frac{3 \sqrt{11}}{11} \right)}}{1331}"," ",0,"(12*x**3 + 54*x**2 + 136*x + 123)/(242*x**4 + 1452*x**3 + 4598*x**2 + 7260*x + 6050) + 12*sqrt(11)*atan(2*sqrt(11)*x/11 + 3*sqrt(11)/11)/1331","A",0
148,1,36,0,0.145328," ","integrate((x**4+x**2+1)/(x**2+1)**4,x)","\frac{21 x^{5} + 40 x^{3} + 27 x}{48 x^{6} + 144 x^{4} + 144 x^{2} + 48} + \frac{7 \operatorname{atan}{\left(x \right)}}{16}"," ",0,"(21*x**5 + 40*x**3 + 27*x)/(48*x**6 + 144*x**4 + 144*x**2 + 48) + 7*atan(x)/16","A",0
149,1,323,0,1.010072," ","integrate((A*x+B)/(a*x**2+2*b*x+c)**2,x)","- \frac{\sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(- A b + B a\right) \log{\left(x + \frac{- A b^{2} + B a b - a^{2} c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(- A b + B a\right) + 2 a b^{2} c \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(- A b + B a\right) - b^{4} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(- A b + B a\right)}{- A a b + B a^{2}} \right)}}{4} + \frac{\sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(- A b + B a\right) \log{\left(x + \frac{- A b^{2} + B a b + a^{2} c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(- A b + B a\right) - 2 a b^{2} c \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(- A b + B a\right) + b^{4} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(- A b + B a\right)}{- A a b + B a^{2}} \right)}}{4} + \frac{- A c + B b + x \left(- A b + B a\right)}{2 a c^{2} - 2 b^{2} c + x^{2} \left(2 a^{2} c - 2 a b^{2}\right) + x \left(4 a b c - 4 b^{3}\right)}"," ",0,"-sqrt(-1/(a*c - b**2)**3)*(-A*b + B*a)*log(x + (-A*b**2 + B*a*b - a**2*c**2*sqrt(-1/(a*c - b**2)**3)*(-A*b + B*a) + 2*a*b**2*c*sqrt(-1/(a*c - b**2)**3)*(-A*b + B*a) - b**4*sqrt(-1/(a*c - b**2)**3)*(-A*b + B*a))/(-A*a*b + B*a**2))/4 + sqrt(-1/(a*c - b**2)**3)*(-A*b + B*a)*log(x + (-A*b**2 + B*a*b + a**2*c**2*sqrt(-1/(a*c - b**2)**3)*(-A*b + B*a) - 2*a*b**2*c*sqrt(-1/(a*c - b**2)**3)*(-A*b + B*a) + b**4*sqrt(-1/(a*c - b**2)**3)*(-A*b + B*a))/(-A*a*b + B*a**2))/4 + (-A*c + B*b + x*(-A*b + B*a))/(2*a*c**2 - 2*b**2*c + x**2*(2*a**2*c - 2*a*b**2) + x*(4*a*b*c - 4*b**3))","B",0
150,1,31,0,0.141147," ","integrate((5*x**3-27*x**2+55*x-41)/(x**2-4*x+5)**2,x)","\frac{1 - x}{x^{2} - 4 x + 5} + \frac{5 \log{\left(x^{2} - 4 x + 5 \right)}}{2} + 2 \operatorname{atan}{\left(x - 2 \right)}"," ",0,"(1 - x)/(x**2 - 4*x + 5) + 5*log(x**2 - 4*x + 5)/2 + 2*atan(x - 2)","A",0
151,1,53,0,0.165874," ","integrate(1/(x**3-1)**2,x)","- \frac{x}{3 x^{3} - 3} - \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + x + 1 \right)}}{9} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"-x/(3*x**3 - 3) - 2*log(x - 1)/9 + log(x**2 + x + 1)/9 + 2*sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/9","A",0
152,1,32,0,0.150171," ","integrate((3*x**4+4)/x**2/(x**2+1)**3,x)","\frac{- 57 x^{4} - 103 x^{2} - 32}{8 x^{5} + 16 x^{3} + 8 x} - \frac{57 \operatorname{atan}{\left(x \right)}}{8}"," ",0,"(-57*x**4 - 103*x**2 - 32)/(8*x**5 + 16*x**3 + 8*x) - 57*atan(x)/8","A",0
153,1,46,0,0.146852," ","integrate(x/(x**6+1),x)","\frac{\log{\left(x^{2} + 1 \right)}}{6} - \frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"log(x**2 + 1)/6 - log(x**4 - x**2 + 1)/12 + sqrt(3)*atan(2*sqrt(3)*x**2/3 - sqrt(3)/3)/6","A",0
154,1,14,0,2.480635," ","integrate((-1+x**(-1+n))/(-n*x+x**n),x)","\begin{cases} \frac{\log{\left(x - \frac{x^{n}}{n} \right)}}{n} & \text{for}\: n \neq 0 \\- x + \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x - x**n/n)/n, Ne(n, 0)), (-x + log(x), True))","A",0
155,1,42,0,0.127822," ","integrate(x**3/(3*x**4-2*x**2+1),x)","\frac{\log{\left(x^{4} - \frac{2 x^{2}}{3} + \frac{1}{3} \right)}}{12} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} x^{2}}{2} - \frac{\sqrt{2}}{2} \right)}}{12}"," ",0,"log(x**4 - 2*x**2/3 + 1/3)/12 + sqrt(2)*atan(3*sqrt(2)*x**2/2 - sqrt(2)/2)/12","A",0
156,1,24,0,0.120637," ","integrate(x**5/(3*x**4+x**2-4),x)","\frac{x^{2}}{6} + \frac{\log{\left(x^{2} - 1 \right)}}{14} - \frac{8 \log{\left(x^{2} + \frac{4}{3} \right)}}{63}"," ",0,"x**2/6 + log(x**2 - 1)/14 - 8*log(x**2 + 4/3)/63","A",0
157,1,15,0,0.112293," ","integrate(x**2/(x**6-10*x**3+9),x)","\frac{\log{\left(x^{3} - 9 \right)}}{24} - \frac{\log{\left(x^{3} - 1 \right)}}{24}"," ",0,"log(x**3 - 9)/24 - log(x**3 - 1)/24","A",0
158,1,29,0,0.115082," ","integrate((x**3-4*x**2+1)/(-2+x)**4,x)","\frac{- 6 x^{2} + 30 x - 29}{3 x^{3} - 18 x^{2} + 36 x - 24} + \log{\left(x - 2 \right)}"," ",0,"(-6*x**2 + 30*x - 29)/(3*x**3 - 18*x**2 + 36*x - 24) + log(x - 2)","A",0
159,1,70,0,0.165842," ","integrate(x**3/(-1+x)**12,x)","\frac{- 165 x^{3} + 55 x^{2} - 11 x + 1}{1320 x^{11} - 14520 x^{10} + 72600 x^{9} - 217800 x^{8} + 435600 x^{7} - 609840 x^{6} + 609840 x^{5} - 435600 x^{4} + 217800 x^{3} - 72600 x^{2} + 14520 x - 1320}"," ",0,"(-165*x**3 + 55*x**2 - 11*x + 1)/(1320*x**11 - 14520*x**10 + 72600*x**9 - 217800*x**8 + 435600*x**7 - 609840*x**6 + 609840*x**5 - 435600*x**4 + 217800*x**3 - 72600*x**2 + 14520*x - 1320)","B",0
160,1,42,0,0.130092," ","integrate((x**4-3*x)/(1+2*x)**5,x)","\frac{384 x^{3} + 432 x^{2} + 368 x + 49}{6144 x^{4} + 12288 x^{3} + 9216 x^{2} + 3072 x + 384} + \frac{\log{\left(2 x + 1 \right)}}{32}"," ",0,"(384*x**3 + 432*x**2 + 368*x + 49)/(6144*x**4 + 12288*x**3 + 9216*x**2 + 3072*x + 384) + log(2*x + 1)/32","A",0
161,1,41,0,0.141669," ","integrate(1/(-1+x)**2/(1+x)**3,x)","\frac{- 3 x^{2} - 3 x + 2}{8 x^{3} + 8 x^{2} - 8 x - 8} - \frac{3 \log{\left(x - 1 \right)}}{16} + \frac{3 \log{\left(x + 1 \right)}}{16}"," ",0,"(-3*x**2 - 3*x + 2)/(8*x**3 + 8*x**2 - 8*x - 8) - 3*log(x - 1)/16 + 3*log(x + 1)/16","A",0
162,1,29,0,0.131263," ","integrate(1/(5-6*x)**2/x**2,x)","\frac{5 - 12 x}{150 x^{2} - 125 x} + \frac{12 \log{\left(x \right)}}{125} - \frac{12 \log{\left(x - \frac{5}{6} \right)}}{125}"," ",0,"(5 - 12*x)/(150*x**2 - 125*x) + 12*log(x)/125 - 12*log(x - 5/6)/125","A",0
163,1,51,0,0.164007," ","integrate(1/(x**2-2*x-3)**3,x)","\frac{3 x^{3} - 9 x^{2} - 11 x + 17}{128 x^{4} - 512 x^{3} - 256 x^{2} + 1536 x + 1152} + \frac{3 \log{\left(x - 3 \right)}}{512} - \frac{3 \log{\left(x + 1 \right)}}{512}"," ",0,"(3*x**3 - 9*x**2 - 11*x + 17)/(128*x**4 - 512*x**3 - 256*x**2 + 1536*x + 1152) + 3*log(x - 3)/512 - 3*log(x + 1)/512","A",0
164,1,42,0,0.168681," ","integrate(1/(x**2-4*x+13)**3,x)","\frac{x^{3} - 6 x^{2} + 27 x - 38}{216 x^{4} - 1728 x^{3} + 9072 x^{2} - 22464 x + 36504} + \frac{\operatorname{atan}{\left(\frac{x}{3} - \frac{2}{3} \right)}}{648}"," ",0,"(x**3 - 6*x**2 + 27*x - 38)/(216*x**4 - 1728*x**3 + 9072*x**2 - 22464*x + 36504) + atan(x/3 - 2/3)/648","A",0
165,1,58,0,0.177732," ","integrate(1/(2+x)**3/(3+x)**4,x)","\frac{60 x^{4} + 630 x^{3} + 2450 x^{2} + 4175 x + 2627}{6 x^{5} + 78 x^{4} + 402 x^{3} + 1026 x^{2} + 1296 x + 648} + 10 \log{\left(x + 2 \right)} - 10 \log{\left(x + 3 \right)}"," ",0,"(60*x**4 + 630*x**3 + 2450*x**2 + 4175*x + 2627)/(6*x**5 + 78*x**4 + 402*x**3 + 1026*x**2 + 1296*x + 648) + 10*log(x + 2) - 10*log(x + 3)","A",0
166,1,49,0,0.115162," ","integrate(x**6/(x**2-2)**2,x)","\frac{x^{3}}{3} + 4 x - \frac{2 x}{x^{2} - 2} + \frac{5 \sqrt{2} \log{\left(x - \sqrt{2} \right)}}{2} - \frac{5 \sqrt{2} \log{\left(x + \sqrt{2} \right)}}{2}"," ",0,"x**3/3 + 4*x - 2*x/(x**2 - 2) + 5*sqrt(2)*log(x - sqrt(2))/2 - 5*sqrt(2)*log(x + sqrt(2))/2","A",0
167,1,39,0,0.154605," ","integrate(x**8/(x**2+4)**4,x)","x + \frac{87 x^{5} + 544 x^{3} + 912 x}{12 x^{6} + 144 x^{4} + 576 x^{2} + 768} - \frac{35 \operatorname{atan}{\left(\frac{x}{2} \right)}}{8}"," ",0,"x + (87*x**5 + 544*x**3 + 912*x)/(12*x**6 + 144*x**4 + 576*x**2 + 768) - 35*atan(x/2)/8","A",0
168,1,42,0,0.142241," ","integrate((-4+7*x)/(3*x**2+2*x+5)**2,x)","\frac{- 19 x - 39}{84 x^{2} + 56 x + 140} - \frac{19 \sqrt{14} \operatorname{atan}{\left(\frac{3 \sqrt{14} x}{14} + \frac{\sqrt{14}}{14} \right)}}{392}"," ",0,"(-19*x - 39)/(84*x**2 + 56*x + 140) - 19*sqrt(14)*atan(3*sqrt(14)*x/14 + sqrt(14)/14)/392","A",0
169,1,58,0,0.169401," ","integrate((5-4*x)/(3*x**2-4*x-2)**2,x)","- \frac{7 x - 18}{60 x^{2} - 80 x - 40} + \frac{7 \sqrt{10} \log{\left(x - \frac{2}{3} + \frac{\sqrt{10}}{3} \right)}}{400} - \frac{7 \sqrt{10} \log{\left(x - \frac{\sqrt{10}}{3} - \frac{2}{3} \right)}}{400}"," ",0,"-(7*x - 18)/(60*x**2 - 80*x - 40) + 7*sqrt(10)*log(x - 2/3 + sqrt(10)/3)/400 - 7*sqrt(10)*log(x - sqrt(10)/3 - 2/3)/400","A",0
170,1,24,0,0.168657," ","integrate(x**5/(x**4+1)**3,x)","\frac{x^{6} - x^{2}}{16 x^{8} + 32 x^{4} + 16} + \frac{\operatorname{atan}{\left(x^{2} \right)}}{16}"," ",0,"(x**6 - x**2)/(16*x**8 + 32*x**4 + 16) + atan(x**2)/16","A",0
171,1,26,0,0.172628," ","integrate(x*(x**2+1)**3/(x**4+2*x**2+2)**2,x)","\frac{\log{\left(x^{4} + 2 x^{2} + 2 \right)}}{4} + \frac{1}{4 x^{4} + 8 x^{2} + 8}"," ",0,"log(x**4 + 2*x**2 + 2)/4 + 1/(4*x**4 + 8*x**2 + 8)","A",0
172,1,20,0,0.281309," ","integrate(x**3/(a**4+x**4)**3,x)","- \frac{1}{8 a^{8} + 16 a^{4} x^{4} + 8 x^{8}}"," ",0,"-1/(8*a**8 + 16*a**4*x**4 + 8*x**8)","A",0
173,1,51,0,0.464457," ","integrate(1/x/(a**4+x**4)**3,x)","\frac{3 a^{4} + 2 x^{4}}{8 a^{16} + 16 a^{12} x^{4} + 8 a^{8} x^{8}} + \frac{\log{\left(x \right)}}{a^{12}} - \frac{\log{\left(a^{4} + x^{4} \right)}}{4 a^{12}}"," ",0,"(3*a**4 + 2*x**4)/(8*a**16 + 16*a**12*x**4 + 8*a**8*x**8) + log(x)/a**12 - log(a**4 + x**4)/(4*a**12)","A",0
174,1,66,0,0.443349," ","integrate(1/x**2/(a**4+x**4)**3,x)","\frac{- 32 a^{8} - 81 a^{4} x^{4} - 45 x^{8}}{32 a^{20} x + 64 a^{16} x^{5} + 32 a^{12} x^{9}} + \frac{\operatorname{RootSum} {\left(268435456 t^{4} + 4100625, \left( t \mapsto t \log{\left(- \frac{2097152 t^{3} a}{91125} + x \right)} \right)\right)}}{a^{13}}"," ",0,"(-32*a**8 - 81*a**4*x**4 - 45*x**8)/(32*a**20*x + 64*a**16*x**5 + 32*a**12*x**9) + RootSum(268435456*_t**4 + 4100625, Lambda(_t, _t*log(-2097152*_t**3*a/91125 + x)))/a**13","A",0
175,1,78,0,0.478419," ","integrate(1/x**3/(a**4+x**4)**3,x)","\frac{- 8 a^{8} - 25 a^{4} x^{4} - 15 x^{8}}{16 a^{20} x^{2} + 32 a^{16} x^{6} + 16 a^{12} x^{10}} + \frac{\frac{15 i \log{\left(- i a^{2} + x^{2} \right)}}{32} - \frac{15 i \log{\left(i a^{2} + x^{2} \right)}}{32}}{a^{14}}"," ",0,"(-8*a**8 - 25*a**4*x**4 - 15*x**8)/(16*a**20*x**2 + 32*a**16*x**6 + 16*a**12*x**10) + (15*I*log(-I*a**2 + x**2)/32 - 15*I*log(I*a**2 + x**2)/32)/a**14","C",0
176,1,27,0,0.180147," ","integrate(x**14/(2*x**5+3)**3,x)","\frac{24 x^{5} + 27}{320 x^{10} + 960 x^{5} + 720} + \frac{\log{\left(2 x^{5} + 3 \right)}}{40}"," ",0,"(24*x**5 + 27)/(320*x**10 + 960*x**5 + 720) + log(2*x**5 + 3)/40","A",0
177,1,37,0,0.300820," ","integrate(x**6/(2*x**5+3)**3,x)","\frac{4 x^{7} - 9 x^{2}}{1200 x^{10} + 3600 x^{5} + 2700} + \operatorname{RootSum} {\left(105468750000000 t^{5} + 1, \left( t \mapsto t \log{\left(- 281250000 t^{3} + x \right)} \right)\right)}"," ",0,"(4*x**7 - 9*x**2)/(1200*x**10 + 3600*x**5 + 2700) + RootSum(105468750000000*_t**5 + 1, Lambda(_t, _t*log(-281250000*_t**3 + x)))","A",0
178,1,58,0,0.171557," ","integrate(9/5/x**2/(-2*x**2+3)**3,x)","- \frac{9 \left(10 x^{4} - 25 x^{2} + 12\right)}{720 x^{5} - 2160 x^{3} + 1620 x} - \frac{\sqrt{6} \log{\left(x - \frac{\sqrt{6}}{2} \right)}}{48} + \frac{\sqrt{6} \log{\left(x + \frac{\sqrt{6}}{2} \right)}}{48}"," ",0,"-9*(10*x**4 - 25*x**2 + 12)/(720*x**5 - 2160*x**3 + 1620*x) - sqrt(6)*log(x - sqrt(6)/2)/48 + sqrt(6)*log(x + sqrt(6)/2)/48","A",0
179,1,32,0,0.150902," ","integrate((3*x**4+4)/x**2/(x**2+1)**3,x)","\frac{- 57 x^{4} - 103 x^{2} - 32}{8 x^{5} + 16 x^{3} + 8 x} - \frac{57 \operatorname{atan}{\left(x \right)}}{8}"," ",0,"(-57*x**4 - 103*x**2 - 32)/(8*x**5 + 16*x**3 + 8*x) - 57*atan(x)/8","A",0
180,1,36,0,0.146654," ","integrate((-x**4+5*x**3+6*x**2-3*x+5)/(x**5-x**4-2*x**3+2*x**2+x-1),x)","- \frac{2 x^{2} + 7 x - 3}{2 x^{3} - 2 x^{2} - 2 x + 2} + \log{\left(x - 1 \right)} - 2 \log{\left(x + 1 \right)}"," ",0,"-(2*x**2 + 7*x - 3)/(2*x**3 - 2*x**2 - 2*x + 2) + log(x - 1) - 2*log(x + 1)","A",0
181,1,60,0,0.228671," ","integrate((x**2+1)/x/(x**3+1)**2,x)","\frac{x^{2} + 1}{3 x^{3} + 3} + \log{\left(x \right)} - \frac{4 \log{\left(x + 1 \right)}}{9} - \frac{5 \log{\left(x^{2} - x + 1 \right)}}{18} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"(x**2 + 1)/(3*x**3 + 3) + log(x) - 4*log(x + 1)/9 - 5*log(x**2 - x + 1)/18 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/9","A",0
182,1,68,0,0.204344," ","integrate((x**2-3*x-2)/(1+x)**2/(x**2+x+1)**2,x)","\frac{- 11 x^{2} - 18 x - 13}{3 x^{3} + 6 x^{2} + 6 x + 3} - \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + x + 1 \right)}}{2} - \frac{25 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"(-11*x**2 - 18*x - 13)/(3*x**3 + 6*x**2 + 6*x + 3) - log(x + 1) + log(x**2 + x + 1)/2 - 25*sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/9","A",0
183,1,34,0,0.160760," ","integrate(1/(1-4*x)**3/(2-3*x),x)","\frac{24 x - 1}{800 x^{2} - 400 x + 50} + \frac{9 \log{\left(x - \frac{2}{3} \right)}}{125} - \frac{9 \log{\left(x - \frac{1}{4} \right)}}{125}"," ",0,"(24*x - 1)/(800*x**2 - 400*x + 50) + 9*log(x - 2/3)/125 - 9*log(x - 1/4)/125","A",0
184,1,39,0,0.188137," ","integrate(x**3/(-5*x**2+2)**7,x)","- \frac{1 - 15 x^{2}}{11718750 x^{12} - 28125000 x^{10} + 28125000 x^{8} - 15000000 x^{6} + 4500000 x^{4} - 720000 x^{2} + 48000}"," ",0,"-(1 - 15*x**2)/(11718750*x**12 - 28125000*x**10 + 28125000*x**8 - 15000000*x**6 + 4500000*x**4 - 720000*x**2 + 48000)","A",0
185,1,36,0,0.132124," ","integrate(x**7/(-5*x**2+2)**3,x)","- \frac{x^{2}}{250} - \frac{2 - 6 x^{2}}{3125 x^{4} - 2500 x^{2} + 500} - \frac{3 \log{\left(5 x^{2} - 2 \right)}}{625}"," ",0,"-x**2/250 - (2 - 6*x**2)/(3125*x**4 - 2500*x**2 + 500) - 3*log(5*x**2 - 2)/625","A",0
186,1,34,0,0.151464," ","integrate(1/(-2+x)**3/(1+x)**2,x)","\frac{2 x^{2} - 5 x - 1}{18 x^{3} - 54 x^{2} + 72} + \frac{\log{\left(x - 2 \right)}}{27} - \frac{\log{\left(x + 1 \right)}}{27}"," ",0,"(2*x**2 - 5*x - 1)/(18*x**3 - 54*x**2 + 72) + log(x - 2)/27 - log(x + 1)/27","A",0
187,1,58,0,0.183615," ","integrate(1/(2+x)**3/(3+x)**4,x)","\frac{60 x^{4} + 630 x^{3} + 2450 x^{2} + 4175 x + 2627}{6 x^{5} + 78 x^{4} + 402 x^{3} + 1026 x^{2} + 1296 x + 648} + 10 \log{\left(x + 2 \right)} - 10 \log{\left(x + 3 \right)}"," ",0,"(60*x**4 + 630*x**3 + 2450*x**2 + 4175*x + 2627)/(6*x**5 + 78*x**4 + 402*x**3 + 1026*x**2 + 1296*x + 648) + 10*log(x + 2) - 10*log(x + 3)","A",0
188,1,31,0,0.093647," ","integrate(x**5/(3+x)**2,x)","\frac{x^{4}}{4} - 2 x^{3} + \frac{27 x^{2}}{2} - 108 x + 405 \log{\left(x + 3 \right)} + \frac{243}{x + 3}"," ",0,"x**4/4 - 2*x**3 + 27*x**2/2 - 108*x + 405*log(x + 3) + 243/(x + 3)","A",0
189,1,39,0,0.067159," ","integrate((c1*x+b1)*(c*x**2+2*b*x+a),x)","a b_{1} x + \frac{c c_{1} x^{4}}{4} + x^{3} \left(\frac{2 b c_{1}}{3} + \frac{b_{1} c}{3}\right) + x^{2} \left(\frac{a c_{1}}{2} + b b_{1}\right)"," ",0,"a*b1*x + c*c1*x**4/4 + x**3*(2*b*c1/3 + b1*c/3) + x**2*(a*c1/2 + b*b1)","A",0
190,1,100,0,0.090544," ","integrate((c1*x+b1)*(c*x**2+2*b*x+a)**2,x)","a^{2} b_{1} x + \frac{c^{2} c_{1} x^{6}}{6} + x^{5} \left(\frac{4 b c c_{1}}{5} + \frac{b_{1} c^{2}}{5}\right) + x^{4} \left(\frac{a c c_{1}}{2} + b^{2} c_{1} + b b_{1} c\right) + x^{3} \left(\frac{4 a b c_{1}}{3} + \frac{2 a b_{1} c}{3} + \frac{4 b^{2} b_{1}}{3}\right) + x^{2} \left(\frac{a^{2} c_{1}}{2} + 2 a b b_{1}\right)"," ",0,"a**2*b1*x + c**2*c1*x**6/6 + x**5*(4*b*c*c1/5 + b1*c**2/5) + x**4*(a*c*c1/2 + b**2*c1 + b*b1*c) + x**3*(4*a*b*c1/3 + 2*a*b1*c/3 + 4*b**2*b1/3) + x**2*(a**2*c1/2 + 2*a*b*b1)","A",0
191,1,189,0,0.102740," ","integrate((c1*x+b1)*(c*x**2+2*b*x+a)**3,x)","a^{3} b_{1} x + \frac{c^{3} c_{1} x^{8}}{8} + x^{7} \left(\frac{6 b c^{2} c_{1}}{7} + \frac{b_{1} c^{3}}{7}\right) + x^{6} \left(\frac{a c^{2} c_{1}}{2} + 2 b^{2} c c_{1} + b b_{1} c^{2}\right) + x^{5} \left(\frac{12 a b c c_{1}}{5} + \frac{3 a b_{1} c^{2}}{5} + \frac{8 b^{3} c_{1}}{5} + \frac{12 b^{2} b_{1} c}{5}\right) + x^{4} \left(\frac{3 a^{2} c c_{1}}{4} + 3 a b^{2} c_{1} + 3 a b b_{1} c + 2 b^{3} b_{1}\right) + x^{3} \left(2 a^{2} b c_{1} + a^{2} b_{1} c + 4 a b^{2} b_{1}\right) + x^{2} \left(\frac{a^{3} c_{1}}{2} + 3 a^{2} b b_{1}\right)"," ",0,"a**3*b1*x + c**3*c1*x**8/8 + x**7*(6*b*c**2*c1/7 + b1*c**3/7) + x**6*(a*c**2*c1/2 + 2*b**2*c*c1 + b*b1*c**2) + x**5*(12*a*b*c*c1/5 + 3*a*b1*c**2/5 + 8*b**3*c1/5 + 12*b**2*b1*c/5) + x**4*(3*a**2*c*c1/4 + 3*a*b**2*c1 + 3*a*b*b1*c + 2*b**3*b1) + x**3*(2*a**2*b*c1 + a**2*b1*c + 4*a*b**2*b1) + x**2*(a**3*c1/2 + 3*a**2*b*b1)","A",0
192,1,313,0,0.127952," ","integrate((c1*x+b1)*(c*x**2+2*b*x+a)**4,x)","a^{4} b_{1} x + \frac{c^{4} c_{1} x^{10}}{10} + x^{9} \left(\frac{8 b c^{3} c_{1}}{9} + \frac{b_{1} c^{4}}{9}\right) + x^{8} \left(\frac{a c^{3} c_{1}}{2} + 3 b^{2} c^{2} c_{1} + b b_{1} c^{3}\right) + x^{7} \left(\frac{24 a b c^{2} c_{1}}{7} + \frac{4 a b_{1} c^{3}}{7} + \frac{32 b^{3} c c_{1}}{7} + \frac{24 b^{2} b_{1} c^{2}}{7}\right) + x^{6} \left(a^{2} c^{2} c_{1} + 8 a b^{2} c c_{1} + 4 a b b_{1} c^{2} + \frac{8 b^{4} c_{1}}{3} + \frac{16 b^{3} b_{1} c}{3}\right) + x^{5} \left(\frac{24 a^{2} b c c_{1}}{5} + \frac{6 a^{2} b_{1} c^{2}}{5} + \frac{32 a b^{3} c_{1}}{5} + \frac{48 a b^{2} b_{1} c}{5} + \frac{16 b^{4} b_{1}}{5}\right) + x^{4} \left(a^{3} c c_{1} + 6 a^{2} b^{2} c_{1} + 6 a^{2} b b_{1} c + 8 a b^{3} b_{1}\right) + x^{3} \left(\frac{8 a^{3} b c_{1}}{3} + \frac{4 a^{3} b_{1} c}{3} + 8 a^{2} b^{2} b_{1}\right) + x^{2} \left(\frac{a^{4} c_{1}}{2} + 4 a^{3} b b_{1}\right)"," ",0,"a**4*b1*x + c**4*c1*x**10/10 + x**9*(8*b*c**3*c1/9 + b1*c**4/9) + x**8*(a*c**3*c1/2 + 3*b**2*c**2*c1 + b*b1*c**3) + x**7*(24*a*b*c**2*c1/7 + 4*a*b1*c**3/7 + 32*b**3*c*c1/7 + 24*b**2*b1*c**2/7) + x**6*(a**2*c**2*c1 + 8*a*b**2*c*c1 + 4*a*b*b1*c**2 + 8*b**4*c1/3 + 16*b**3*b1*c/3) + x**5*(24*a**2*b*c*c1/5 + 6*a**2*b1*c**2/5 + 32*a*b**3*c1/5 + 48*a*b**2*b1*c/5 + 16*b**4*b1/5) + x**4*(a**3*c*c1 + 6*a**2*b**2*c1 + 6*a**2*b*b1*c + 8*a*b**3*b1) + x**3*(8*a**3*b*c1/3 + 4*a**3*b1*c/3 + 8*a**2*b**2*b1) + x**2*(a**4*c1/2 + 4*a**3*b*b1)","A",0
193,0,0,0,0.000000," ","integrate((c1*x+b1)*(c*x**2+2*b*x+a)**n,x)","\int \left(b_{1} + c_{1} x\right) \left(a + 2 b x + c x^{2}\right)^{n}\, dx"," ",0,"Integral((b1 + c1*x)*(a + 2*b*x + c*x**2)**n, x)","F",0
194,1,246,0,0.756603," ","integrate((c1*x+b1)/(c*x**2+2*b*x+a),x)","\left(\frac{c_{1}}{2 c} - \frac{\sqrt{- a c + b^{2}} \left(b c_{1} - b_{1} c\right)}{2 c \left(a c - b^{2}\right)}\right) \log{\left(x + \frac{- 2 a c \left(\frac{c_{1}}{2 c} - \frac{\sqrt{- a c + b^{2}} \left(b c_{1} - b_{1} c\right)}{2 c \left(a c - b^{2}\right)}\right) + a c_{1} + 2 b^{2} \left(\frac{c_{1}}{2 c} - \frac{\sqrt{- a c + b^{2}} \left(b c_{1} - b_{1} c\right)}{2 c \left(a c - b^{2}\right)}\right) - b b_{1}}{b c_{1} - b_{1} c} \right)} + \left(\frac{c_{1}}{2 c} + \frac{\sqrt{- a c + b^{2}} \left(b c_{1} - b_{1} c\right)}{2 c \left(a c - b^{2}\right)}\right) \log{\left(x + \frac{- 2 a c \left(\frac{c_{1}}{2 c} + \frac{\sqrt{- a c + b^{2}} \left(b c_{1} - b_{1} c\right)}{2 c \left(a c - b^{2}\right)}\right) + a c_{1} + 2 b^{2} \left(\frac{c_{1}}{2 c} + \frac{\sqrt{- a c + b^{2}} \left(b c_{1} - b_{1} c\right)}{2 c \left(a c - b^{2}\right)}\right) - b b_{1}}{b c_{1} - b_{1} c} \right)}"," ",0,"(c1/(2*c) - sqrt(-a*c + b**2)*(b*c1 - b1*c)/(2*c*(a*c - b**2)))*log(x + (-2*a*c*(c1/(2*c) - sqrt(-a*c + b**2)*(b*c1 - b1*c)/(2*c*(a*c - b**2))) + a*c1 + 2*b**2*(c1/(2*c) - sqrt(-a*c + b**2)*(b*c1 - b1*c)/(2*c*(a*c - b**2))) - b*b1)/(b*c1 - b1*c)) + (c1/(2*c) + sqrt(-a*c + b**2)*(b*c1 - b1*c)/(2*c*(a*c - b**2)))*log(x + (-2*a*c*(c1/(2*c) + sqrt(-a*c + b**2)*(b*c1 - b1*c)/(2*c*(a*c - b**2))) + a*c1 + 2*b**2*(c1/(2*c) + sqrt(-a*c + b**2)*(b*c1 - b1*c)/(2*c*(a*c - b**2))) - b*b1)/(b*c1 - b1*c))","B",0
195,1,323,0,1.017212," ","integrate((c1*x+b1)/(c*x**2+2*b*x+a)**2,x)","\frac{\sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(b c_{1} - b_{1} c\right) \log{\left(x + \frac{- a^{2} c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(b c_{1} - b_{1} c\right) + 2 a b^{2} c \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(b c_{1} - b_{1} c\right) - b^{4} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(b c_{1} - b_{1} c\right) + b^{2} c_{1} - b b_{1} c}{b c c_{1} - b_{1} c^{2}} \right)}}{4} - \frac{\sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(b c_{1} - b_{1} c\right) \log{\left(x + \frac{a^{2} c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(b c_{1} - b_{1} c\right) - 2 a b^{2} c \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(b c_{1} - b_{1} c\right) + b^{4} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{3}}} \left(b c_{1} - b_{1} c\right) + b^{2} c_{1} - b b_{1} c}{b c c_{1} - b_{1} c^{2}} \right)}}{4} + \frac{- a c_{1} + b b_{1} + x \left(- b c_{1} + b_{1} c\right)}{2 a^{2} c - 2 a b^{2} + x^{2} \left(2 a c^{2} - 2 b^{2} c\right) + x \left(4 a b c - 4 b^{3}\right)}"," ",0,"sqrt(-1/(a*c - b**2)**3)*(b*c1 - b1*c)*log(x + (-a**2*c**2*sqrt(-1/(a*c - b**2)**3)*(b*c1 - b1*c) + 2*a*b**2*c*sqrt(-1/(a*c - b**2)**3)*(b*c1 - b1*c) - b**4*sqrt(-1/(a*c - b**2)**3)*(b*c1 - b1*c) + b**2*c1 - b*b1*c)/(b*c*c1 - b1*c**2))/4 - sqrt(-1/(a*c - b**2)**3)*(b*c1 - b1*c)*log(x + (a**2*c**2*sqrt(-1/(a*c - b**2)**3)*(b*c1 - b1*c) - 2*a*b**2*c*sqrt(-1/(a*c - b**2)**3)*(b*c1 - b1*c) + b**4*sqrt(-1/(a*c - b**2)**3)*(b*c1 - b1*c) + b**2*c1 - b*b1*c)/(b*c*c1 - b1*c**2))/4 + (-a*c1 + b*b1 + x*(-b*c1 + b1*c))/(2*a**2*c - 2*a*b**2 + x**2*(2*a*c**2 - 2*b**2*c) + x*(4*a*b*c - 4*b**3))","B",0
196,1,622,0,1.894493," ","integrate((c1*x+b1)/(c*x**2+2*b*x+a)**3,x)","\frac{3 c \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) \log{\left(x + \frac{- 3 a^{3} c^{4} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) + 9 a^{2} b^{2} c^{3} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) - 9 a b^{4} c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) + 3 b^{6} c \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) + 3 b^{2} c c_{1} - 3 b b_{1} c^{2}}{3 b c^{2} c_{1} - 3 b_{1} c^{3}} \right)}}{16} - \frac{3 c \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) \log{\left(x + \frac{3 a^{3} c^{4} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) - 9 a^{2} b^{2} c^{3} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) + 9 a b^{4} c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) - 3 b^{6} c \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{5}}} \left(b c_{1} - b_{1} c\right) + 3 b^{2} c c_{1} - 3 b b_{1} c^{2}}{3 b c^{2} c_{1} - 3 b_{1} c^{3}} \right)}}{16} + \frac{- 2 a^{2} c c_{1} - a b^{2} c_{1} + 5 a b b_{1} c - 2 b^{3} b_{1} + x^{3} \left(- 3 b c^{2} c_{1} + 3 b_{1} c^{3}\right) + x^{2} \left(- 9 b^{2} c c_{1} + 9 b b_{1} c^{2}\right) + x \left(- 5 a b c c_{1} + 5 a b_{1} c^{2} - 4 b^{3} c_{1} + 4 b^{2} b_{1} c\right)}{8 a^{4} c^{2} - 16 a^{3} b^{2} c + 8 a^{2} b^{4} + x^{4} \left(8 a^{2} c^{4} - 16 a b^{2} c^{3} + 8 b^{4} c^{2}\right) + x^{3} \left(32 a^{2} b c^{3} - 64 a b^{3} c^{2} + 32 b^{5} c\right) + x^{2} \left(16 a^{3} c^{3} - 48 a b^{4} c + 32 b^{6}\right) + x \left(32 a^{3} b c^{2} - 64 a^{2} b^{3} c + 32 a b^{5}\right)}"," ",0,"3*c*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c)*log(x + (-3*a**3*c**4*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c) + 9*a**2*b**2*c**3*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c) - 9*a*b**4*c**2*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c) + 3*b**6*c*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c) + 3*b**2*c*c1 - 3*b*b1*c**2)/(3*b*c**2*c1 - 3*b1*c**3))/16 - 3*c*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c)*log(x + (3*a**3*c**4*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c) - 9*a**2*b**2*c**3*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c) + 9*a*b**4*c**2*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c) - 3*b**6*c*sqrt(-1/(a*c - b**2)**5)*(b*c1 - b1*c) + 3*b**2*c*c1 - 3*b*b1*c**2)/(3*b*c**2*c1 - 3*b1*c**3))/16 + (-2*a**2*c*c1 - a*b**2*c1 + 5*a*b*b1*c - 2*b**3*b1 + x**3*(-3*b*c**2*c1 + 3*b1*c**3) + x**2*(-9*b**2*c*c1 + 9*b*b1*c**2) + x*(-5*a*b*c*c1 + 5*a*b1*c**2 - 4*b**3*c1 + 4*b**2*b1*c))/(8*a**4*c**2 - 16*a**3*b**2*c + 8*a**2*b**4 + x**4*(8*a**2*c**4 - 16*a*b**2*c**3 + 8*b**4*c**2) + x**3*(32*a**2*b*c**3 - 64*a*b**3*c**2 + 32*b**5*c) + x**2*(16*a**3*c**3 - 48*a*b**4*c + 32*b**6) + x*(32*a**3*b*c**2 - 64*a**2*b**3*c + 32*a*b**5))","B",0
197,1,1027,0,3.058684," ","integrate((c1*x+b1)/(c*x**2+2*b*x+a)**4,x)","\frac{5 c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) \log{\left(x + \frac{- 5 a^{4} c^{6} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) + 20 a^{3} b^{2} c^{5} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) - 30 a^{2} b^{4} c^{4} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) + 20 a b^{6} c^{3} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) - 5 b^{8} c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) + 5 b^{2} c^{2} c_{1} - 5 b b_{1} c^{3}}{5 b c^{3} c_{1} - 5 b_{1} c^{4}} \right)}}{32} - \frac{5 c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) \log{\left(x + \frac{5 a^{4} c^{6} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) - 20 a^{3} b^{2} c^{5} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) + 30 a^{2} b^{4} c^{4} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) - 20 a b^{6} c^{3} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) + 5 b^{8} c^{2} \sqrt{- \frac{1}{\left(a c - b^{2}\right)^{7}}} \left(b c_{1} - b_{1} c\right) + 5 b^{2} c^{2} c_{1} - 5 b b_{1} c^{3}}{5 b c^{3} c_{1} - 5 b_{1} c^{4}} \right)}}{32} + \frac{- 8 a^{3} c^{2} c_{1} - 9 a^{2} b^{2} c c_{1} + 33 a^{2} b b_{1} c^{2} + 2 a b^{4} c_{1} - 26 a b^{3} b_{1} c + 8 b^{5} b_{1} + x^{5} \left(- 15 b c^{4} c_{1} + 15 b_{1} c^{5}\right) + x^{4} \left(- 75 b^{2} c^{3} c_{1} + 75 b b_{1} c^{4}\right) + x^{3} \left(- 40 a b c^{3} c_{1} + 40 a b_{1} c^{4} - 110 b^{3} c^{2} c_{1} + 110 b^{2} b_{1} c^{3}\right) + x^{2} \left(- 120 a b^{2} c^{2} c_{1} + 120 a b b_{1} c^{3} - 30 b^{4} c c_{1} + 30 b^{3} b_{1} c^{2}\right) + x \left(- 33 a^{2} b c^{2} c_{1} + 33 a^{2} b_{1} c^{3} - 54 a b^{3} c c_{1} + 54 a b^{2} b_{1} c^{2} + 12 b^{5} c_{1} - 12 b^{4} b_{1} c\right)}{48 a^{6} c^{3} - 144 a^{5} b^{2} c^{2} + 144 a^{4} b^{4} c - 48 a^{3} b^{6} + x^{6} \left(48 a^{3} c^{6} - 144 a^{2} b^{2} c^{5} + 144 a b^{4} c^{4} - 48 b^{6} c^{3}\right) + x^{5} \left(288 a^{3} b c^{5} - 864 a^{2} b^{3} c^{4} + 864 a b^{5} c^{3} - 288 b^{7} c^{2}\right) + x^{4} \left(144 a^{4} c^{5} + 144 a^{3} b^{2} c^{4} - 1296 a^{2} b^{4} c^{3} + 1584 a b^{6} c^{2} - 576 b^{8} c\right) + x^{3} \left(576 a^{4} b c^{4} - 1344 a^{3} b^{3} c^{3} + 576 a^{2} b^{5} c^{2} + 576 a b^{7} c - 384 b^{9}\right) + x^{2} \left(144 a^{5} c^{4} + 144 a^{4} b^{2} c^{3} - 1296 a^{3} b^{4} c^{2} + 1584 a^{2} b^{6} c - 576 a b^{8}\right) + x \left(288 a^{5} b c^{3} - 864 a^{4} b^{3} c^{2} + 864 a^{3} b^{5} c - 288 a^{2} b^{7}\right)}"," ",0,"5*c**2*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c)*log(x + (-5*a**4*c**6*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) + 20*a**3*b**2*c**5*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) - 30*a**2*b**4*c**4*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) + 20*a*b**6*c**3*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) - 5*b**8*c**2*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) + 5*b**2*c**2*c1 - 5*b*b1*c**3)/(5*b*c**3*c1 - 5*b1*c**4))/32 - 5*c**2*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c)*log(x + (5*a**4*c**6*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) - 20*a**3*b**2*c**5*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) + 30*a**2*b**4*c**4*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) - 20*a*b**6*c**3*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) + 5*b**8*c**2*sqrt(-1/(a*c - b**2)**7)*(b*c1 - b1*c) + 5*b**2*c**2*c1 - 5*b*b1*c**3)/(5*b*c**3*c1 - 5*b1*c**4))/32 + (-8*a**3*c**2*c1 - 9*a**2*b**2*c*c1 + 33*a**2*b*b1*c**2 + 2*a*b**4*c1 - 26*a*b**3*b1*c + 8*b**5*b1 + x**5*(-15*b*c**4*c1 + 15*b1*c**5) + x**4*(-75*b**2*c**3*c1 + 75*b*b1*c**4) + x**3*(-40*a*b*c**3*c1 + 40*a*b1*c**4 - 110*b**3*c**2*c1 + 110*b**2*b1*c**3) + x**2*(-120*a*b**2*c**2*c1 + 120*a*b*b1*c**3 - 30*b**4*c*c1 + 30*b**3*b1*c**2) + x*(-33*a**2*b*c**2*c1 + 33*a**2*b1*c**3 - 54*a*b**3*c*c1 + 54*a*b**2*b1*c**2 + 12*b**5*c1 - 12*b**4*b1*c))/(48*a**6*c**3 - 144*a**5*b**2*c**2 + 144*a**4*b**4*c - 48*a**3*b**6 + x**6*(48*a**3*c**6 - 144*a**2*b**2*c**5 + 144*a*b**4*c**4 - 48*b**6*c**3) + x**5*(288*a**3*b*c**5 - 864*a**2*b**3*c**4 + 864*a*b**5*c**3 - 288*b**7*c**2) + x**4*(144*a**4*c**5 + 144*a**3*b**2*c**4 - 1296*a**2*b**4*c**3 + 1584*a*b**6*c**2 - 576*b**8*c) + x**3*(576*a**4*b*c**4 - 1344*a**3*b**3*c**3 + 576*a**2*b**5*c**2 + 576*a*b**7*c - 384*b**9) + x**2*(144*a**5*c**4 + 144*a**4*b**2*c**3 - 1296*a**3*b**4*c**2 + 1584*a**2*b**6*c - 576*a*b**8) + x*(288*a**5*b*c**3 - 864*a**4*b**3*c**2 + 864*a**3*b**5*c - 288*a**2*b**7))","B",0
198,-1,0,0,0.000000," ","integrate((c1*x+b1)/((c*x**2+2*b*x+a)**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,1,46,0,0.117073," ","integrate(x/(2*x**2+6*x+3),x)","\left(\frac{1}{4} - \frac{\sqrt{3}}{4}\right) \log{\left(x - \frac{\sqrt{3}}{2} + \frac{3}{2} \right)} + \left(\frac{1}{4} + \frac{\sqrt{3}}{4}\right) \log{\left(x + \frac{\sqrt{3}}{2} + \frac{3}{2} \right)}"," ",0,"(1/4 - sqrt(3)/4)*log(x - sqrt(3)/2 + 3/2) + (1/4 + sqrt(3)/4)*log(x + sqrt(3)/2 + 3/2)","A",0
200,1,76,0,0.165358," ","integrate((-3+2*x)/(2*x**2+6*x+3)**3,x)","\frac{- 8 x^{3} - 36 x^{2} - 44 x - 13}{16 x^{4} + 96 x^{3} + 192 x^{2} + 144 x + 36} - \frac{\sqrt{3} \log{\left(x - \frac{\sqrt{3}}{2} + \frac{3}{2} \right)}}{6} + \frac{\sqrt{3} \log{\left(x + \frac{\sqrt{3}}{2} + \frac{3}{2} \right)}}{6}"," ",0,"(-8*x**3 - 36*x**2 - 44*x - 13)/(16*x**4 + 96*x**3 + 192*x**2 + 144*x + 36) - sqrt(3)*log(x - sqrt(3)/2 + 3/2)/6 + sqrt(3)*log(x + sqrt(3)/2 + 3/2)/6","A",0
201,1,31,0,0.129632," ","integrate((-1+x)/(x**2+5*x+4)**2,x)","\frac{7 x + 13}{9 x^{2} + 45 x + 36} + \frac{7 \log{\left(x + 1 \right)}}{27} - \frac{7 \log{\left(x + 4 \right)}}{27}"," ",0,"(7*x + 13)/(9*x**2 + 45*x + 36) + 7*log(x + 1)/27 - 7*log(x + 4)/27","A",0
202,1,88,0,0.223372," ","integrate(1/(x**2+3*x+2)**5,x)","\frac{840 x^{7} + 8820 x^{6} + 38920 x^{5} + 93450 x^{4} + 131768 x^{3} + 109116 x^{2} + 49176 x + 9315}{12 x^{8} + 144 x^{7} + 744 x^{6} + 2160 x^{5} + 3852 x^{4} + 4320 x^{3} + 2976 x^{2} + 1152 x + 192} + 70 \log{\left(x + 1 \right)} - 70 \log{\left(x + 2 \right)}"," ",0,"(840*x**7 + 8820*x**6 + 38920*x**5 + 93450*x**4 + 131768*x**3 + 109116*x**2 + 49176*x + 9315)/(12*x**8 + 144*x**7 + 744*x**6 + 2160*x**5 + 3852*x**4 + 4320*x**3 + 2976*x**2 + 1152*x + 192) + 70*log(x + 1) - 70*log(x + 2)","A",0
203,1,80,0,0.232689," ","integrate(1/x**3/(2*x**2-6*x+7)**2,x)","\frac{80 \log{\left(x \right)}}{2401} - \frac{40 \log{\left(x^{2} - 3 x + \frac{7}{2} \right)}}{2401} + \frac{234 \sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5} x}{5} - \frac{3 \sqrt{5}}{5} \right)}}{60025} + \frac{- 276 x^{3} + 814 x^{2} - 630 x - 245}{6860 x^{4} - 20580 x^{3} + 24010 x^{2}}"," ",0,"80*log(x)/2401 - 40*log(x**2 - 3*x + 7/2)/2401 + 234*sqrt(5)*atan(2*sqrt(5)*x/5 - 3*sqrt(5)/5)/60025 + (-276*x**3 + 814*x**2 - 630*x - 245)/(6860*x**4 - 20580*x**3 + 24010*x**2)","A",0
204,1,90,0,0.210145," ","integrate(x**9/(x**2+3*x+2)**5,x)","\frac{- 17496 x^{7} - 184200 x^{6} - 813888 x^{5} - 1955853 x^{4} - 2759400 x^{3} - 2286008 x^{2} - 1030560 x - 195280}{12 x^{8} + 144 x^{7} + 744 x^{6} + 2160 x^{5} + 3852 x^{4} + 4320 x^{3} + 2976 x^{2} + 1152 x + 192} - 1471 \log{\left(x + 1 \right)} + 1472 \log{\left(x + 2 \right)}"," ",0,"(-17496*x**7 - 184200*x**6 - 813888*x**5 - 1955853*x**4 - 2759400*x**3 - 2286008*x**2 - 1030560*x - 195280)/(12*x**8 + 144*x**7 + 744*x**6 + 2160*x**5 + 3852*x**4 + 4320*x**3 + 2976*x**2 + 1152*x + 192) - 1471*log(x + 1) + 1472*log(x + 2)","A",0
205,1,90,0,0.228156," ","integrate((1+2*x)**2/(2*x**2+5*x+3)**5,x)","\frac{238080 x^{7} + 2083200 x^{6} + 7757440 x^{5} + 15934000 x^{4} + 19495776 x^{3} + 14209160 x^{2} + 5712464 x + 977397}{192 x^{8} + 1920 x^{7} + 8352 x^{6} + 20640 x^{5} + 31692 x^{4} + 30960 x^{3} + 18792 x^{2} + 6480 x + 972} + 2480 \log{\left(x + 1 \right)} - 2480 \log{\left(x + \frac{3}{2} \right)}"," ",0,"(238080*x**7 + 2083200*x**6 + 7757440*x**5 + 15934000*x**4 + 19495776*x**3 + 14209160*x**2 + 5712464*x + 977397)/(192*x**8 + 1920*x**7 + 8352*x**6 + 20640*x**5 + 31692*x**4 + 30960*x**3 + 18792*x**2 + 6480*x + 972) + 2480*log(x + 1) - 2480*log(x + 3/2)","A",0
206,1,37,0,0.254067," ","integrate((-b*x**2+a)**3/x**7,x)","- b^{3} \log{\left(x \right)} - \frac{2 a^{3} - 9 a^{2} b x^{2} + 18 a b^{2} x^{4}}{12 x^{6}}"," ",0,"-b**3*log(x) - (2*a**3 - 9*a**2*b*x**2 + 18*a*b**2*x**4)/(12*x**6)","A",0
207,1,102,0,0.685166," ","integrate(x**13/(a**4+x**4)**5,x)","\frac{- 15 a^{12} x^{2} - 55 a^{8} x^{6} - 73 a^{4} x^{10} + 15 x^{14}}{768 a^{20} + 3072 a^{16} x^{4} + 4608 a^{12} x^{8} + 3072 a^{8} x^{12} + 768 a^{4} x^{16}} + \frac{- \frac{5 i \log{\left(- i a^{2} + x^{2} \right)}}{512} + \frac{5 i \log{\left(i a^{2} + x^{2} \right)}}{512}}{a^{6}}"," ",0,"(-15*a**12*x**2 - 55*a**8*x**6 - 73*a**4*x**10 + 15*x**14)/(768*a**20 + 3072*a**16*x**4 + 4608*a**12*x**8 + 3072*a**8*x**12 + 768*a**4*x**16) + (-5*I*log(-I*a**2 + x**2)/512 + 5*I*log(I*a**2 + x**2)/512)/a**6","C",0
208,1,42,0,2.595208," ","integrate(x**(3/2)*(x**2+1)*(-x+2*x**(1/2))**2,x)","\frac{2 x^{\frac{13}{2}}}{13} + \frac{8 x^{\frac{11}{2}}}{11} + \frac{2 x^{\frac{9}{2}}}{9} + \frac{8 x^{\frac{7}{2}}}{7} - \frac{2 x^{6}}{3} - x^{4}"," ",0,"2*x**(13/2)/13 + 8*x**(11/2)/11 + 2*x**(9/2)/9 + 8*x**(7/2)/7 - 2*x**6/3 - x**4","A",0
209,1,48,0,2.745385," ","integrate((-3*x**(3/5)+x**(3/2))**2*(-1/3*x**(2/3)+4*x**(3/2)),x)","\frac{60 x^{\frac{113}{30}}}{113} - \frac{45 x^{\frac{43}{15}}}{43} + \frac{360 x^{\frac{37}{10}}}{37} - \frac{120 x^{\frac{23}{5}}}{23} - \frac{x^{\frac{14}{3}}}{14} + \frac{8 x^{\frac{11}{2}}}{11}"," ",0,"60*x**(113/30)/113 - 45*x**(43/15)/43 + 360*x**(37/10)/37 - 120*x**(23/5)/23 - x**(14/3)/14 + 8*x**(11/2)/11","A",0
210,1,19,0,0.137968," ","integrate(1/(1+(1+x)**(1/2)),x)","2 \sqrt{x + 1} - 2 \log{\left(\sqrt{x + 1} + 1 \right)}"," ",0,"2*sqrt(x + 1) - 2*log(sqrt(x + 1) + 1)","A",0
211,1,22,0,0.971455," ","integrate(x/(1+(1+x)**(1/2)),x)","\frac{2 x \sqrt{x + 1}}{3} - x + \frac{2 \sqrt{x + 1}}{3}"," ",0,"2*x*sqrt(x + 1)/3 - x + 2*sqrt(x + 1)/3","B",0
212,1,20,0,0.161494," ","integrate((1+(1+x)**(1/2))/(-1+(1+x)**(1/2)),x)","x + 4 \sqrt{x + 1} + 4 \log{\left(\sqrt{x + 1} - 1 \right)}"," ",0,"x + 4*sqrt(x + 1) + 4*log(sqrt(x + 1) - 1)","A",0
213,0,0,0,0.000000," ","integrate(1/((1+x)**(2/3)-(1+x)**(1/2)),x)","\int \frac{1}{\left(x + 1\right)^{\frac{2}{3}} - \sqrt{x + 1}}\, dx"," ",0,"Integral(1/((x + 1)**(2/3) - sqrt(x + 1)), x)","F",0
214,1,134,0,1.349720," ","integrate((1+x**(1/4))**(1/3)/x**(1/2),x)","\frac{12 x^{\frac{7}{4}} \sqrt[3]{\sqrt[4]{x} + 1}}{7 x^{\frac{5}{4}} + 7 x} - \frac{6 x^{\frac{5}{4}} \sqrt[3]{\sqrt[4]{x} + 1}}{7 x^{\frac{5}{4}} + 7 x} + \frac{9 x^{\frac{5}{4}}}{7 x^{\frac{5}{4}} + 7 x} + \frac{15 x^{\frac{3}{2}} \sqrt[3]{\sqrt[4]{x} + 1}}{7 x^{\frac{5}{4}} + 7 x} - \frac{9 x \sqrt[3]{\sqrt[4]{x} + 1}}{7 x^{\frac{5}{4}} + 7 x} + \frac{9 x}{7 x^{\frac{5}{4}} + 7 x}"," ",0,"12*x**(7/4)*(x**(1/4) + 1)**(1/3)/(7*x**(5/4) + 7*x) - 6*x**(5/4)*(x**(1/4) + 1)**(1/3)/(7*x**(5/4) + 7*x) + 9*x**(5/4)/(7*x**(5/4) + 7*x) + 15*x**(3/2)*(x**(1/4) + 1)**(1/3)/(7*x**(5/4) + 7*x) - 9*x*(x**(1/4) + 1)**(1/3)/(7*x**(5/4) + 7*x) + 9*x/(7*x**(5/4) + 7*x)","B",0
215,1,3966,0,3.268250," ","integrate(1/x**3/(1+x)**(3/2),x)","\begin{cases} - \frac{30 \left(x + 1\right)^{\frac{17}{2}} \operatorname{acoth}{\left(\sqrt{x + 1} \right)}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{15 i \pi \left(x + 1\right)^{\frac{17}{2}}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{240 \left(x + 1\right)^{\frac{15}{2}} \operatorname{acoth}{\left(\sqrt{x + 1} \right)}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{120 i \pi \left(x + 1\right)^{\frac{15}{2}}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{840 \left(x + 1\right)^{\frac{13}{2}} \operatorname{acoth}{\left(\sqrt{x + 1} \right)}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{420 i \pi \left(x + 1\right)^{\frac{13}{2}}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{1680 \left(x + 1\right)^{\frac{11}{2}} \operatorname{acoth}{\left(\sqrt{x + 1} \right)}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{840 i \pi \left(x + 1\right)^{\frac{11}{2}}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{2100 \left(x + 1\right)^{\frac{9}{2}} \operatorname{acoth}{\left(\sqrt{x + 1} \right)}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{1050 i \pi \left(x + 1\right)^{\frac{9}{2}}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{1680 \left(x + 1\right)^{\frac{7}{2}} \operatorname{acoth}{\left(\sqrt{x + 1} \right)}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{840 i \pi \left(x + 1\right)^{\frac{7}{2}}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{840 \left(x + 1\right)^{\frac{5}{2}} \operatorname{acoth}{\left(\sqrt{x + 1} \right)}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{420 i \pi \left(x + 1\right)^{\frac{5}{2}}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{240 \left(x + 1\right)^{\frac{3}{2}} \operatorname{acoth}{\left(\sqrt{x + 1} \right)}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{120 i \pi \left(x + 1\right)^{\frac{3}{2}}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{30 \sqrt{x + 1} \operatorname{acoth}{\left(\sqrt{x + 1} \right)}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{15 i \pi \sqrt{x + 1}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{30 \left(x + 1\right)^{8}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{230 \left(x + 1\right)^{7}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{766 \left(x + 1\right)^{6}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{1446 \left(x + 1\right)^{5}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{1690 \left(x + 1\right)^{4}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{1250 \left(x + 1\right)^{3}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{570 \left(x + 1\right)^{2}}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} - \frac{146 \left(x + 1\right)}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} + \frac{16}{8 \left(x + 1\right)^{\frac{17}{2}} - 64 \left(x + 1\right)^{\frac{15}{2}} + 224 \left(x + 1\right)^{\frac{13}{2}} - 448 \left(x + 1\right)^{\frac{11}{2}} + 560 \left(x + 1\right)^{\frac{9}{2}} - 448 \left(x + 1\right)^{\frac{7}{2}} + 224 \left(x + 1\right)^{\frac{5}{2}} - 64 \left(x + 1\right)^{\frac{3}{2}} + 8 \sqrt{x + 1}} & \text{for}\: \left|{x + 1}\right| > 1 \\- \frac{15 \left(x + 1\right)^{\frac{17}{2}} \operatorname{atanh}{\left(\sqrt{x + 1} \right)}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} + \frac{120 \left(x + 1\right)^{\frac{15}{2}} \operatorname{atanh}{\left(\sqrt{x + 1} \right)}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} - \frac{420 \left(x + 1\right)^{\frac{13}{2}} \operatorname{atanh}{\left(\sqrt{x + 1} \right)}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} + \frac{840 \left(x + 1\right)^{\frac{11}{2}} \operatorname{atanh}{\left(\sqrt{x + 1} \right)}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} - \frac{1050 \left(x + 1\right)^{\frac{9}{2}} \operatorname{atanh}{\left(\sqrt{x + 1} \right)}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} + \frac{840 \left(x + 1\right)^{\frac{7}{2}} \operatorname{atanh}{\left(\sqrt{x + 1} \right)}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} - \frac{420 \left(x + 1\right)^{\frac{5}{2}} \operatorname{atanh}{\left(\sqrt{x + 1} \right)}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} + \frac{120 \left(x + 1\right)^{\frac{3}{2}} \operatorname{atanh}{\left(\sqrt{x + 1} \right)}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} - \frac{15 \sqrt{x + 1} \operatorname{atanh}{\left(\sqrt{x + 1} \right)}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} + \frac{15 \left(x + 1\right)^{8}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} - \frac{115 \left(x + 1\right)^{7}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} + \frac{383 \left(x + 1\right)^{6}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} - \frac{723 \left(x + 1\right)^{5}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} + \frac{845 \left(x + 1\right)^{4}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} - \frac{625 \left(x + 1\right)^{3}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} + \frac{285 \left(x + 1\right)^{2}}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} - \frac{73 \left(x + 1\right)}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} + \frac{8}{4 \left(x + 1\right)^{\frac{17}{2}} - 32 \left(x + 1\right)^{\frac{15}{2}} + 112 \left(x + 1\right)^{\frac{13}{2}} - 224 \left(x + 1\right)^{\frac{11}{2}} + 280 \left(x + 1\right)^{\frac{9}{2}} - 224 \left(x + 1\right)^{\frac{7}{2}} + 112 \left(x + 1\right)^{\frac{5}{2}} - 32 \left(x + 1\right)^{\frac{3}{2}} + 4 \sqrt{x + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*(x + 1)**(17/2)*acoth(sqrt(x + 1))/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 15*I*pi*(x + 1)**(17/2)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 240*(x + 1)**(15/2)*acoth(sqrt(x + 1))/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 120*I*pi*(x + 1)**(15/2)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 840*(x + 1)**(13/2)*acoth(sqrt(x + 1))/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 420*I*pi*(x + 1)**(13/2)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 1680*(x + 1)**(11/2)*acoth(sqrt(x + 1))/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 840*I*pi*(x + 1)**(11/2)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 2100*(x + 1)**(9/2)*acoth(sqrt(x + 1))/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 1050*I*pi*(x + 1)**(9/2)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 1680*(x + 1)**(7/2)*acoth(sqrt(x + 1))/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 840*I*pi*(x + 1)**(7/2)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 840*(x + 1)**(5/2)*acoth(sqrt(x + 1))/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 420*I*pi*(x + 1)**(5/2)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 240*(x + 1)**(3/2)*acoth(sqrt(x + 1))/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 120*I*pi*(x + 1)**(3/2)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 30*sqrt(x + 1)*acoth(sqrt(x + 1))/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 15*I*pi*sqrt(x + 1)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 30*(x + 1)**8/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 230*(x + 1)**7/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 766*(x + 1)**6/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 1446*(x + 1)**5/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 1690*(x + 1)**4/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 1250*(x + 1)**3/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 570*(x + 1)**2/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) - 146*(x + 1)/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)) + 16/(8*(x + 1)**(17/2) - 64*(x + 1)**(15/2) + 224*(x + 1)**(13/2) - 448*(x + 1)**(11/2) + 560*(x + 1)**(9/2) - 448*(x + 1)**(7/2) + 224*(x + 1)**(5/2) - 64*(x + 1)**(3/2) + 8*sqrt(x + 1)), Abs(x + 1) > 1), (-15*(x + 1)**(17/2)*atanh(sqrt(x + 1))/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) + 120*(x + 1)**(15/2)*atanh(sqrt(x + 1))/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) - 420*(x + 1)**(13/2)*atanh(sqrt(x + 1))/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) + 840*(x + 1)**(11/2)*atanh(sqrt(x + 1))/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) - 1050*(x + 1)**(9/2)*atanh(sqrt(x + 1))/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) + 840*(x + 1)**(7/2)*atanh(sqrt(x + 1))/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) - 420*(x + 1)**(5/2)*atanh(sqrt(x + 1))/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) + 120*(x + 1)**(3/2)*atanh(sqrt(x + 1))/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) - 15*sqrt(x + 1)*atanh(sqrt(x + 1))/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) + 15*(x + 1)**8/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) - 115*(x + 1)**7/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) + 383*(x + 1)**6/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) - 723*(x + 1)**5/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) + 845*(x + 1)**4/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) - 625*(x + 1)**3/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) + 285*(x + 1)**2/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) - 73*(x + 1)/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)) + 8/(4*(x + 1)**(17/2) - 32*(x + 1)**(15/2) + 112*(x + 1)**(13/2) - 224*(x + 1)**(11/2) + 280*(x + 1)**(9/2) - 224*(x + 1)**(7/2) + 112*(x + 1)**(5/2) - 32*(x + 1)**(3/2) + 4*sqrt(x + 1)), True))","B",0
216,1,971,0,20.367250," ","integrate(1/(1-x)**(7/2)/x**5,x)","\begin{cases} - \frac{45045 i x^{7} \operatorname{asin}{\left(\frac{1}{\sqrt{x}} \right)}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac{45045 i x^{6} \sqrt{x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac{135135 i x^{6} \operatorname{asin}{\left(\frac{1}{\sqrt{x}} \right)}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac{105105 i x^{5} \sqrt{x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac{135135 i x^{5} \operatorname{asin}{\left(\frac{1}{\sqrt{x}} \right)}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac{69069 i x^{4} \sqrt{x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac{45045 i x^{4} \operatorname{asin}{\left(\frac{1}{\sqrt{x}} \right)}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac{6435 i x^{3} \sqrt{x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac{1430 i x^{2} \sqrt{x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac{520 i x \sqrt{x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac{240 i \sqrt{x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} & \text{for}\: \left|{x}\right| > 1 \\- \frac{45045 x^{7} \log{\left(x \right)}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac{90090 x^{7} \log{\left(\sqrt{1 - x} + 1 \right)}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{45045 i \pi x^{7}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac{90090 x^{6} \sqrt{1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac{135135 x^{6} \log{\left(x \right)}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{270270 x^{6} \log{\left(\sqrt{1 - x} + 1 \right)}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac{135135 i \pi x^{6}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{210210 x^{5} \sqrt{1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{135135 x^{5} \log{\left(x \right)}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac{270270 x^{5} \log{\left(\sqrt{1 - x} + 1 \right)}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{135135 i \pi x^{5}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac{138138 x^{4} \sqrt{1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac{45045 x^{4} \log{\left(x \right)}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{90090 x^{4} \log{\left(\sqrt{1 - x} + 1 \right)}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac{45045 i \pi x^{4}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{12870 x^{3} \sqrt{1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{2860 x^{2} \sqrt{1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{1040 x \sqrt{1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac{480 \sqrt{1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-45045*I*x**7*asin(1/sqrt(x))/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) + 45045*I*x**6*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) + 135135*I*x**6*asin(1/sqrt(x))/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 105105*I*x**5*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 135135*I*x**5*asin(1/sqrt(x))/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) + 69069*I*x**4*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) + 45045*I*x**4*asin(1/sqrt(x))/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 6435*I*x**3*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 1430*I*x**2*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 520*I*x*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 240*I*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4), Abs(x) > 1), (-45045*x**7*log(x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 90090*x**7*log(sqrt(1 - x) + 1)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 45045*I*pi*x**7/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 90090*x**6*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 135135*x**6*log(x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 270270*x**6*log(sqrt(1 - x) + 1)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 135135*I*pi*x**6/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 210210*x**5*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 135135*x**5*log(x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 270270*x**5*log(sqrt(1 - x) + 1)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 135135*I*pi*x**5/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 138138*x**4*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 45045*x**4*log(x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 90090*x**4*log(sqrt(1 - x) + 1)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 45045*I*pi*x**4/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 12870*x**3*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 2860*x**2*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 1040*x*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 480*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4), True))","C",0
217,-1,0,0,0.000000," ","integrate(1/(-1+x)**(2/3)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,0,0,0,0.000000," ","integrate(((1-x)/(1+x))**(1/2),x)","\int \sqrt{\frac{1 - x}{x + 1}}\, dx"," ",0,"Integral(sqrt((1 - x)/(x + 1)), x)","F",0
219,0,0,0,0.000000," ","integrate(x*((-a+x)/(b-x))**(1/2),x)","\int x \sqrt{\frac{- a + x}{b - x}}\, dx"," ",0,"Integral(x*sqrt((-a + x)/(b - x)), x)","F",0
220,0,0,0,0.000000," ","integrate((-5+x)**(1/2)*(3+x)**(1/2)/(-1+x)/(x**2-25),x)","\int \frac{\sqrt{x + 3}}{\sqrt{x - 5} \left(x - 1\right) \left(x + 5\right)}\, dx"," ",0,"Integral(sqrt(x + 3)/(sqrt(x - 5)*(x - 1)*(x + 5)), x)","F",0
221,-1,0,0,0.000000," ","integrate(x**2*(-x**2+1)**(1/4)*(1+x)**(1/2)/(1-x)**(1/2)/((1-x)**(1/2)-(1+x)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,0,0,0,0.000000," ","integrate(x*(1+x)**(2/3)*(1-x)**(1/2)/(-(1-x)**(5/6)*(1+x)**(1/3)+(1-x)**(2/3)*(1+x)**(1/2)),x)","\int \frac{x \sqrt{1 - x} \left(x + 1\right)^{\frac{2}{3}}}{- \left(1 - x\right)^{\frac{5}{6}} \sqrt[3]{x + 1} + \left(1 - x\right)^{\frac{2}{3}} \sqrt{x + 1}}\, dx"," ",0,"Integral(x*sqrt(1 - x)*(x + 1)**(2/3)/(-(1 - x)**(5/6)*(x + 1)**(1/3) + (1 - x)**(2/3)*sqrt(x + 1)), x)","F",0
223,0,0,0,0.000000," ","integrate(1/((-1+x)**4*(1+x)**2)**(1/3),x)","\int \frac{1}{\sqrt[3]{\left(x - 1\right)^{4} \left(x + 1\right)^{2}}}\, dx"," ",0,"Integral(((x - 1)**4*(x + 1)**2)**(-1/3), x)","F",0
224,0,0,0,0.000000," ","integrate(1/((-1+x)**3*(2+x)**5)**(1/4),x)","\int \frac{1}{\sqrt[4]{\left(x - 1\right)^{3} \left(x + 2\right)^{5}}}\, dx"," ",0,"Integral(((x - 1)**3*(x + 2)**5)**(-1/4), x)","F",0
225,0,0,0,0.000000," ","integrate(1/((-1+x)**7*(1+x)**2)**(1/3),x)","\int \frac{1}{\sqrt[3]{\left(x - 1\right)^{7} \left(x + 1\right)^{2}}}\, dx"," ",0,"Integral(((x - 1)**7*(x + 1)**2)**(-1/3), x)","F",0
226,0,0,0,0.000000," ","integrate(1/((-1+x)**2*(1+x))**(1/3),x)","\int \frac{1}{\sqrt[3]{\left(x - 1\right)^{2} \left(x + 1\right)}}\, dx"," ",0,"Integral(((x - 1)**2*(x + 1))**(-1/3), x)","F",0
227,0,0,0,0.000000," ","integrate((1/x+x)/((-2+x)*(1+x)**3)**(1/2),x)","\int \frac{x^{2} + 1}{x \sqrt{\left(x - 2\right) \left(x + 1\right)^{3}}}\, dx"," ",0,"Integral((x**2 + 1)/(x*sqrt((x - 2)*(x + 1)**3)), x)","F",0
228,0,0,0,0.000000," ","integrate(((-1+x)**2*(1+x))**(1/3)/x**2,x)","\int \frac{\sqrt[3]{\left(x - 1\right)^{2} \left(x + 1\right)}}{x^{2}}\, dx"," ",0,"Integral(((x - 1)**2*(x + 1))**(1/3)/x**2, x)","F",0
229,0,0,0,0.000000," ","integrate(1/(x**2-2*x-3)**(5/2),x)","\int \frac{1}{\left(x^{2} - 2 x - 3\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((x**2 - 2*x - 3)**(-5/2), x)","F",0
230,0,0,0,0.000000," ","integrate(1/(x**3-5*x**2+3*x+9)**(1/2),x)","\int \frac{1}{\sqrt{x^{3} - 5 x^{2} + 3 x + 9}}\, dx"," ",0,"Integral(1/sqrt(x**3 - 5*x**2 + 3*x + 9), x)","F",0
231,0,0,0,0.000000," ","integrate(1/(x**3-5*x**2+3*x+9)**(3/2),x)","\int \frac{1}{\left(x^{3} - 5 x^{2} + 3 x + 9\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x**3 - 5*x**2 + 3*x + 9)**(-3/2), x)","F",0
232,0,0,0,0.000000," ","integrate(1/(x**3-5*x**2+3*x+9)**(1/3),x)","\int \frac{1}{\sqrt[3]{x^{3} - 5 x^{2} + 3 x + 9}}\, dx"," ",0,"Integral((x**3 - 5*x**2 + 3*x + 9)**(-1/3), x)","F",0
233,0,0,0,0.000000," ","integrate(1/(x**3-5*x**2+3*x+9)**(2/3),x)","\int \frac{1}{\left(x^{3} - 5 x^{2} + 3 x + 9\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((x**3 - 5*x**2 + 3*x + 9)**(-2/3), x)","F",0
234,0,0,0,0.000000," ","integrate(1/(x**3-5*x**2+3*x+9)**(4/3),x)","\int \frac{1}{\left(x^{3} - 5 x^{2} + 3 x + 9\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((x**3 - 5*x**2 + 3*x + 9)**(-4/3), x)","F",0
235,0,0,0,0.000000," ","integrate(1/(-2*x**2+3*x+4)**(1/2),x)","\int \frac{1}{\sqrt{- 2 x^{2} + 3 x + 4}}\, dx"," ",0,"Integral(1/sqrt(-2*x**2 + 3*x + 4), x)","F",0
236,0,0,0,0.000000," ","integrate(1/(-x**2+4*x-3)**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} + 4 x - 3}}\, dx"," ",0,"Integral(1/sqrt(-x**2 + 4*x - 3), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(-3*x**2-5*x-2)**(1/2),x)","\int \frac{1}{\sqrt{- 3 x^{2} - 5 x - 2}}\, dx"," ",0,"Integral(1/sqrt(-3*x**2 - 5*x - 2), x)","F",0
238,0,0,0,0.000000," ","integrate(1/(x**2+4)/(-x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 4\right)}\, dx"," ",0,"Integral(1/(sqrt(-(x - 1)*(x + 1))*(x**2 + 4)), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(x**2+4)/(4*x**2+1)**(1/2),x)","\int \frac{1}{\left(x^{2} + 4\right) \sqrt{4 x^{2} + 1}}\, dx"," ",0,"Integral(1/((x**2 + 4)*sqrt(4*x**2 + 1)), x)","F",0
240,1,61,0,5.718566," ","integrate(x/(-x**2+3)/(-x**2+5)**(1/2),x)","- \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2}}{\sqrt{5 - x^{2}}} \right)}}{2} & \text{for}\: \frac{1}{5 - x^{2}} > \frac{1}{2} \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2}}{\sqrt{5 - x^{2}}} \right)}}{2} & \text{for}\: \frac{1}{5 - x^{2}} < \frac{1}{2} \end{cases}"," ",0,"-Piecewise((-sqrt(2)*acoth(sqrt(2)/sqrt(5 - x**2))/2, 1/(5 - x**2) > 1/2), (-sqrt(2)*atanh(sqrt(2)/sqrt(5 - x**2))/2, 1/(5 - x**2) < 1/2))","A",0
241,1,24,0,5.537314," ","integrate(x/(-x**2+5)/(-x**2+3)**(1/2),x)","- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{3 - x^{2}}}{2} \right)}}{2}"," ",0,"-sqrt(2)*atan(sqrt(2)*sqrt(3 - x**2)/2)/2","A",0
242,0,0,0,0.000000," ","integrate(1/(x**4-1)/(x**2+2)**(1/2),x)","\int \frac{1}{\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right) \sqrt{x^{2} + 2}}\, dx"," ",0,"Integral(1/((x - 1)*(x + 1)*(x**2 + 1)*sqrt(x**2 + 2)), x)","F",0
243,0,0,0,0.000000," ","integrate(x/(x**2-1)/(x**2+2*x+4)**(1/2),x)","\int \frac{x}{\left(x - 1\right) \left(x + 1\right) \sqrt{x^{2} + 2 x + 4}}\, dx"," ",0,"Integral(x/((x - 1)*(x + 1)*sqrt(x**2 + 2*x + 4)), x)","F",0
244,0,0,0,0.000000," ","integrate(1/(x**3-8)/(x**2+2*x+5)**(1/2),x)","\int \frac{1}{\left(x - 2\right) \left(x^{2} + 2 x + 4\right) \sqrt{x^{2} + 2 x + 5}}\, dx"," ",0,"Integral(1/((x - 2)*(x**2 + 2*x + 4)*sqrt(x**2 + 2*x + 5)), x)","F",0
245,0,0,0,0.000000," ","integrate(x/(x**2+x+4)/(4*x**2+4*x+5)**(1/2),x)","\int \frac{x}{\left(x^{2} + x + 4\right) \sqrt{4 x^{2} + 4 x + 5}}\, dx"," ",0,"Integral(x/((x**2 + x + 4)*sqrt(4*x**2 + 4*x + 5)), x)","F",0
246,0,0,0,0.000000," ","integrate((3+x)/(x**2+1)/(x**2+x+1)**(1/2),x)","\int \frac{x + 3}{\left(x^{2} + 1\right) \sqrt{x^{2} + x + 1}}\, dx"," ",0,"Integral((x + 3)/((x**2 + 1)*sqrt(x**2 + x + 1)), x)","F",0
247,0,0,0,0.000000," ","integrate((1+2*x)/(3*x**2+4*x+4)/(x**2+6*x-1)**(1/2),x)","\int \frac{2 x + 1}{\sqrt{x^{2} + 6 x - 1} \left(3 x^{2} + 4 x + 4\right)}\, dx"," ",0,"Integral((2*x + 1)/(sqrt(x**2 + 6*x - 1)*(3*x**2 + 4*x + 4)), x)","F",0
248,0,0,0,0.000000," ","integrate((A*x+B)/(5*x**2-18*x+17)/(10*x**2-22*x+13)**(1/2),x)","\int \frac{A x + B}{\left(5 x^{2} - 18 x + 17\right) \sqrt{10 x^{2} - 22 x + 13}}\, dx"," ",0,"Integral((A*x + B)/((5*x**2 - 18*x + 17)*sqrt(10*x**2 - 22*x + 13)), x)","F",0
249,0,0,0,0.000000," ","integrate((-2+x)/(5*x**2-18*x+17)/(10*x**2-22*x+13)**(1/2),x)","\int \frac{x - 2}{\left(5 x^{2} - 18 x + 17\right) \sqrt{10 x^{2} - 22 x + 13}}\, dx"," ",0,"Integral((x - 2)/((5*x**2 - 18*x + 17)*sqrt(10*x**2 - 22*x + 13)), x)","F",0
250,1,155,0,4.513782," ","integrate(x**4*(-x**2+5)**(1/2),x)","\begin{cases} \frac{i x^{7}}{6 \sqrt{x^{2} - 5}} - \frac{25 i x^{5}}{24 \sqrt{x^{2} - 5}} - \frac{25 i x^{3}}{48 \sqrt{x^{2} - 5}} + \frac{125 i x}{16 \sqrt{x^{2} - 5}} - \frac{125 i \operatorname{acosh}{\left(\frac{\sqrt{5} x}{5} \right)}}{16} & \text{for}\: \frac{\left|{x^{2}}\right|}{5} > 1 \\- \frac{x^{7}}{6 \sqrt{5 - x^{2}}} + \frac{25 x^{5}}{24 \sqrt{5 - x^{2}}} + \frac{25 x^{3}}{48 \sqrt{5 - x^{2}}} - \frac{125 x}{16 \sqrt{5 - x^{2}}} + \frac{125 \operatorname{asin}{\left(\frac{\sqrt{5} x}{5} \right)}}{16} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x**7/(6*sqrt(x**2 - 5)) - 25*I*x**5/(24*sqrt(x**2 - 5)) - 25*I*x**3/(48*sqrt(x**2 - 5)) + 125*I*x/(16*sqrt(x**2 - 5)) - 125*I*acosh(sqrt(5)*x/5)/16, Abs(x**2)/5 > 1), (-x**7/(6*sqrt(5 - x**2)) + 25*x**5/(24*sqrt(5 - x**2)) + 25*x**3/(48*sqrt(5 - x**2)) - 125*x/(16*sqrt(5 - x**2)) + 125*asin(sqrt(5)*x/5)/16, True))","A",0
251,1,41,0,2.494180," ","integrate(1/x**6/(x**2+2)**(1/2),x)","- \frac{\sqrt{1 + \frac{2}{x^{2}}}}{15} + \frac{\sqrt{1 + \frac{2}{x^{2}}}}{15 x^{2}} - \frac{\sqrt{1 + \frac{2}{x^{2}}}}{10 x^{4}}"," ",0,"-sqrt(1 + 2/x**2)/15 + sqrt(1 + 2/x**2)/(15*x**2) - sqrt(1 + 2/x**2)/(10*x**4)","A",0
252,1,139,0,9.959685," ","integrate(1/(2*x**2+3)**(7/2),x)","\frac{32 x^{5}}{1620 x^{4} \sqrt{2 x^{2} + 3} + 4860 x^{2} \sqrt{2 x^{2} + 3} + 3645 \sqrt{2 x^{2} + 3}} + \frac{120 x^{3}}{1620 x^{4} \sqrt{2 x^{2} + 3} + 4860 x^{2} \sqrt{2 x^{2} + 3} + 3645 \sqrt{2 x^{2} + 3}} + \frac{135 x}{1620 x^{4} \sqrt{2 x^{2} + 3} + 4860 x^{2} \sqrt{2 x^{2} + 3} + 3645 \sqrt{2 x^{2} + 3}}"," ",0,"32*x**5/(1620*x**4*sqrt(2*x**2 + 3) + 4860*x**2*sqrt(2*x**2 + 3) + 3645*sqrt(2*x**2 + 3)) + 120*x**3/(1620*x**4*sqrt(2*x**2 + 3) + 4860*x**2*sqrt(2*x**2 + 3) + 3645*sqrt(2*x**2 + 3)) + 135*x/(1620*x**4*sqrt(2*x**2 + 3) + 4860*x**2*sqrt(2*x**2 + 3) + 3645*sqrt(2*x**2 + 3))","B",0
253,1,53,0,3.000164," ","integrate(x/(1+x**2+a*(x**2+1)**(1/2)),x)","- \frac{a \left(- \frac{\log{\left(2 a + 2 \sqrt{x^{2} + 1} \right)}}{a} + \frac{\log{\left(- 2 \sqrt{x^{2} + 1} \right)}}{a}\right)}{2} + \frac{\log{\left(a \sqrt{x^{2} + 1} + x^{2} + 1 \right)}}{2}"," ",0,"-a*(-log(2*a + 2*sqrt(x**2 + 1))/a + log(-2*sqrt(x**2 + 1))/a)/2 + log(a*sqrt(x**2 + 1) + x**2 + 1)/2","B",0
254,1,29,0,12.849657," ","integrate((x**2-x+1)/(x**2+1)**(3/2),x)","\frac{x^{2} \operatorname{asinh}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{asinh}{\left(x \right)}}{x^{2} + 1} + \frac{1}{\sqrt{x^{2} + 1}}"," ",0,"x**2*asinh(x)/(x**2 + 1) + asinh(x)/(x**2 + 1) + 1/sqrt(x**2 + 1)","B",0
255,0,0,0,0.000000," ","integrate((x**2+1)**(1/2)/(x**2+2),x)","\int \frac{\sqrt{x^{2} + 1}}{x^{2} + 2}\, dx"," ",0,"Integral(sqrt(x**2 + 1)/(x**2 + 2), x)","F",0
256,0,0,0,0.000000," ","integrate(1/(x**2+2)**2/(x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(x**2 + 1)*(x**2 + 2)**2), x)","F",0
257,0,0,0,0.000000," ","integrate(x**2/(x**2-6)/(x**2-2)**(1/2),x)","\int \frac{x^{2}}{\left(x^{2} - 6\right) \sqrt{x^{2} - 2}}\, dx"," ",0,"Integral(x**2/((x**2 - 6)*sqrt(x**2 - 2)), x)","F",0
258,0,0,0,0.000000," ","integrate((x**2+5)/(x**2+1)**2/(-x**2+1)**(1/2),x)","\int \frac{x^{2} + 5}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral((x**2 + 5)/(sqrt(-(x - 1)*(x + 1))*(x**2 + 1)**2), x)","F",0
259,0,0,0,0.000000," ","integrate((4*x-(-x**2+1)**(1/2))/(5+(-x**2+1)**(1/2)),x)","\int \frac{4 x - \sqrt{1 - x^{2}}}{\sqrt{1 - x^{2}} + 5}\, dx"," ",0,"Integral((4*x - sqrt(1 - x**2))/(sqrt(1 - x**2) + 5), x)","F",0
260,-1,0,0,0.000000," ","integrate(x**2*(2-(x**2+1)**(1/2))/(1-x**3+(x**2+1)**(3/2))/(x**2+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,0,0,0,0.000000," ","integrate(x*(2*r*x-x**2)**(1/2),x)","\int x \sqrt{- x \left(- 2 r + x\right)}\, dx"," ",0,"Integral(x*sqrt(-x*(-2*r + x)), x)","F",0
262,0,0,0,0.000000," ","integrate(x**2*(2*r*x-x**2)**(1/2),x)","\int x^{2} \sqrt{- x \left(- 2 r + x\right)}\, dx"," ",0,"Integral(x**2*sqrt(-x*(-2*r + x)), x)","F",0
263,0,0,0,0.000000," ","integrate(x**3*(2*r*x-x**2)**(1/2),x)","\int x^{3} \sqrt{- x \left(- 2 r + x\right)}\, dx"," ",0,"Integral(x**3*sqrt(-x*(-2*r + x)), x)","F",0
264,0,0,0,0.000000," ","integrate(1/(x**2-1)/(x**2+2*x)**(1/2),x)","\int \frac{1}{\sqrt{x \left(x + 2\right)} \left(x - 1\right) \left(x + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(x*(x + 2))*(x - 1)*(x + 1)), x)","F",0
265,0,0,0,0.000000," ","integrate((-2+3*x)/(1+x)**3/(-x**2+2*x)**(1/2),x)","\int \frac{3 x - 2}{\sqrt{- x \left(x - 2\right)} \left(x + 1\right)^{3}}\, dx"," ",0,"Integral((3*x - 2)/(sqrt(-x*(x - 2))*(x + 1)**3), x)","F",0
266,0,0,0,0.000000," ","integrate(1/(x**2+x+1)**(1/2),x)","\int \frac{1}{\sqrt{x^{2} + x + 1}}\, dx"," ",0,"Integral(1/sqrt(x**2 + x + 1), x)","F",0
267,0,0,0,0.000000," ","integrate(x**3/(x**2+x+1)**(1/2),x)","\int \frac{x^{3}}{\sqrt{x^{2} + x + 1}}\, dx"," ",0,"Integral(x**3/sqrt(x**2 + x + 1), x)","F",0
268,0,0,0,0.000000," ","integrate(1/(x**2+x+1)**(3/2),x)","\int \frac{1}{\left(x^{2} + x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x**2 + x + 1)**(-3/2), x)","F",0
269,0,0,0,0.000000," ","integrate(x/(x**2+x+1)**(3/2),x)","\int \frac{x}{\left(x^{2} + x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(x**2 + x + 1)**(3/2), x)","F",0
270,0,0,0,0.000000," ","integrate(x**3/(x**2+x+1)**(3/2),x)","\int \frac{x^{3}}{\left(x^{2} + x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/(x**2 + x + 1)**(3/2), x)","F",0
271,0,0,0,0.000000," ","integrate(x**2*(x**2+x+1)**(1/2),x)","\int x^{2} \sqrt{x^{2} + x + 1}\, dx"," ",0,"Integral(x**2*sqrt(x**2 + x + 1), x)","F",0
272,0,0,0,0.000000," ","integrate((x**2+x+1)**(3/2),x)","\int \left(x^{2} + x + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((x**2 + x + 1)**(3/2), x)","F",0
273,0,0,0,0.000000," ","integrate((x**2+x+1)**(5/2),x)","\int \left(x^{2} + x + 1\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((x**2 + x + 1)**(5/2), x)","F",0
274,0,0,0,0.000000," ","integrate(1/x**2/(x**2+x+1)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{x^{2} + x + 1}}\, dx"," ",0,"Integral(1/(x**2*sqrt(x**2 + x + 1)), x)","F",0
275,0,0,0,0.000000," ","integrate(1/x**3/(x**2+x+1)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{x^{2} + x + 1}}\, dx"," ",0,"Integral(1/(x**3*sqrt(x**2 + x + 1)), x)","F",0
276,0,0,0,0.000000," ","integrate(1/x**2/(x**2+x+1)**(3/2),x)","\int \frac{1}{x^{2} \left(x^{2} + x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(x**2 + x + 1)**(3/2)), x)","F",0
277,0,0,0,0.000000," ","integrate(1/x**3/(x**2+x+1)**(3/2),x)","\int \frac{1}{x^{3} \left(x^{2} + x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(x**2 + x + 1)**(3/2)), x)","F",0
278,0,0,0,0.000000," ","integrate(1/(1+x)/(x**2+x+1)**(1/2),x)","\int \frac{1}{\left(x + 1\right) \sqrt{x^{2} + x + 1}}\, dx"," ",0,"Integral(1/((x + 1)*sqrt(x**2 + x + 1)), x)","F",0
279,0,0,0,0.000000," ","integrate(1/(x**3-x)/(x**2+2*x+4)**(1/2),x)","\int \frac{1}{x \left(x - 1\right) \left(x + 1\right) \sqrt{x^{2} + 2 x + 4}}\, dx"," ",0,"Integral(1/(x*(x - 1)*(x + 1)*sqrt(x**2 + 2*x + 4)), x)","F",0
280,0,0,0,0.000000," ","integrate((x**2+2*x+4)**(1/2)/(-1+x)**2,x)","\int \frac{\sqrt{x^{2} + 2 x + 4}}{\left(x - 1\right)^{2}}\, dx"," ",0,"Integral(sqrt(x**2 + 2*x + 4)/(x - 1)**2, x)","F",0
281,0,0,0,0.000000," ","integrate((3+2*x)/(x**2+2*x+3)**2/(x**2+2*x+4)**(1/2),x)","\int \frac{2 x + 3}{\left(x^{2} + 2 x + 3\right)^{2} \sqrt{x^{2} + 2 x + 4}}\, dx"," ",0,"Integral((2*x + 3)/((x**2 + 2*x + 3)**2*sqrt(x**2 + 2*x + 4)), x)","F",0
282,0,0,0,0.000000," ","integrate((2*x**3+3*x**2)/(2*x**2+x-3)/(x**2+2*x-3)**(1/2),x)","\int \frac{x^{2}}{\sqrt{\left(x - 1\right) \left(x + 3\right)} \left(x - 1\right)}\, dx"," ",0,"Integral(x**2/(sqrt((x - 1)*(x + 3))*(x - 1)), x)","F",0
283,0,0,0,0.000000," ","integrate((x**4+1)/(x**2+x+1)/(x**2+x+2)**(1/2),x)","\int \frac{x^{4} + 1}{\left(x^{2} + x + 1\right) \sqrt{x^{2} + x + 2}}\, dx"," ",0,"Integral((x**4 + 1)/((x**2 + x + 1)*sqrt(x**2 + x + 2)), x)","F",0
284,0,0,0,0.000000," ","integrate(1/(x**2+2*x+4)**(7/2),x)","\int \frac{1}{\left(x^{2} + 2 x + 4\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((x**2 + 2*x + 4)**(-7/2), x)","F",0
285,0,0,0,0.000000," ","integrate(1/(3*x**2+8*x+1)**(5/2),x)","\int \frac{1}{\left(3 x^{2} + 8 x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((3*x**2 + 8*x + 1)**(-5/2), x)","F",0
286,0,0,0,0.000000," ","integrate(1/(-3*x**2+4*x+5)**(5/2),x)","\int \frac{1}{\left(- 3 x^{2} + 4 x + 5\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-3*x**2 + 4*x + 5)**(-5/2), x)","F",0
287,0,0,0,0.000000," ","integrate(1/(1+(x**2+2*x+2)**(1/2)),x)","\int \frac{1}{\sqrt{x^{2} + 2 x + 2} + 1}\, dx"," ",0,"Integral(1/(sqrt(x**2 + 2*x + 2) + 1), x)","F",0
288,0,0,0,0.000000," ","integrate(1/(x+(x**2+x+1)**(1/2)),x)","\int \frac{1}{x + \sqrt{x^{2} + x + 1}}\, dx"," ",0,"Integral(1/(x + sqrt(x**2 + x + 1)), x)","F",0
289,0,0,0,0.000000," ","integrate(x**2/(1+2*x+2*(x**2+x+1)**(1/2)),x)","\int \frac{x^{2}}{2 x + 2 \sqrt{x^{2} + x + 1} + 1}\, dx"," ",0,"Integral(x**2/(2*x + 2*sqrt(x**2 + x + 1) + 1), x)","F",0
290,0,0,0,0.000000," ","integrate((-3*x+(x**2+x+1)**(1/2))/(-1+(x**2+x+1)**(1/2)),x)","- \int \frac{3 x}{\sqrt{x^{2} + x + 1} - 1}\, dx - \int \left(- \frac{\sqrt{x^{2} + x + 1}}{\sqrt{x^{2} + x + 1} - 1}\right)\, dx"," ",0,"-Integral(3*x/(sqrt(x**2 + x + 1) - 1), x) - Integral(-sqrt(x**2 + x + 1)/(sqrt(x**2 + x + 1) - 1), x)","F",0
291,0,0,0,0.000000," ","integrate((1+x)/(-(x**2+x+1)**(1/2)+(x**2+2*x+4)**(1/2)),x)","\int \frac{x + 1}{- \sqrt{x^{2} + x + 1} + \sqrt{x^{2} + 2 x + 4}}\, dx"," ",0,"Integral((x + 1)/(-sqrt(x**2 + x + 1) + sqrt(x**2 + 2*x + 4)), x)","F",0
292,1,131,0,3.076636," ","integrate(1/x**3/(-1+x)**(1/2),x)","\begin{cases} \frac{3 i \operatorname{acosh}{\left(\frac{1}{\sqrt{x}} \right)}}{4} - \frac{3 i}{4 \sqrt{x} \sqrt{-1 + \frac{1}{x}}} + \frac{i}{4 x^{\frac{3}{2}} \sqrt{-1 + \frac{1}{x}}} + \frac{i}{2 x^{\frac{5}{2}} \sqrt{-1 + \frac{1}{x}}} & \text{for}\: \frac{1}{\left|{x}\right|} > 1 \\- \frac{3 \operatorname{asin}{\left(\frac{1}{\sqrt{x}} \right)}}{4} + \frac{3}{4 \sqrt{x} \sqrt{1 - \frac{1}{x}}} - \frac{1}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x}}} - \frac{1}{2 x^{\frac{5}{2}} \sqrt{1 - \frac{1}{x}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*I*acosh(1/sqrt(x))/4 - 3*I/(4*sqrt(x)*sqrt(-1 + 1/x)) + I/(4*x**(3/2)*sqrt(-1 + 1/x)) + I/(2*x**(5/2)*sqrt(-1 + 1/x)), 1/Abs(x) > 1), (-3*asin(1/sqrt(x))/4 + 3/(4*sqrt(x)*sqrt(1 - 1/x)) - 1/(4*x**(3/2)*sqrt(1 - 1/x)) - 1/(2*x**(5/2)*sqrt(1 - 1/x)), True))","A",0
293,1,10,0,0.981330," ","integrate(1/(1-3/x)**(4/3)/x**2,x)","- \frac{1}{\sqrt[3]{1 - \frac{3}{x}}}"," ",0,"-1/(1 - 3/x)**(1/3)","A",0
294,1,541,0,2.271670," ","integrate((-1+3*x)**(4/3)/x**2,x)","\frac{189 \sqrt[3]{3} \left(x - \frac{1}{3}\right)^{\frac{4}{3}} e^{\frac{i \pi}{3}} \Gamma\left(\frac{7}{3}\right)}{9 \left(x - \frac{1}{3}\right) e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 3 e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{84 \sqrt[3]{3} \sqrt[3]{x - \frac{1}{3}} e^{\frac{i \pi}{3}} \Gamma\left(\frac{7}{3}\right)}{9 \left(x - \frac{1}{3}\right) e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 3 e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{84 \left(x - \frac{1}{3}\right) \log{\left(- \sqrt[3]{3} \sqrt[3]{x - \frac{1}{3}} e^{\frac{i \pi}{3}} + 1 \right)} \Gamma\left(\frac{7}{3}\right)}{9 \left(x - \frac{1}{3}\right) e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 3 e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{84 \left(x - \frac{1}{3}\right) e^{\frac{i \pi}{3}} \log{\left(- \sqrt[3]{3} \sqrt[3]{x - \frac{1}{3}} e^{i \pi} + 1 \right)} \Gamma\left(\frac{7}{3}\right)}{9 \left(x - \frac{1}{3}\right) e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 3 e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{84 \left(x - \frac{1}{3}\right) e^{\frac{2 i \pi}{3}} \log{\left(- \sqrt[3]{3} \sqrt[3]{x - \frac{1}{3}} e^{\frac{5 i \pi}{3}} + 1 \right)} \Gamma\left(\frac{7}{3}\right)}{9 \left(x - \frac{1}{3}\right) e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 3 e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{28 \log{\left(- \sqrt[3]{3} \sqrt[3]{x - \frac{1}{3}} e^{\frac{i \pi}{3}} + 1 \right)} \Gamma\left(\frac{7}{3}\right)}{9 \left(x - \frac{1}{3}\right) e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 3 e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{28 e^{\frac{i \pi}{3}} \log{\left(- \sqrt[3]{3} \sqrt[3]{x - \frac{1}{3}} e^{i \pi} + 1 \right)} \Gamma\left(\frac{7}{3}\right)}{9 \left(x - \frac{1}{3}\right) e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 3 e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{28 e^{\frac{2 i \pi}{3}} \log{\left(- \sqrt[3]{3} \sqrt[3]{x - \frac{1}{3}} e^{\frac{5 i \pi}{3}} + 1 \right)} \Gamma\left(\frac{7}{3}\right)}{9 \left(x - \frac{1}{3}\right) e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 3 e^{\frac{i \pi}{3}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"189*3**(1/3)*(x - 1/3)**(4/3)*exp(I*pi/3)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) + 84*3**(1/3)*(x - 1/3)**(1/3)*exp(I*pi/3)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) + 84*(x - 1/3)*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(I*pi/3) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) - 84*(x - 1/3)*exp(I*pi/3)*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(I*pi) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) + 84*(x - 1/3)*exp(2*I*pi/3)*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(5*I*pi/3) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) + 28*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(I*pi/3) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) - 28*exp(I*pi/3)*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(I*pi) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3)) + 28*exp(2*I*pi/3)*log(-3**(1/3)*(x - 1/3)**(1/3)*exp_polar(5*I*pi/3) + 1)*gamma(7/3)/(9*(x - 1/3)*exp(I*pi/3)*gamma(10/3) + 3*exp(I*pi/3)*gamma(10/3))","C",0
295,1,180,0,1.754862," ","integrate((4-3*x)**(4/3)*x**2,x)","\begin{cases} - \frac{9 x^{4} \sqrt[3]{3 x - 4} e^{\frac{i \pi}{3}}}{13} + \frac{84 x^{3} \sqrt[3]{3 x - 4} e^{\frac{i \pi}{3}}}{65} - \frac{32 x^{2} \sqrt[3]{3 x - 4} e^{\frac{i \pi}{3}}}{455} - \frac{64 x \sqrt[3]{3 x - 4} e^{\frac{i \pi}{3}}}{455} - \frac{256 \sqrt[3]{3 x - 4} e^{\frac{i \pi}{3}}}{455} & \text{for}\: \frac{3 \left|{x}\right|}{4} > 1 \\- \frac{9 x^{4} \sqrt[3]{4 - 3 x}}{13} + \frac{84 x^{3} \sqrt[3]{4 - 3 x}}{65} - \frac{32 x^{2} \sqrt[3]{4 - 3 x}}{455} - \frac{64 x \sqrt[3]{4 - 3 x}}{455} - \frac{256 \sqrt[3]{4 - 3 x}}{455} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*x**4*(3*x - 4)**(1/3)*exp(I*pi/3)/13 + 84*x**3*(3*x - 4)**(1/3)*exp(I*pi/3)/65 - 32*x**2*(3*x - 4)**(1/3)*exp(I*pi/3)/455 - 64*x*(3*x - 4)**(1/3)*exp(I*pi/3)/455 - 256*(3*x - 4)**(1/3)*exp(I*pi/3)/455, 3*Abs(x)/4 > 1), (-9*x**4*(4 - 3*x)**(1/3)/13 + 84*x**3*(4 - 3*x)**(1/3)/65 - 32*x**2*(4 - 3*x)**(1/3)/455 - 64*x*(4 - 3*x)**(1/3)/455 - 256*(4 - 3*x)**(1/3)/455, True))","B",0
296,1,51,0,2.092639," ","integrate((1-2*x**(1/3))**(3/4)/x,x)","- \frac{3 \cdot 2^{\frac{3}{4}} \sqrt[4]{x} e^{\frac{3 i \pi}{4}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{1}{2 \sqrt[3]{x}}} \right)}}{\Gamma\left(\frac{1}{4}\right)}"," ",0,"-3*2**(3/4)*x**(1/4)*exp(3*I*pi/4)*gamma(-3/4)*hyper((-3/4, -3/4), (1/4,), 1/(2*x**(1/3)))/gamma(1/4)","C",0
297,1,3305,0,2.246994," ","integrate(x/(3-2*x**(1/2))**(3/4),x)","\begin{cases} \frac{1280 \sqrt[4]{3} x^{\frac{25}{2}} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{26304 \sqrt[4]{3} x^{\frac{23}{2}} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{200016 \sqrt[4]{3} x^{\frac{21}{2}} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{331776 \sqrt{3} x^{\frac{21}{2}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{2123820 \sqrt[4]{3} x^{\frac{19}{2}} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{2488320 \sqrt{3} x^{\frac{19}{2}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{1609632 \sqrt[4]{3} x^{\frac{17}{2}} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{1679616 \sqrt{3} x^{\frac{17}{2}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{8960 \sqrt[4]{3} x^{12} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{18432 \sqrt[4]{3} x^{11} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{36864 \sqrt{3} x^{11}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{965520 \sqrt[4]{3} x^{10} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{1244160 \sqrt{3} x^{10}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{2548584 \sqrt[4]{3} x^{9} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{2799360 \sqrt{3} x^{9}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{419904 \sqrt[4]{3} x^{8} \sqrt[4]{2 \sqrt{x} - 3} e^{- \frac{3 i \pi}{4}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{419904 \sqrt{3} x^{8}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} & \text{for}\: \frac{2 \left|{\sqrt{x}}\right|}{3} > 1 \\- \frac{1280 \sqrt[4]{3} x^{\frac{25}{2}} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{26304 \sqrt[4]{3} x^{\frac{23}{2}} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{200016 \sqrt[4]{3} x^{\frac{21}{2}} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{331776 \sqrt{3} x^{\frac{21}{2}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{2123820 \sqrt[4]{3} x^{\frac{19}{2}} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{2488320 \sqrt{3} x^{\frac{19}{2}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{1609632 \sqrt[4]{3} x^{\frac{17}{2}} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{1679616 \sqrt{3} x^{\frac{17}{2}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{8960 \sqrt[4]{3} x^{12} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{18432 \sqrt[4]{3} x^{11} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{36864 \sqrt{3} x^{11}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{965520 \sqrt[4]{3} x^{10} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{1244160 \sqrt{3} x^{10}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{2548584 \sqrt[4]{3} x^{9} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{2799360 \sqrt{3} x^{9}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} - \frac{419904 \sqrt[4]{3} x^{8} \sqrt[4]{3 - 2 \sqrt{x}}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} + \frac{419904 \sqrt{3} x^{8}}{- 37440 \sqrt[4]{3} x^{\frac{21}{2}} - 280800 \sqrt[4]{3} x^{\frac{19}{2}} - 189540 \sqrt[4]{3} x^{\frac{17}{2}} + 4160 \sqrt[4]{3} x^{11} + 140400 \sqrt[4]{3} x^{10} + 315900 \sqrt[4]{3} x^{9} + 47385 \sqrt[4]{3} x^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1280*3**(1/4)*x**(25/2)*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 26304*3**(1/4)*x**(23/2)*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 200016*3**(1/4)*x**(21/2)*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 331776*sqrt(3)*x**(21/2)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 2123820*3**(1/4)*x**(19/2)*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 2488320*sqrt(3)*x**(19/2)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 1609632*3**(1/4)*x**(17/2)*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 1679616*sqrt(3)*x**(17/2)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 8960*3**(1/4)*x**12*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 18432*3**(1/4)*x**11*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 36864*sqrt(3)*x**11/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 965520*3**(1/4)*x**10*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 1244160*sqrt(3)*x**10/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 2548584*3**(1/4)*x**9*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 2799360*sqrt(3)*x**9/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 419904*3**(1/4)*x**8*(2*sqrt(x) - 3)**(1/4)*exp(-3*I*pi/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 419904*sqrt(3)*x**8/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8), 2*Abs(sqrt(x))/3 > 1), (-1280*3**(1/4)*x**(25/2)*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 26304*3**(1/4)*x**(23/2)*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 200016*3**(1/4)*x**(21/2)*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 331776*sqrt(3)*x**(21/2)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 2123820*3**(1/4)*x**(19/2)*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 2488320*sqrt(3)*x**(19/2)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 1609632*3**(1/4)*x**(17/2)*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 1679616*sqrt(3)*x**(17/2)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 8960*3**(1/4)*x**12*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 18432*3**(1/4)*x**11*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 36864*sqrt(3)*x**11/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 965520*3**(1/4)*x**10*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 1244160*sqrt(3)*x**10/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 2548584*3**(1/4)*x**9*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 2799360*sqrt(3)*x**9/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) - 419904*3**(1/4)*x**8*(3 - 2*sqrt(x))**(1/4)/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8) + 419904*sqrt(3)*x**8/(-37440*3**(1/4)*x**(21/2) - 280800*3**(1/4)*x**(19/2) - 189540*3**(1/4)*x**(17/2) + 4160*3**(1/4)*x**11 + 140400*3**(1/4)*x**10 + 315900*3**(1/4)*x**9 + 47385*3**(1/4)*x**8), True))","B",0
298,1,44,0,5.631570," ","integrate((-1+2*x**(1/2))**(5/4)/x**2,x)","- \frac{4 \sqrt[4]{2} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{e^{2 i \pi}}{2 \sqrt{x}}} \right)}}{x^{\frac{3}{8}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-4*2**(1/4)*gamma(3/4)*hyper((-5/4, 3/4), (7/4,), exp_polar(2*I*pi)/(2*sqrt(x)))/(x**(3/8)*gamma(7/4))","C",0
299,1,26,0,0.536761," ","integrate(x**6*(x**7+1)**(1/3),x)","\frac{3 x^{7} \sqrt[3]{x^{7} + 1}}{28} + \frac{3 \sqrt[3]{x^{7} + 1}}{28}"," ",0,"3*x**7*(x**7 + 1)**(1/3)/28 + 3*(x**7 + 1)**(1/3)/28","B",0
300,1,12,0,0.537023," ","integrate(x**6/(x**7+1)**(5/3),x)","- \frac{3}{14 \left(x^{7} + 1\right)^{\frac{2}{3}}}"," ",0,"-3/(14*(x**7 + 1)**(2/3))","A",0
301,1,42,0,1.015767," ","integrate(1/x/(2*x**7-27)**(2/3),x)","- \frac{\sqrt[3]{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{27 e^{2 i \pi}}{2 x^{7}}} \right)}}{14 x^{\frac{14}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-2**(1/3)*gamma(2/3)*hyper((2/3, 2/3), (5/3,), 27*exp_polar(2*I*pi)/(2*x**7))/(14*x**(14/3)*gamma(5/3))","C",0
302,1,34,0,1.417298," ","integrate((x**7+1)**(2/3)/x**8,x)","- \frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{e^{i \pi}}{x^{7}}} \right)}}{7 x^{\frac{7}{3}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-gamma(1/3)*hyper((-2/3, 1/3), (4/3,), exp_polar(I*pi)/x**7)/(7*x**(7/3)*gamma(4/3))","C",0
303,1,41,0,1.028888," ","integrate((4*x**4+3)**(1/4)/x**2,x)","\frac{\sqrt[4]{3} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{4 x^{4} e^{i \pi}}{3}} \right)}}{4 x \Gamma\left(\frac{3}{4}\right)}"," ",0,"3**(1/4)*gamma(-1/4)*hyper((-1/4, -1/4), (3/4,), 4*x**4*exp_polar(I*pi)/3)/(4*x*gamma(3/4))","C",0
304,1,41,0,1.569585," ","integrate(x**2*(4*x**4+3)**(5/4),x)","\frac{3 \sqrt[4]{3} x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{4 x^{4} e^{i \pi}}{3}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}"," ",0,"3*3**(1/4)*x**3*gamma(3/4)*hyper((-5/4, 3/4), (7/4,), 4*x**4*exp_polar(I*pi)/3)/(4*gamma(7/4))","C",0
305,1,39,0,1.316965," ","integrate(x**6*(4*x**4+3)**(1/4),x)","\frac{\sqrt[4]{3} x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{4 x^{4} e^{i \pi}}{3}} \right)}}{4 \Gamma\left(\frac{11}{4}\right)}"," ",0,"3**(1/4)*x**7*gamma(7/4)*hyper((-1/4, 7/4), (11/4,), 4*x**4*exp_polar(I*pi)/3)/(4*gamma(11/4))","C",0
306,0,0,0,0.000000," ","integrate((x*(-x**2+1))**(1/3),x)","\int \sqrt[3]{x \left(1 - x^{2}\right)}\, dx"," ",0,"Integral((x*(1 - x**2))**(1/3), x)","F",0
307,0,0,0,0.000000," ","integrate(((1+x**(1/3))*x)**(1/2),x)","\int \sqrt{x \left(\sqrt[3]{x} + 1\right)}\, dx"," ",0,"Integral(sqrt(x*(x**(1/3) + 1)), x)","F",0
308,0,0,0,0.000000," ","integrate(x**3/(x**4-1)/(2*x**8+1)**(1/2),x)","\int \frac{x^{3}}{\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right) \sqrt{2 x^{8} + 1}}\, dx"," ",0,"Integral(x**3/((x - 1)*(x + 1)*(x**2 + 1)*sqrt(2*x**8 + 1)), x)","F",0
309,0,0,0,0.000000," ","integrate(x**9*(x**10+x**5+1)**(1/2),x)","\int x^{9} \sqrt{\left(x^{2} + x + 1\right) \left(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\right)}\, dx"," ",0,"Integral(x**9*sqrt((x**2 + x + 1)*(x**8 - x**7 + x**5 - x**4 + x**3 - x + 1)), x)","F",0
310,0,0,0,0.000000," ","integrate(1/x**5/(x**4+2*x**2+4)**(1/2),x)","\int \frac{1}{x^{5} \sqrt{x^{4} + 2 x^{2} + 4}}\, dx"," ",0,"Integral(1/(x**5*sqrt(x**4 + 2*x**2 + 4)), x)","F",0
311,0,0,0,0.000000," ","integrate((x**2-1)/x/(x**4+3*x**2+1)**(1/2),x)","\int \frac{\left(x - 1\right) \left(x + 1\right)}{x \sqrt{x^{4} + 3 x^{2} + 1}}\, dx"," ",0,"Integral((x - 1)*(x + 1)/(x*sqrt(x**4 + 3*x**2 + 1)), x)","F",0
312,1,36,0,1.310309," ","integrate((2*x**3-3*x)*(x**4-3*x**2)**(3/5),x)","\frac{5 x^{4} \left(x^{4} - 3 x^{2}\right)^{\frac{3}{5}}}{16} - \frac{15 x^{2} \left(x^{4} - 3 x^{2}\right)^{\frac{3}{5}}}{16}"," ",0,"5*x**4*(x**4 - 3*x**2)**(3/5)/16 - 15*x**2*(x**4 - 3*x**2)**(3/5)/16","B",0
313,1,221,0,3.943660," ","integrate((-2*x**5+3*x**8-x**2*(3*x**3-1)**(2/3))/(3*x**3-1)**(3/4),x)","- \frac{4 \left(3 x^{3} - 1\right)^{\frac{11}{12}}}{33} - 2 \left(\begin{cases} \frac{4 x^{3} \sqrt[4]{3 x^{3} - 1}}{45} + \frac{16 \sqrt[4]{3 x^{3} - 1}}{135} & \text{for}\: 3 \left|{x^{3}}\right| > 1 \\- \frac{4 x^{3} \sqrt[4]{1 - 3 x^{3}} e^{- \frac{3 i \pi}{4}}}{45} - \frac{16 \sqrt[4]{1 - 3 x^{3}} e^{- \frac{3 i \pi}{4}}}{135} & \text{otherwise} \end{cases}\right) + 3 \left(\begin{cases} \frac{4 x^{6} \sqrt[4]{3 x^{3} - 1}}{81} + \frac{32 x^{3} \sqrt[4]{3 x^{3} - 1}}{1215} + \frac{128 \sqrt[4]{3 x^{3} - 1}}{3645} & \text{for}\: 3 \left|{x^{3}}\right| > 1 \\\frac{4 x^{6} \sqrt[4]{1 - 3 x^{3}} e^{\frac{i \pi}{4}}}{81} + \frac{32 x^{3} \sqrt[4]{1 - 3 x^{3}} e^{\frac{i \pi}{4}}}{1215} + \frac{128 \sqrt[4]{1 - 3 x^{3}} e^{\frac{i \pi}{4}}}{3645} & \text{otherwise} \end{cases}\right)"," ",0,"-4*(3*x**3 - 1)**(11/12)/33 - 2*Piecewise((4*x**3*(3*x**3 - 1)**(1/4)/45 + 16*(3*x**3 - 1)**(1/4)/135, 3*Abs(x**3) > 1), (-4*x**3*(1 - 3*x**3)**(1/4)*exp(-3*I*pi/4)/45 - 16*(1 - 3*x**3)**(1/4)*exp(-3*I*pi/4)/135, True)) + 3*Piecewise((4*x**6*(3*x**3 - 1)**(1/4)/81 + 32*x**3*(3*x**3 - 1)**(1/4)/1215 + 128*(3*x**3 - 1)**(1/4)/3645, 3*Abs(x**3) > 1), (4*x**6*(1 - 3*x**3)**(1/4)*exp(I*pi/4)/81 + 32*x**3*(1 - 3*x**3)**(1/4)*exp(I*pi/4)/1215 + 128*(1 - 3*x**3)**(1/4)*exp(I*pi/4)/3645, True))","C",0
314,0,0,0,0.000000," ","integrate(1/(x**3-1)/(x**3+2)**(1/3),x)","\int \frac{1}{\left(x - 1\right) \sqrt[3]{x^{3} + 2} \left(x^{2} + x + 1\right)}\, dx"," ",0,"Integral(1/((x - 1)*(x**3 + 2)**(1/3)*(x**2 + x + 1)), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(x**4+1)/(x**4+2)**(1/4),x)","\int \frac{1}{\left(x^{4} + 1\right) \sqrt[4]{x^{4} + 2}}\, dx"," ",0,"Integral(1/((x**4 + 1)*(x**4 + 2)**(1/4)), x)","F",0
316,1,71,0,2.004708," ","integrate((x**3-1)/(x**3+2)**(1/3),x)","\frac{2^{\frac{2}{3}} x^{4} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{x^{3} e^{i \pi}}{2}} \right)}}{6 \Gamma\left(\frac{7}{3}\right)} - \frac{2^{\frac{2}{3}} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3} e^{i \pi}}{2}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}"," ",0,"2**(2/3)*x**4*gamma(4/3)*hyper((1/3, 4/3), (7/3,), x**3*exp_polar(I*pi)/2)/(6*gamma(7/3)) - 2**(2/3)*x*gamma(1/3)*hyper((1/3, 1/3), (4/3,), x**3*exp_polar(I*pi)/2)/(6*gamma(4/3))","C",0
317,0,0,0,0.000000," ","integrate((x**4+1)**(3/4)/(x**4+2)**2,x)","\int \frac{\left(x^{4} + 1\right)^{\frac{3}{4}}}{\left(x^{4} + 2\right)^{2}}\, dx"," ",0,"Integral((x**4 + 1)**(3/4)/(x**4 + 2)**2, x)","F",0
318,-1,0,0,0.000000," ","integrate((x**5-2)**2/(x**5+3)**(16/5),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,0,0,0,0.000000," ","integrate(1/(x**3+3*x**2+3*x)/(x**3+3*x**2+3*x+3)**(1/3),x)","\int \frac{1}{x \left(x^{2} + 3 x + 3\right) \sqrt[3]{x^{3} + 3 x^{2} + 3 x + 3}}\, dx"," ",0,"Integral(1/(x*(x**2 + 3*x + 3)*(x**3 + 3*x**2 + 3*x + 3)**(1/3)), x)","F",0
320,0,0,0,0.000000," ","integrate((-x**2+1)/(x**2+1)/(x**4+1)**(1/2),x)","- \int \frac{x^{2}}{x^{2} \sqrt{x^{4} + 1} + \sqrt{x^{4} + 1}}\, dx - \int \left(- \frac{1}{x^{2} \sqrt{x^{4} + 1} + \sqrt{x^{4} + 1}}\right)\, dx"," ",0,"-Integral(x**2/(x**2*sqrt(x**4 + 1) + sqrt(x**4 + 1)), x) - Integral(-1/(x**2*sqrt(x**4 + 1) + sqrt(x**4 + 1)), x)","F",0
321,0,0,0,0.000000," ","integrate((x**2+1)/(-x**2+1)/(x**4+1)**(1/2),x)","- \int \frac{x^{2}}{x^{2} \sqrt{x^{4} + 1} - \sqrt{x^{4} + 1}}\, dx - \int \frac{1}{x^{2} \sqrt{x^{4} + 1} - \sqrt{x^{4} + 1}}\, dx"," ",0,"-Integral(x**2/(x**2*sqrt(x**4 + 1) - sqrt(x**4 + 1)), x) - Integral(1/(x**2*sqrt(x**4 + 1) - sqrt(x**4 + 1)), x)","F",0
322,1,14,0,9.512628," ","integrate((x**2+1)/x/(x**4+1)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{1}{x^{2}} \right)}}{2} + \frac{\operatorname{asinh}{\left(x^{2} \right)}}{2}"," ",0,"-asinh(x**(-2))/2 + asinh(x**2)/2","A",0
323,1,14,0,5.573349," ","integrate((x**2-1)/x/(x**4+1)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{1}{x^{2}} \right)}}{2} + \frac{\operatorname{asinh}{\left(x^{2} \right)}}{2}"," ",0,"asinh(x**(-2))/2 + asinh(x**2)/2","A",0
324,0,0,0,0.000000," ","integrate((x**2+1)/(-x**2+1)/(x**4+x**2+1)**(1/2),x)","- \int \frac{x^{2}}{x^{2} \sqrt{x^{4} + x^{2} + 1} - \sqrt{x^{4} + x^{2} + 1}}\, dx - \int \frac{1}{x^{2} \sqrt{x^{4} + x^{2} + 1} - \sqrt{x^{4} + x^{2} + 1}}\, dx"," ",0,"-Integral(x**2/(x**2*sqrt(x**4 + x**2 + 1) - sqrt(x**4 + x**2 + 1)), x) - Integral(1/(x**2*sqrt(x**4 + x**2 + 1) - sqrt(x**4 + x**2 + 1)), x)","F",0
325,0,0,0,0.000000," ","integrate((-x**2+1)/(x**2+1)/(x**4+x**2+1)**(1/2),x)","- \int \frac{x^{2}}{x^{2} \sqrt{x^{4} + x^{2} + 1} + \sqrt{x^{4} + x^{2} + 1}}\, dx - \int \left(- \frac{1}{x^{2} \sqrt{x^{4} + x^{2} + 1} + \sqrt{x^{4} + x^{2} + 1}}\right)\, dx"," ",0,"-Integral(x**2/(x**2*sqrt(x**4 + x**2 + 1) + sqrt(x**4 + x**2 + 1)), x) - Integral(-1/(x**2*sqrt(x**4 + x**2 + 1) + sqrt(x**4 + x**2 + 1)), x)","F",0
326,0,0,0,0.000000," ","integrate((x**4-1)/x**2/(x**4+x**2+1)**(1/2),x)","\int \frac{\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right)}{x^{2} \sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}\, dx"," ",0,"Integral((x - 1)*(x + 1)*(x**2 + 1)/(x**2*sqrt((x**2 - x + 1)*(x**2 + x + 1))), x)","F",0
327,0,0,0,0.000000," ","integrate((-x**2+1)/(2*a*x+x**2+1)/(2*a*x**3+x**4+2*b*x**2+2*a*x+1)**(1/2),x)","- \int \frac{x^{2}}{2 a x \sqrt{2 a x^{3} + 2 a x + 2 b x^{2} + x^{4} + 1} + x^{2} \sqrt{2 a x^{3} + 2 a x + 2 b x^{2} + x^{4} + 1} + \sqrt{2 a x^{3} + 2 a x + 2 b x^{2} + x^{4} + 1}}\, dx - \int \left(- \frac{1}{2 a x \sqrt{2 a x^{3} + 2 a x + 2 b x^{2} + x^{4} + 1} + x^{2} \sqrt{2 a x^{3} + 2 a x + 2 b x^{2} + x^{4} + 1} + \sqrt{2 a x^{3} + 2 a x + 2 b x^{2} + x^{4} + 1}}\right)\, dx"," ",0,"-Integral(x**2/(2*a*x*sqrt(2*a*x**3 + 2*a*x + 2*b*x**2 + x**4 + 1) + x**2*sqrt(2*a*x**3 + 2*a*x + 2*b*x**2 + x**4 + 1) + sqrt(2*a*x**3 + 2*a*x + 2*b*x**2 + x**4 + 1)), x) - Integral(-1/(2*a*x*sqrt(2*a*x**3 + 2*a*x + 2*b*x**2 + x**4 + 1) + x**2*sqrt(2*a*x**3 + 2*a*x + 2*b*x**2 + x**4 + 1) + sqrt(2*a*x**3 + 2*a*x + 2*b*x**2 + x**4 + 1)), x)","F",0
328,0,0,0,0.000000," ","integrate(1/(x**4+1)/(-x**2+(x**4+1)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} + \sqrt{x^{4} + 1}} \left(x^{4} + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(-x**2 + sqrt(x**4 + 1))*(x**4 + 1)), x)","F",0
329,0,0,0,0.000000," ","integrate(1/(1+x**(2*n))/(-x**2+(1+x**(2*n))**(1/n))**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} + \left(x^{2 n} + 1\right)^{\frac{1}{n}}} \left(x^{2 n} + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(-x**2 + (x**(2*n) + 1)**(1/n))*(x**(2*n) + 1)), x)","F",0
330,1,10,0,0.061781," ","integrate(cos(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
331,1,8,0,0.068156," ","integrate(cos(x)**3,x)","- \frac{\sin^{3}{\left(x \right)}}{3} + \sin{\left(x \right)}"," ",0,"-sin(x)**3/3 + sin(x)","A",0
332,1,24,0,0.064265," ","integrate(sin(x)**4,x)","\frac{3 x}{8} - \frac{\sin^{3}{\left(x \right)} \cos{\left(x \right)}}{4} - \frac{3 \sin{\left(x \right)} \cos{\left(x \right)}}{8}"," ",0,"3*x/8 - sin(x)**3*cos(x)/4 - 3*sin(x)*cos(x)/8","A",0
333,1,36,0,0.065364," ","integrate(cos(x)**6,x)","\frac{5 x}{16} + \frac{\sin{\left(x \right)} \cos^{5}{\left(x \right)}}{6} + \frac{5 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{24} + \frac{5 \sin{\left(x \right)} \cos{\left(x \right)}}{16}"," ",0,"5*x/16 + sin(x)*cos(x)**5/6 + 5*sin(x)*cos(x)**3/24 + 5*sin(x)*cos(x)/16","A",0
334,1,48,0,0.065879," ","integrate(sin(x)**8,x)","\frac{35 x}{128} - \frac{\sin^{7}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{7 \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{48} - \frac{35 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{192} - \frac{35 \sin{\left(x \right)} \cos{\left(x \right)}}{128}"," ",0,"35*x/128 - sin(x)**7*cos(x)/8 - 7*sin(x)**5*cos(x)/48 - 35*sin(x)**3*cos(x)/192 - 35*sin(x)*cos(x)/128","A",0
335,1,99,0,0.649567," ","integrate(cos(1/4*pi+1/2*x)**4,x)","\frac{3 x \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{8} + \frac{3 x \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \cos^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{4} + \frac{3 x \cos^{4}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{8} + \frac{3 \sin^{3}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \cos{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{4} + \frac{5 \sin{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \cos^{3}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{4}"," ",0,"3*x*sin(x/2 + pi/4)**4/8 + 3*x*sin(x/2 + pi/4)**2*cos(x/2 + pi/4)**2/4 + 3*x*cos(x/2 + pi/4)**4/8 + 3*sin(x/2 + pi/4)**3*cos(x/2 + pi/4)/4 + 5*sin(x/2 + pi/4)*cos(x/2 + pi/4)**3/4","B",0
336,1,39,0,0.340654," ","integrate(-cos(5/12*pi+3*x)**3,x)","- \frac{2 \sin^{3}{\left(3 x + \frac{5 \pi}{12} \right)}}{9} - \frac{\sin{\left(3 x + \frac{5 \pi}{12} \right)} \cos^{2}{\left(3 x + \frac{5 \pi}{12} \right)}}{3}"," ",0,"-2*sin(3*x + 5*pi/12)**3/9 - sin(3*x + 5*pi/12)*cos(3*x + 5*pi/12)**2/3","A",0
337,1,32,0,0.064595," ","integrate(1/sin(x)**6,x)","- \frac{8 \cos{\left(x \right)}}{15 \sin{\left(x \right)}} - \frac{4 \cos{\left(x \right)}}{15 \sin^{3}{\left(x \right)}} - \frac{\cos{\left(x \right)}}{5 \sin^{5}{\left(x \right)}}"," ",0,"-8*cos(x)/(15*sin(x)) - 4*cos(x)/(15*sin(x)**3) - cos(x)/(5*sin(x)**5)","A",0
338,1,60,0,0.171927," ","integrate(csc(x)**7,x)","- \frac{- 15 \cos^{5}{\left(x \right)} + 40 \cos^{3}{\left(x \right)} - 33 \cos{\left(x \right)}}{48 \cos^{6}{\left(x \right)} - 144 \cos^{4}{\left(x \right)} + 144 \cos^{2}{\left(x \right)} - 48} + \frac{5 \log{\left(\cos{\left(x \right)} - 1 \right)}}{32} - \frac{5 \log{\left(\cos{\left(x \right)} + 1 \right)}}{32}"," ",0,"-(-15*cos(x)**5 + 40*cos(x)**3 - 33*cos(x))/(48*cos(x)**6 - 144*cos(x)**4 + 144*cos(x)**2 - 48) + 5*log(cos(x) - 1)/32 - 5*log(cos(x) + 1)/32","A",0
339,1,66,0,0.065686," ","integrate(1/cos(x)**12,x)","\frac{256 \sin{\left(x \right)}}{693 \cos{\left(x \right)}} + \frac{128 \sin{\left(x \right)}}{693 \cos^{3}{\left(x \right)}} + \frac{32 \sin{\left(x \right)}}{231 \cos^{5}{\left(x \right)}} + \frac{80 \sin{\left(x \right)}}{693 \cos^{7}{\left(x \right)}} + \frac{10 \sin{\left(x \right)}}{99 \cos^{9}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{11 \cos^{11}{\left(x \right)}}"," ",0,"256*sin(x)/(693*cos(x)) + 128*sin(x)/(693*cos(x)**3) + 32*sin(x)/(231*cos(x)**5) + 80*sin(x)/(693*cos(x)**7) + 10*sin(x)/(99*cos(x)**9) + sin(x)/(11*cos(x)**11)","A",0
340,1,388,0,1.305335," ","integrate(1/cos(1/4*pi+3*x)**3,x)","- \frac{\log{\left(\tan{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 1 \right)} \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 12 \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 6} + \frac{2 \log{\left(\tan{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 1 \right)} \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 12 \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 6} - \frac{\log{\left(\tan{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 1 \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 12 \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 6} + \frac{\log{\left(\tan{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 1 \right)} \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 12 \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 6} - \frac{2 \log{\left(\tan{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 1 \right)} \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 12 \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 6} + \frac{\log{\left(\tan{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 1 \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 12 \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 6} + \frac{2 \tan^{3}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 12 \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 6} + \frac{2 \tan{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)}}{6 \tan^{4}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} - 12 \tan^{2}{\left(\frac{3 x}{2} + \frac{\pi}{8} \right)} + 6}"," ",0,"-log(tan(3*x/2 + pi/8) - 1)*tan(3*x/2 + pi/8)**4/(6*tan(3*x/2 + pi/8)**4 - 12*tan(3*x/2 + pi/8)**2 + 6) + 2*log(tan(3*x/2 + pi/8) - 1)*tan(3*x/2 + pi/8)**2/(6*tan(3*x/2 + pi/8)**4 - 12*tan(3*x/2 + pi/8)**2 + 6) - log(tan(3*x/2 + pi/8) - 1)/(6*tan(3*x/2 + pi/8)**4 - 12*tan(3*x/2 + pi/8)**2 + 6) + log(tan(3*x/2 + pi/8) + 1)*tan(3*x/2 + pi/8)**4/(6*tan(3*x/2 + pi/8)**4 - 12*tan(3*x/2 + pi/8)**2 + 6) - 2*log(tan(3*x/2 + pi/8) + 1)*tan(3*x/2 + pi/8)**2/(6*tan(3*x/2 + pi/8)**4 - 12*tan(3*x/2 + pi/8)**2 + 6) + log(tan(3*x/2 + pi/8) + 1)/(6*tan(3*x/2 + pi/8)**4 - 12*tan(3*x/2 + pi/8)**2 + 6) + 2*tan(3*x/2 + pi/8)**3/(6*tan(3*x/2 + pi/8)**4 - 12*tan(3*x/2 + pi/8)**2 + 6) + 2*tan(3*x/2 + pi/8)/(6*tan(3*x/2 + pi/8)**4 - 12*tan(3*x/2 + pi/8)**2 + 6)","B",0
341,1,31,0,0.075587," ","integrate(tan(x)**6,x)","- x + \frac{\sin^{5}{\left(x \right)}}{5 \cos^{5}{\left(x \right)}} - \frac{\sin^{3}{\left(x \right)}}{3 \cos^{3}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}"," ",0,"-x + sin(x)**5/(5*cos(x)**5) - sin(x)**3/(3*cos(x)**3) + sin(x)/cos(x)","A",0
342,1,19,0,0.108463," ","integrate(1/tan(x)**5,x)","\frac{4 \sin^{2}{\left(x \right)} - 1}{4 \sin^{4}{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}"," ",0,"(4*sin(x)**2 - 1)/(4*sin(x)**4) + log(sin(x))","A",0
343,1,20,0,0.212886," ","integrate(cot(1/4*pi+1/3*x)**4,x)","x - \cot^{3}{\left(\frac{x}{3} + \frac{\pi}{4} \right)} + 3 \cot{\left(\frac{x}{3} + \frac{\pi}{4} \right)}"," ",0,"x - cot(x/3 + pi/4)**3 + 3*cot(x/3 + pi/4)","A",0
344,1,56,0,0.068085," ","integrate(cos(x)**6*sin(x)**4,x)","\frac{3 x}{256} + \frac{\sin{\left(x \right)} \cos^{9}{\left(x \right)}}{10} - \frac{11 \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{80} + \frac{\sin{\left(x \right)} \cos^{5}{\left(x \right)}}{160} + \frac{\sin{\left(x \right)} \cos^{3}{\left(x \right)}}{128} + \frac{3 \sin{\left(x \right)} \cos{\left(x \right)}}{256}"," ",0,"3*x/256 + sin(x)*cos(x)**9/10 - 11*sin(x)*cos(x)**7/80 + sin(x)*cos(x)**5/160 + sin(x)*cos(x)**3/128 + 3*sin(x)*cos(x)/256","A",0
345,1,27,0,0.071826," ","integrate(cos(x)**6*sin(x)**7,x)","\frac{\cos^{13}{\left(x \right)}}{13} - \frac{3 \cos^{11}{\left(x \right)}}{11} + \frac{\cos^{9}{\left(x \right)}}{3} - \frac{\cos^{7}{\left(x \right)}}{7}"," ",0,"cos(x)**13/13 - 3*cos(x)**11/11 + cos(x)**9/3 - cos(x)**7/7","A",0
346,1,44,0,0.098543," ","integrate(sin(x)**11/cos(x),x)","- \log{\left(\cos{\left(x \right)} \right)} + \frac{\cos^{10}{\left(x \right)}}{10} - \frac{5 \cos^{8}{\left(x \right)}}{8} + \frac{5 \cos^{6}{\left(x \right)}}{3} - \frac{5 \cos^{4}{\left(x \right)}}{2} + \frac{5 \cos^{2}{\left(x \right)}}{2}"," ",0,"-log(cos(x)) + cos(x)**10/10 - 5*cos(x)**8/8 + 5*cos(x)**6/3 - 5*cos(x)**4/2 + 5*cos(x)**2/2","A",0
347,1,44,0,0.076351," ","integrate(1/cos(x)**6/sin(x)**6,x)","- \frac{256 \cos{\left(2 x \right)}}{15 \sin{\left(2 x \right)}} - \frac{128 \cos{\left(2 x \right)}}{15 \sin^{3}{\left(2 x \right)}} - \frac{32 \cos{\left(2 x \right)}}{5 \sin^{5}{\left(2 x \right)}}"," ",0,"-256*cos(2*x)/(15*sin(2*x)) - 128*cos(2*x)/(15*sin(2*x)**3) - 32*cos(2*x)/(5*sin(2*x)**5)","A",0
348,1,14,0,0.072322," ","integrate(cos(x)**2*sin(x)**2,x)","\frac{x}{8} - \frac{\sin{\left(2 x \right)} \cos{\left(2 x \right)}}{16}"," ",0,"x/8 - sin(2*x)*cos(2*x)/16","A",0
349,1,31,0,0.073423," ","integrate(cos(x)**4*sin(x)**4,x)","\frac{3 x}{128} - \frac{\sin^{3}{\left(2 x \right)} \cos{\left(2 x \right)}}{128} - \frac{3 \sin{\left(2 x \right)} \cos{\left(2 x \right)}}{256}"," ",0,"3*x/128 - sin(2*x)**3*cos(2*x)/128 - 3*sin(2*x)*cos(2*x)/256","A",0
350,1,46,0,0.074793," ","integrate(cos(x)**6*sin(x)**6,x)","\frac{5 x}{1024} - \frac{\sin^{5}{\left(2 x \right)} \cos{\left(2 x \right)}}{768} - \frac{5 \sin^{3}{\left(2 x \right)} \cos{\left(2 x \right)}}{3072} - \frac{5 \sin{\left(2 x \right)} \cos{\left(2 x \right)}}{2048}"," ",0,"5*x/1024 - sin(2*x)**5*cos(2*x)/768 - 5*sin(2*x)**3*cos(2*x)/3072 - 5*sin(2*x)*cos(2*x)/2048","A",0
351,1,61,0,0.075771," ","integrate(cos(x)**8*sin(x)**8,x)","\frac{35 x}{32768} - \frac{\sin^{7}{\left(2 x \right)} \cos{\left(2 x \right)}}{4096} - \frac{7 \sin^{5}{\left(2 x \right)} \cos{\left(2 x \right)}}{24576} - \frac{35 \sin^{3}{\left(2 x \right)} \cos{\left(2 x \right)}}{98304} - \frac{35 \sin{\left(2 x \right)} \cos{\left(2 x \right)}}{65536}"," ",0,"35*x/32768 - sin(2*x)**7*cos(2*x)/4096 - 7*sin(2*x)**5*cos(2*x)/24576 - 35*sin(2*x)**3*cos(2*x)/98304 - 35*sin(2*x)*cos(2*x)/65536","A",0
352,0,0,0,0.000000," ","integrate(cos(x)**(2*m)*sin(x)**(2*m),x)","\int \sin^{2 m}{\left(x \right)} \cos^{2 m}{\left(x \right)}\, dx"," ",0,"Integral(sin(x)**(2*m)*cos(x)**(2*m), x)","F",0
353,1,54,0,1.655955," ","integrate(1/cos(1/4*pi+2*x)/sin(1/4*pi+2*x)**3,x)","- \frac{\log{\left(\tan{\left(x + \frac{\pi}{8} \right)} - 1 \right)}}{2} - \frac{\log{\left(\tan{\left(x + \frac{\pi}{8} \right)} + 1 \right)}}{2} + \frac{\log{\left(\tan{\left(x + \frac{\pi}{8} \right)} \right)}}{2} - \frac{\tan^{2}{\left(x + \frac{\pi}{8} \right)}}{16} - \frac{1}{16 \tan^{2}{\left(x + \frac{\pi}{8} \right)}}"," ",0,"-log(tan(x + pi/8) - 1)/2 - log(tan(x + pi/8) + 1)/2 + log(tan(x + pi/8))/2 - tan(x + pi/8)**2/16 - 1/(16*tan(x + pi/8)**2)","B",0
354,1,17,0,0.070210," ","integrate(sec(x)**2*tan(x)**2,x)","- \frac{\sin{\left(x \right)}}{3 \cos{\left(x \right)}} + \frac{\sin{\left(x \right)}}{3 \cos^{3}{\left(x \right)}}"," ",0,"-sin(x)/(3*cos(x)) + sin(x)/(3*cos(x)**3)","B",0
355,1,15,0,0.097878," ","integrate(cot(x)**3*csc(x),x)","- \frac{1 - 3 \sin^{2}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}}"," ",0,"-(1 - 3*sin(x)**2)/(3*sin(x)**3)","A",0
356,1,7,0,0.070551," ","integrate(sec(x)**3*tan(x),x)","\frac{1}{3 \cos^{3}{\left(x \right)}}"," ",0,"1/(3*cos(x)**3)","A",0
357,1,41,0,0.152132," ","integrate(cot(x)**2*csc(x)**3,x)","\frac{- \cos^{3}{\left(x \right)} - \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 8} - \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{16} + \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{16}"," ",0,"(-cos(x)**3 - cos(x))/(8*cos(x)**4 - 16*cos(x)**2 + 8) - log(cos(x) - 1)/16 + log(cos(x) + 1)/16","A",0
358,1,15,0,0.100766," ","integrate(cos(x)**3/sin(x)**7,x)","- \frac{2 - 3 \sin^{2}{\left(x \right)}}{12 \sin^{6}{\left(x \right)}}"," ",0,"-(2 - 3*sin(x)**2)/(12*sin(x)**6)","A",0
359,1,39,0,178.370394," ","integrate(sec(x)**(3/2)*tan(x)**5,x)","\frac{2 \tan^{4}{\left(x \right)} \sec^{\frac{3}{2}}{\left(x \right)}}{11} - \frac{16 \tan^{2}{\left(x \right)} \sec^{\frac{3}{2}}{\left(x \right)}}{77} + \frac{64 \sec^{\frac{3}{2}}{\left(x \right)}}{231}"," ",0,"2*tan(x)**4*sec(x)**(3/2)/11 - 16*tan(x)**2*sec(x)**(3/2)/77 + 64*sec(x)**(3/2)/231","A",0
360,0,0,0,0.000000," ","integrate(sec(x)**4*tan(x)**(3/2),x)","\int \tan^{\frac{3}{2}}{\left(x \right)} \sec^{4}{\left(x \right)}\, dx"," ",0,"Integral(tan(x)**(3/2)*sec(x)**4, x)","F",0
361,1,56,0,0.161556," ","integrate(cot(x)**4*csc(x)**3,x)","- \frac{- 3 \cos^{5}{\left(x \right)} - 8 \cos^{3}{\left(x \right)} + 3 \cos{\left(x \right)}}{48 \cos^{6}{\left(x \right)} - 144 \cos^{4}{\left(x \right)} + 144 \cos^{2}{\left(x \right)} - 48} + \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{32} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{32}"," ",0,"-(-3*cos(x)**5 - 8*cos(x)**3 + 3*cos(x))/(48*cos(x)**6 - 144*cos(x)**4 + 144*cos(x)**2 - 48) + log(cos(x) - 1)/32 - log(cos(x) + 1)/32","A",0
362,0,0,0,0.000000," ","integrate(sec(1/4*pi+1/2*x)**3*tan(1/4*pi+1/2*x)**2,x)","\int \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \sec^{3}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}\, dx"," ",0,"Integral(tan(x/2 + pi/4)**2*sec(x/2 + pi/4)**3, x)","F",0
363,-1,0,0,0.000000," ","integrate((1+cot(x)**3)*(a*sec(x)**2-sin(2*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,1,148,0,1.600130," ","integrate((4-3*cos(x))*(1-1/2*sin(x))**4,x)","\frac{3 x \sin^{4}{\left(x \right)}}{32} + \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} + 3 x \sin^{2}{\left(x \right)} + \frac{3 x \cos^{4}{\left(x \right)}}{32} + 3 x \cos^{2}{\left(x \right)} + 4 x - \frac{3 \sin^{5}{\left(x \right)}}{80} + \frac{3 \sin^{4}{\left(x \right)}}{8} - \frac{5 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{32} - \frac{3 \sin^{3}{\left(x \right)}}{2} + 2 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{32} - 3 \sin{\left(x \right)} \cos{\left(x \right)} - 3 \sin{\left(x \right)} + \frac{4 \cos^{3}{\left(x \right)}}{3} - 3 \cos^{2}{\left(x \right)} + 8 \cos{\left(x \right)}"," ",0,"3*x*sin(x)**4/32 + 3*x*sin(x)**2*cos(x)**2/16 + 3*x*sin(x)**2 + 3*x*cos(x)**4/32 + 3*x*cos(x)**2 + 4*x - 3*sin(x)**5/80 + 3*sin(x)**4/8 - 5*sin(x)**3*cos(x)/32 - 3*sin(x)**3/2 + 2*sin(x)**2*cos(x) - 3*sin(x)*cos(x)**3/32 - 3*sin(x)*cos(x) - 3*sin(x) + 4*cos(x)**3/3 - 3*cos(x)**2 + 8*cos(x)","A",0
365,1,39,0,0.584747," ","integrate((1/2-3*cot(x))*(3-2*cot(x))**3,x)","- \frac{285 x}{2} - 2 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} + 4 \log{\left(\tan{\left(x \right)} \right)} - \frac{156}{\tan{\left(x \right)}} + \frac{56}{\tan^{2}{\left(x \right)}} - \frac{8}{\tan^{3}{\left(x \right)}}"," ",0,"-285*x/2 - 2*log(tan(x)**2 + 1) + 4*log(tan(x)) - 156/tan(x) + 56/tan(x)**2 - 8/tan(x)**3","A",0
366,1,24,0,17.462060," ","integrate(cos(5*x)/cos(x)**5,x)","16 x - \frac{20 \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{5 \tan^{3}{\left(x \right)}}{3} + 5 \tan{\left(x \right)}"," ",0,"16*x - 20*sin(x)/cos(x) + 5*tan(x)**3/3 + 5*tan(x)","A",0
367,1,24,0,1.697624," ","integrate(cos(4*x)/cos(x),x)","- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} - \frac{8 \sin^{3}{\left(x \right)}}{3}"," ",0,"-log(sin(x) - 1)/2 + log(sin(x) + 1)/2 - 8*sin(x)**3/3","A",0
368,1,20,0,0.551332," ","integrate(cos(x)*cos(4*x),x)","- \frac{\sin{\left(x \right)} \cos{\left(4 x \right)}}{15} + \frac{4 \sin{\left(4 x \right)} \cos{\left(x \right)}}{15}"," ",0,"-sin(x)*cos(4*x)/15 + 4*sin(4*x)*cos(x)/15","A",0
369,1,75,0,17.154069," ","integrate(cos(4*x)/cos(x)**5,x)","- \frac{35 \log{\left(\sin{\left(x \right)} - 1 \right)}}{16} + \frac{35 \log{\left(\sin{\left(x \right)} + 1 \right)}}{16} - \frac{3 \sin^{3}{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} + \frac{5 \sin{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} + \frac{8 \sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2}"," ",0,"-35*log(sin(x) - 1)/16 + 35*log(sin(x) + 1)/16 - 3*sin(x)**3/(8*sin(x)**4 - 16*sin(x)**2 + 8) + 5*sin(x)/(8*sin(x)**4 - 16*sin(x)**2 + 8) + 8*sin(x)/(2*sin(x)**2 - 2)","B",0
370,1,139,0,24.528801," ","integrate(cos(x)**4*cos(4*x),x)","\frac{x \sin^{4}{\left(x \right)} \cos{\left(4 x \right)}}{16} - \frac{x \sin^{3}{\left(x \right)} \sin{\left(4 x \right)} \cos{\left(x \right)}}{4} - \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} \cos{\left(4 x \right)}}{8} + \frac{x \sin{\left(x \right)} \sin{\left(4 x \right)} \cos^{3}{\left(x \right)}}{4} + \frac{x \cos^{4}{\left(x \right)} \cos{\left(4 x \right)}}{16} - \frac{\sin^{4}{\left(x \right)} \sin{\left(4 x \right)}}{24} - \frac{5 \sin^{3}{\left(x \right)} \cos{\left(x \right)} \cos{\left(4 x \right)}}{48} - \frac{11 \sin{\left(x \right)} \cos^{3}{\left(x \right)} \cos{\left(4 x \right)}}{48} + \frac{7 \sin{\left(4 x \right)} \cos^{4}{\left(x \right)}}{24}"," ",0,"x*sin(x)**4*cos(4*x)/16 - x*sin(x)**3*sin(4*x)*cos(x)/4 - 3*x*sin(x)**2*cos(x)**2*cos(4*x)/8 + x*sin(x)*sin(4*x)*cos(x)**3/4 + x*cos(x)**4*cos(4*x)/16 - sin(x)**4*sin(4*x)/24 - 5*sin(x)**3*cos(x)*cos(4*x)/48 - 11*sin(x)*cos(x)**3*cos(4*x)/48 + 7*sin(4*x)*cos(x)**4/24","B",0
371,1,22,0,24.839165," ","integrate(cos(5*x)/sin(x)**5,x)","8 \log{\left(\sin^{2}{\left(x \right)} \right)} + \frac{6}{\sin^{2}{\left(x \right)}} - \frac{1}{4 \sin^{4}{\left(x \right)}}"," ",0,"8*log(sin(x)**2) + 6/sin(x)**2 - 1/(4*sin(x)**4)","A",0
372,1,14,0,5.887005," ","integrate(sin(4*x)/sin(x)**4,x)","- 8 \log{\left(\sin{\left(x \right)} \right)} - \frac{2}{\sin^{2}{\left(x \right)}}"," ",0,"-8*log(sin(x)) - 2/sin(x)**2","A",0
373,0,0,0,0.000000," ","integrate(cos(x)/sin(x)/(2+sin(2*x)),x)","\int \frac{\cos{\left(x \right)}}{\left(\sin{\left(2 x \right)} + 2\right) \sin{\left(x \right)}}\, dx"," ",0,"Integral(cos(x)/((sin(2*x) + 2)*sin(x)), x)","F",0
374,0,0,0,0.000000," ","integrate(cos(x)**2/cos(3*x)/sin(x),x)","\int \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} \cos{\left(3 x \right)}}\, dx"," ",0,"Integral(cos(x)**2/(sin(x)*cos(3*x)), x)","F",0
375,-1,0,0,0.000000," ","integrate(sin(2*x)/(cos(x)**4+sin(x)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,1,107,0,9.890781," ","integrate(1/(4+sin(x)+cos(x)*3**(1/2)),x)","- \frac{71049062919648516608727362362371223166654224256969 \sqrt{3} \left(\operatorname{atan}{\left(- \frac{\tan{\left(\frac{x}{2} \right)}}{2} + \frac{2 \sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} + \frac{\sqrt{3}}{6} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{-213147188758945549826182087087113669499962672770907 + 123060586806989187969890042718152127140914603059700 \sqrt{3}} + \frac{123060586806989187969890042718152127140914603059700 \left(\operatorname{atan}{\left(- \frac{\tan{\left(\frac{x}{2} \right)}}{2} + \frac{2 \sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} + \frac{\sqrt{3}}{6} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{-213147188758945549826182087087113669499962672770907 + 123060586806989187969890042718152127140914603059700 \sqrt{3}}"," ",0,"-71049062919648516608727362362371223166654224256969*sqrt(3)*(atan(-tan(x/2)/2 + 2*sqrt(3)*tan(x/2)/3 + sqrt(3)/6) + pi*floor((x/2 - pi/2)/pi))/(-213147188758945549826182087087113669499962672770907 + 123060586806989187969890042718152127140914603059700*sqrt(3)) + 123060586806989187969890042718152127140914603059700*(atan(-tan(x/2)/2 + 2*sqrt(3)*tan(x/2)/3 + sqrt(3)/6) + pi*floor((x/2 - pi/2)/pi))/(-213147188758945549826182087087113669499962672770907 + 123060586806989187969890042718152127140914603059700*sqrt(3))","B",0
377,1,39,0,0.590583," ","integrate(1/(3+4*cos(x)+4*sin(x)),x)","\frac{\sqrt{23} \log{\left(\tan{\left(\frac{x}{2} \right)} - 4 + \sqrt{23} \right)}}{23} - \frac{\sqrt{23} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{23} - 4 \right)}}{23}"," ",0,"sqrt(23)*log(tan(x/2) - 4 + sqrt(23))/23 - sqrt(23)*log(tan(x/2) - sqrt(23) - 4)/23","A",0
378,1,219,0,13.650721," ","integrate(1/(4-3*cos(x)**2+5*sin(x)**2),x)","\frac{4478554083 \sqrt{17 - 12 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{17 - 12 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2305195203 + 1630019160 \sqrt{2}} + \frac{3166815962 \sqrt{2} \sqrt{17 - 12 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{17 - 12 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2305195203 + 1630019160 \sqrt{2}} + \frac{131836323 \sqrt{12 \sqrt{2} + 17} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{12 \sqrt{2} + 17}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2305195203 + 1630019160 \sqrt{2}} + \frac{93222358 \sqrt{2} \sqrt{12 \sqrt{2} + 17} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{12 \sqrt{2} + 17}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2305195203 + 1630019160 \sqrt{2}}"," ",0,"4478554083*sqrt(17 - 12*sqrt(2))*(atan(tan(x/2)/sqrt(17 - 12*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(2305195203 + 1630019160*sqrt(2)) + 3166815962*sqrt(2)*sqrt(17 - 12*sqrt(2))*(atan(tan(x/2)/sqrt(17 - 12*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(2305195203 + 1630019160*sqrt(2)) + 131836323*sqrt(12*sqrt(2) + 17)*(atan(tan(x/2)/sqrt(12*sqrt(2) + 17)) + pi*floor((x/2 - pi/2)/pi))/(2305195203 + 1630019160*sqrt(2)) + 93222358*sqrt(2)*sqrt(12*sqrt(2) + 17)*(atan(tan(x/2)/sqrt(12*sqrt(2) + 17)) + pi*floor((x/2 - pi/2)/pi))/(2305195203 + 1630019160*sqrt(2))","B",0
379,1,102,0,0.491695," ","integrate(1/(4+4*cot(x)+tan(x)),x)","\frac{8 x \tan{\left(x \right)}}{50 \tan{\left(x \right)} + 100} + \frac{16 x}{50 \tan{\left(x \right)} + 100} - \frac{6 \log{\left(\tan{\left(x \right)} + 2 \right)} \tan{\left(x \right)}}{50 \tan{\left(x \right)} + 100} - \frac{12 \log{\left(\tan{\left(x \right)} + 2 \right)}}{50 \tan{\left(x \right)} + 100} + \frac{3 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan{\left(x \right)}}{50 \tan{\left(x \right)} + 100} + \frac{6 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{50 \tan{\left(x \right)} + 100} + \frac{20}{50 \tan{\left(x \right)} + 100}"," ",0,"8*x*tan(x)/(50*tan(x) + 100) + 16*x/(50*tan(x) + 100) - 6*log(tan(x) + 2)*tan(x)/(50*tan(x) + 100) - 12*log(tan(x) + 2)/(50*tan(x) + 100) + 3*log(tan(x)**2 + 1)*tan(x)/(50*tan(x) + 100) + 6*log(tan(x)**2 + 1)/(50*tan(x) + 100) + 20/(50*tan(x) + 100)","B",0
380,0,0,0,0.000000," ","integrate(1/(2*sec(x)+sin(x))**2,x)","\int \frac{1}{\left(\sin{\left(x \right)} + 2 \sec{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((sin(x) + 2*sec(x))**(-2), x)","F",0
381,0,0,0,0.000000," ","integrate(1/(cos(x)+2*sec(x))**2,x)","\int \frac{1}{\left(\cos{\left(x \right)} + 2 \sec{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((cos(x) + 2*sec(x))**(-2), x)","F",0
382,1,252,0,0.560624," ","integrate((5-tan(x)-6*tan(x)**2)/(1+3*tan(x))**3,x)","- \frac{603 x \tan^{2}{\left(x \right)}}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} - \frac{402 x \tan{\left(x \right)}}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} - \frac{67 x}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} - \frac{504 \log{\left(\tan{\left(x \right)} + \frac{1}{3} \right)} \tan^{2}{\left(x \right)}}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} - \frac{336 \log{\left(\tan{\left(x \right)} + \frac{1}{3} \right)} \tan{\left(x \right)}}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} - \frac{56 \log{\left(\tan{\left(x \right)} + \frac{1}{3} \right)}}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} + \frac{252 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)}}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} + \frac{168 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan{\left(x \right)}}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} + \frac{28 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} - \frac{435 \tan{\left(x \right)}}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250} - \frac{320}{2250 \tan^{2}{\left(x \right)} + 1500 \tan{\left(x \right)} + 250}"," ",0,"-603*x*tan(x)**2/(2250*tan(x)**2 + 1500*tan(x) + 250) - 402*x*tan(x)/(2250*tan(x)**2 + 1500*tan(x) + 250) - 67*x/(2250*tan(x)**2 + 1500*tan(x) + 250) - 504*log(tan(x) + 1/3)*tan(x)**2/(2250*tan(x)**2 + 1500*tan(x) + 250) - 336*log(tan(x) + 1/3)*tan(x)/(2250*tan(x)**2 + 1500*tan(x) + 250) - 56*log(tan(x) + 1/3)/(2250*tan(x)**2 + 1500*tan(x) + 250) + 252*log(tan(x)**2 + 1)*tan(x)**2/(2250*tan(x)**2 + 1500*tan(x) + 250) + 168*log(tan(x)**2 + 1)*tan(x)/(2250*tan(x)**2 + 1500*tan(x) + 250) + 28*log(tan(x)**2 + 1)/(2250*tan(x)**2 + 1500*tan(x) + 250) - 435*tan(x)/(2250*tan(x)**2 + 1500*tan(x) + 250) - 320/(2250*tan(x)**2 + 1500*tan(x) + 250)","B",0
383,1,76,0,5.464135," ","integrate(cos(x)**2/cos(3*x),x)","- \frac{\log{\left(\sin{\left(3 x \right)} - 1 \right)}}{12} + \frac{\log{\left(\sin{\left(3 x \right)} + 1 \right)}}{12} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{6} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{6} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 4 \tan{\left(\frac{x}{2} \right)} + 1 \right)}}{12} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)} + 1 \right)}}{12}"," ",0,"-log(sin(3*x) - 1)/12 + log(sin(3*x) + 1)/12 - log(tan(x/2) - 1)/6 + log(tan(x/2) + 1)/6 - log(tan(x/2)**2 - 4*tan(x/2) + 1)/12 + log(tan(x/2)**2 + 4*tan(x/2) + 1)/12","B",0
384,0,0,0,0.000000," ","integrate(sin(x)/cos(2*x),x)","\int \frac{\sin{\left(x \right)}}{\cos{\left(2 x \right)}}\, dx"," ",0,"Integral(sin(x)/cos(2*x), x)","F",0
385,1,22,0,1.128433," ","integrate(sin(x)**2/cos(2*x),x)","- \frac{x}{2} - \frac{\log{\left(\sin{\left(2 x \right)} - 1 \right)}}{8} + \frac{\log{\left(\sin{\left(2 x \right)} + 1 \right)}}{8}"," ",0,"-x/2 - log(sin(2*x) - 1)/8 + log(sin(2*x) + 1)/8","A",0
386,0,0,0,0.000000," ","integrate(sin(x)**3/cos(3*x),x)","\int \frac{\sin^{3}{\left(x \right)}}{\cos{\left(3 x \right)}}\, dx"," ",0,"Integral(sin(x)**3/cos(3*x), x)","F",0
387,1,17,0,1.334461," ","integrate(cos(x)/sin(3*x),x)","- \frac{\log{\left(4 \sin^{2}{\left(x \right)} - 3 \right)}}{6} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{3}"," ",0,"-log(4*sin(x)**2 - 3)/6 + log(sin(x))/3","A",0
388,1,294,0,8.135118," ","integrate(sin(x)/sin(4*x),x)","\frac{27720 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{110880 \sqrt{2} + 156808} + \frac{39202 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{39202 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{27720 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{110880 \sqrt{2} + 156808} + \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} + \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} + \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} + \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} - \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{110880 \sqrt{2} + 156808}"," ",0,"27720*sqrt(2)*log(tan(x/2) - 1)/(110880*sqrt(2) + 156808) + 39202*log(tan(x/2) - 1)/(110880*sqrt(2) + 156808) - 39202*log(tan(x/2) + 1)/(110880*sqrt(2) + 156808) - 27720*sqrt(2)*log(tan(x/2) + 1)/(110880*sqrt(2) + 156808) + 27720*log(tan(x/2) - 1 + sqrt(2))/(110880*sqrt(2) + 156808) + 19601*sqrt(2)*log(tan(x/2) - 1 + sqrt(2))/(110880*sqrt(2) + 156808) + 27720*log(tan(x/2) + 1 + sqrt(2))/(110880*sqrt(2) + 156808) + 19601*sqrt(2)*log(tan(x/2) + 1 + sqrt(2))/(110880*sqrt(2) + 156808) - 19601*sqrt(2)*log(tan(x/2) - sqrt(2) - 1)/(110880*sqrt(2) + 156808) - 27720*log(tan(x/2) - sqrt(2) - 1)/(110880*sqrt(2) + 156808) - 19601*sqrt(2)*log(tan(x/2) - sqrt(2) + 1)/(110880*sqrt(2) + 156808) - 27720*log(tan(x/2) - sqrt(2) + 1)/(110880*sqrt(2) + 156808)","B",0
389,1,294,0,20.128572," ","integrate(sin(x)**3/sin(4*x),x)","\frac{4093147632754948 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} + \frac{2894292447518688 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} - \frac{4093147632754948 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} - \frac{2894292447518688 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} + \frac{1447146223759344 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} + \frac{1023286908188737 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} + \frac{1447146223759344 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} + \frac{1023286908188737 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} - \frac{1447146223759344 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} - \frac{1023286908188737 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} - \frac{1447146223759344 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}} - \frac{1023286908188737 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{16372590531019792 + 11577169790074752 \sqrt{2}}"," ",0,"4093147632754948*log(tan(x/2) - 1)/(16372590531019792 + 11577169790074752*sqrt(2)) + 2894292447518688*sqrt(2)*log(tan(x/2) - 1)/(16372590531019792 + 11577169790074752*sqrt(2)) - 4093147632754948*log(tan(x/2) + 1)/(16372590531019792 + 11577169790074752*sqrt(2)) - 2894292447518688*sqrt(2)*log(tan(x/2) + 1)/(16372590531019792 + 11577169790074752*sqrt(2)) + 1447146223759344*log(tan(x/2) - 1 + sqrt(2))/(16372590531019792 + 11577169790074752*sqrt(2)) + 1023286908188737*sqrt(2)*log(tan(x/2) - 1 + sqrt(2))/(16372590531019792 + 11577169790074752*sqrt(2)) + 1447146223759344*log(tan(x/2) + 1 + sqrt(2))/(16372590531019792 + 11577169790074752*sqrt(2)) + 1023286908188737*sqrt(2)*log(tan(x/2) + 1 + sqrt(2))/(16372590531019792 + 11577169790074752*sqrt(2)) - 1447146223759344*log(tan(x/2) - sqrt(2) - 1)/(16372590531019792 + 11577169790074752*sqrt(2)) - 1023286908188737*sqrt(2)*log(tan(x/2) - sqrt(2) - 1)/(16372590531019792 + 11577169790074752*sqrt(2)) - 1447146223759344*log(tan(x/2) - sqrt(2) + 1)/(16372590531019792 + 11577169790074752*sqrt(2)) - 1023286908188737*sqrt(2)*log(tan(x/2) - sqrt(2) + 1)/(16372590531019792 + 11577169790074752*sqrt(2))","B",0
390,0,0,0,0.000000," ","integrate((1+sin(2*x))**(1/2),x)","\int \sqrt{\sin{\left(2 x \right)} + 1}\, dx"," ",0,"Integral(sqrt(sin(2*x) + 1), x)","F",0
391,0,0,0,0.000000," ","integrate((1-sin(2*x))**(1/2),x)","\int \sqrt{1 - \sin{\left(2 x \right)}}\, dx"," ",0,"Integral(sqrt(1 - sin(2*x)), x)","F",0
392,0,0,0,0.000000," ","integrate(1/(1+cos(2*x))**(1/2),x)","\int \frac{1}{\sqrt{\cos{\left(2 x \right)} + 1}}\, dx"," ",0,"Integral(1/sqrt(cos(2*x) + 1), x)","F",0
393,0,0,0,0.000000," ","integrate(1/(1-cos(2*x))**(1/2),x)","\int \frac{1}{\sqrt{1 - \cos{\left(2 x \right)}}}\, dx"," ",0,"Integral(1/sqrt(1 - cos(2*x)), x)","F",0
394,0,0,0,0.000000," ","integrate(1/(1-cos(3*x))**(3/2),x)","\int \frac{1}{\left(1 - \cos{\left(3 x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((1 - cos(3*x))**(-3/2), x)","F",0
395,0,0,0,0.000000," ","integrate((1-sin(2/3*x))**(5/2),x)","\int \left(1 - \sin{\left(\frac{2 x}{3} \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((1 - sin(2*x/3))**(5/2), x)","F",0
396,-1,0,0,0.000000," ","integrate(cos(x)*(-cos(x)**2+2*(1+2*sin(x))**(1/4))/(1+2*sin(x))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,0,0,0,0.000000," ","integrate(tan(x)**(1/2),x)","\int \sqrt{\tan{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(tan(x)), x)","F",0
398,0,0,0,0.000000," ","integrate(1/tan(5*x)**(1/3),x)","\int \frac{1}{\sqrt[3]{\tan{\left(5 x \right)}}}\, dx"," ",0,"Integral(tan(5*x)**(-1/3), x)","F",0
399,0,0,0,0.000000," ","integrate(1/(4+3*tan(2*x))**(3/2),x)","\int \frac{1}{\left(3 \tan{\left(2 x \right)} + 4\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((3*tan(2*x) + 4)**(-3/2), x)","F",0
400,0,0,0,0.000000," ","integrate((-(4-3*tan(x))**(1/2)+3*tan(x))/cos(x)**2/(4-3*tan(x))**(3/2),x)","- \int \frac{\sqrt{4 - 3 \tan{\left(x \right)}}}{- 3 \sqrt{4 - 3 \tan{\left(x \right)}} \cos^{2}{\left(x \right)} \tan{\left(x \right)} + 4 \sqrt{4 - 3 \tan{\left(x \right)}} \cos^{2}{\left(x \right)}}\, dx - \int \left(- \frac{3 \tan{\left(x \right)}}{- 3 \sqrt{4 - 3 \tan{\left(x \right)}} \cos^{2}{\left(x \right)} \tan{\left(x \right)} + 4 \sqrt{4 - 3 \tan{\left(x \right)}} \cos^{2}{\left(x \right)}}\right)\, dx"," ",0,"-Integral(sqrt(4 - 3*tan(x))/(-3*sqrt(4 - 3*tan(x))*cos(x)**2*tan(x) + 4*sqrt(4 - 3*tan(x))*cos(x)**2), x) - Integral(-3*tan(x)/(-3*sqrt(4 - 3*tan(x))*cos(x)**2*tan(x) + 4*sqrt(4 - 3*tan(x))*cos(x)**2), x)","F",0
401,0,0,0,0.000000," ","integrate(tan(x)/(-1+tan(x)**(1/2))**2,x)","\int \frac{\tan{\left(x \right)}}{\left(\sqrt{\tan{\left(x \right)}} - 1\right)^{2}}\, dx"," ",0,"Integral(tan(x)/(sqrt(tan(x)) - 1)**2, x)","F",0
402,-1,0,0,0.000000," ","integrate(sin(x)/sin(2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate(cos(x)/sin(2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,-1,0,0,0.000000," ","integrate(sin(x)*sin(2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,-1,0,0,0.000000," ","integrate((cos(x)-sin(x))*sin(2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,-1,0,0,0.000000," ","integrate(sin(x)**7/sin(2*x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
407,-1,0,0,0.000000," ","integrate(cos(x)**7/sin(2*x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
408,-1,0,0,0.000000," ","integrate(sin(2*x)**(3/2)/sin(x)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate(1/cos(x)**3/sin(2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate(1/sin(x)/sin(2*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(cos(x)**3*(cos(2*x)-3*tan(x))/(sin(x)**2-sin(2*x))/sin(2*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate((sin(x)/cos(x)**5)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,0,0,0,0.000000," ","integrate((sin(x)**5/cos(x))**(1/2),x)","\int \sqrt{\frac{\sin^{5}{\left(x \right)}}{\cos{\left(x \right)}}}\, dx"," ",0,"Integral(sqrt(sin(x)**5/cos(x)), x)","F",0
414,-1,0,0,0.000000," ","integrate((sin(x)**2/cos(x)**14)**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,-1,0,0,0.000000," ","integrate(1/(cos(x)**11*sin(x)**13)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate((cos(2*x)-sin(2*x)**(1/2))/(cos(x)**3*sin(x))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-1,0,0,0.000000," ","integrate((-2*sin(2*x)+(cos(x)*sin(x)**3)**(1/2))/(-(cos(x)**3*sin(x))**(1/2)+tan(x)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,-1,0,0,0.000000," ","integrate(((sin(x)/cos(x)**7)**(1/3)-3*tan(x))/(cos(x)**5*sin(x))**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,-1,0,0,0.000000," ","integrate((1+2*cos(x)**2)**(5/2)*sin(x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,-1,0,0,0.000000," ","integrate(cos(x)*(5*cos(x)**2+sin(x)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,-1,0,0,0.000000," ","integrate(cos(x)*(-cos(x)**2-5*sin(x)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,-1,0,0,0.000000," ","integrate(sin(x)/(5*cos(x)**2-2*sin(x)**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-1,0,0,0.000000," ","integrate(cos(x)*cos(2*x)/(2-5*sin(x)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate(sin(5*x)/(5*cos(x)**2+9*sin(x)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate(cos(x)*cos(2*x)*sin(3*x)/(-5+4*sin(x)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate((-2*cos(x)**3*(-1+sin(x))+cos(2*x)*sin(x))/sin(x)**2/(-5+sin(x)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,0,0,0,0.000000," ","integrate(cos(3*x)/(-(-1+8*cos(x)**2)**(1/2)+(3*cos(x)**2-sin(x)**2)**(1/2)),x)","\int \frac{\cos{\left(3 x \right)}}{\sqrt{- \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}} - \sqrt{8 \cos^{2}{\left(x \right)} - 1}}\, dx"," ",0,"Integral(cos(3*x)/(sqrt(-sin(x)**2 + 3*cos(x)**2) - sqrt(8*cos(x)**2 - 1)), x)","F",0
428,-1,0,0,0.000000," ","integrate((2-3*sin(x)**2)**(3/5)*sin(4*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,0,0,0,0.000000," ","integrate(cos(x)*cos(2*x)**(1/2),x)","\int \cos{\left(x \right)} \sqrt{\cos{\left(2 x \right)}}\, dx"," ",0,"Integral(cos(x)*sqrt(cos(2*x)), x)","F",0
430,-1,0,0,0.000000," ","integrate(cos(2*x)**(3/2)*sin(x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,0,0,0,0.000000," ","integrate(sin(x)/cos(2*x)**(5/2),x)","\int \frac{\sin{\left(x \right)}}{\cos^{\frac{5}{2}}{\left(2 x \right)}}\, dx"," ",0,"Integral(sin(x)/cos(2*x)**(5/2), x)","F",0
432,-1,0,0,0.000000," ","integrate(cos(2*x)**(3/2)/cos(x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((3*sin(x)**3-cos(x)*sin(4*x))/cos(2*x)**(7/2)/csc(x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,0,0,0,0.000000," ","integrate((4-5*sec(x)**2)**(3/2),x)","\int \left(4 - 5 \sec^{2}{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((4 - 5*sec(x)**2)**(3/2), x)","F",0
435,0,0,0,0.000000," ","integrate(1/(4-5*sec(x)**2)**(3/2),x)","\int \frac{1}{\left(4 - 5 \sec^{2}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((4 - 5*sec(x)**2)**(-3/2), x)","F",0
436,0,0,0,0.000000," ","integrate((-2*cot(x)**2+sin(x))/(1+5*tan(x)**2)**(3/2),x)","- \int \left(- \frac{\sin{\left(x \right)}}{5 \sqrt{5 \tan^{2}{\left(x \right)} + 1} \tan^{2}{\left(x \right)} + \sqrt{5 \tan^{2}{\left(x \right)} + 1}}\right)\, dx - \int \frac{2 \cot^{2}{\left(x \right)}}{5 \sqrt{5 \tan^{2}{\left(x \right)} + 1} \tan^{2}{\left(x \right)} + \sqrt{5 \tan^{2}{\left(x \right)} + 1}}\, dx"," ",0,"-Integral(-sin(x)/(5*sqrt(5*tan(x)**2 + 1)*tan(x)**2 + sqrt(5*tan(x)**2 + 1)), x) - Integral(2*cot(x)**2/(5*sqrt(5*tan(x)**2 + 1)*tan(x)**2 + sqrt(5*tan(x)**2 + 1)), x)","F",0
437,0,0,0,0.000000," ","integrate((-3+cos(2*x))/cos(x)**4/(4-cot(x)**2)**(1/2),x)","\int \frac{\cos{\left(2 x \right)} - 3}{\sqrt{- \left(\cot{\left(x \right)} - 2\right) \left(\cot{\left(x \right)} + 2\right)} \cos^{4}{\left(x \right)}}\, dx"," ",0,"Integral((cos(2*x) - 3)/(sqrt(-(cot(x) - 2)*(cot(x) + 2))*cos(x)**4), x)","F",0
438,-1,0,0,0.000000," ","integrate((3+sin(x)**2)*tan(x)**3/(-2+cos(x)**2)/(5-4*sec(x)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate((sec(x)**2-3*(4*sec(x)**2+5*tan(x)**2)**(1/2)*tan(x))/sin(x)**2/(4*sec(x)**2+5*tan(x)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,0,0,0,0.000000," ","integrate(tan(x)*(1+5*tan(x)**2)**(5/2),x)","\int \left(5 \tan^{2}{\left(x \right)} + 1\right)^{\frac{5}{2}} \tan{\left(x \right)}\, dx"," ",0,"Integral((5*tan(x)**2 + 1)**(5/2)*tan(x), x)","F",0
441,1,46,0,8.112399," ","integrate(tan(x)/(1+5*tan(x)**2)**(5/2),x)","\frac{\operatorname{atan}{\left(\frac{\sqrt{5 \tan^{2}{\left(x \right)} + 1}}{2} \right)}}{32} + \frac{1}{16 \sqrt{5 \tan^{2}{\left(x \right)} + 1}} - \frac{1}{12 \left(5 \tan^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}}}"," ",0,"atan(sqrt(5*tan(x)**2 + 1)/2)/32 + 1/(16*sqrt(5*tan(x)**2 + 1)) - 1/(12*(5*tan(x)**2 + 1)**(3/2))","A",0
442,0,0,0,0.000000," ","integrate(tan(x)/(a**3+b**3*tan(x)**2)**(1/3),x)","\int \frac{\tan{\left(x \right)}}{\sqrt[3]{a^{3} + b^{3} \tan^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(tan(x)/(a**3 + b**3*tan(x)**2)**(1/3), x)","F",0
443,0,0,0,0.000000," ","integrate(tan(x)*(1-7*tan(x)**2)**(2/3),x)","\int \left(1 - 7 \tan^{2}{\left(x \right)}\right)^{\frac{2}{3}} \tan{\left(x \right)}\, dx"," ",0,"Integral((1 - 7*tan(x)**2)**(2/3)*tan(x), x)","F",0
444,0,0,0,0.000000," ","integrate(cot(x)/(a**4+b**4*csc(x)**2)**(1/4),x)","\int \frac{\cot{\left(x \right)}}{\sqrt[4]{a^{4} + b^{4} \csc^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(cot(x)/(a**4 + b**4*csc(x)**2)**(1/4), x)","F",0
445,0,0,0,0.000000," ","integrate(cot(x)/(a**4-b**4*csc(x)**2)**(1/4),x)","\int \frac{\cot{\left(x \right)}}{\sqrt[4]{\left(a^{2} - b^{2} \csc{\left(x \right)}\right) \left(a^{2} + b^{2} \csc{\left(x \right)}\right)}}\, dx"," ",0,"Integral(cot(x)/((a**2 - b**2*csc(x))*(a**2 + b**2*csc(x)))**(1/4), x)","F",0
446,-1,0,0,0.000000," ","integrate(tan(x)*((1-3*sec(x)**2)**(1/3)*sin(x)**2+3*tan(x)**2)/cos(x)**2/(1-3*sec(x)**2)**(5/6)/(1-(1-3*sec(x)**2)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,-1,0,0,0.000000," ","integrate((-cos(2*x)+2*tan(x)**2)/cos(x)**2/(tan(x)*tan(2*x))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,0,0,0,0.000000," ","integrate(tan(x)/(a**3-b**3*cos(x)**n)**(4/3),x)","\int \frac{\tan{\left(x \right)}}{\left(a^{3} - b^{3} \cos^{n}{\left(x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(tan(x)/(a**3 - b**3*cos(x)**n)**(4/3), x)","F",0
449,-1,0,0,0.000000," ","integrate((1+2*cos(x)**9)**(5/6)*tan(x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate(cot(x)*sin(x)**9/(2-5*sin(x)**3)**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,0,0,0,0.000000," ","integrate(tan(x)*(1+(1-8*tan(x)**2)**(1/3))/cos(x)**2/(1-8*tan(x)**2)**(2/3),x)","\int \frac{\left(\sqrt[3]{1 - 8 \tan^{2}{\left(x \right)}} + 1\right) \tan{\left(x \right)}}{\left(1 - 8 \tan^{2}{\left(x \right)}\right)^{\frac{2}{3}} \cos^{2}{\left(x \right)}}\, dx"," ",0,"Integral(((1 - 8*tan(x)**2)**(1/3) + 1)*tan(x)/((1 - 8*tan(x)**2)**(2/3)*cos(x)**2), x)","F",0
452,0,0,0,0.000000," ","integrate(cot(x)*(1+(1-8*tan(x)**2)**(1/3))/cos(x)**2/(1-8*tan(x)**2)**(2/3),x)","\int \frac{\left(\sqrt[3]{1 - 8 \tan^{2}{\left(x \right)}} + 1\right) \cot{\left(x \right)}}{\left(1 - 8 \tan^{2}{\left(x \right)}\right)^{\frac{2}{3}} \cos^{2}{\left(x \right)}}\, dx"," ",0,"Integral(((1 - 8*tan(x)**2)**(1/3) + 1)*cot(x)/((1 - 8*tan(x)**2)**(2/3)*cos(x)**2), x)","F",0
453,0,0,0,0.000000," ","integrate((5*cos(x)**2-(-1+5*sin(x)**2)**(1/2))*tan(x)/(-1+5*sin(x)**2)**(1/4)/(2+(-1+5*sin(x)**2)**(1/2)),x)","\int \frac{\left(- \sqrt{5 \sin^{2}{\left(x \right)} - 1} + 5 \cos^{2}{\left(x \right)}\right) \tan{\left(x \right)}}{\left(\sqrt{5 \sin^{2}{\left(x \right)} - 1} + 2\right) \sqrt[4]{5 \sin^{2}{\left(x \right)} - 1}}\, dx"," ",0,"Integral((-sqrt(5*sin(x)**2 - 1) + 5*cos(x)**2)*tan(x)/((sqrt(5*sin(x)**2 - 1) + 2)*(5*sin(x)**2 - 1)**(1/4)), x)","F",0
454,-1,0,0,0.000000," ","integrate(cos(x)**4*cos(2*x)**(2/3)*tan(x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
455,-1,0,0,0.000000," ","integrate(sin(x)**6*tan(x)/cos(2*x)**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,0,0,0,0.000000," ","integrate((tan(x)*tan(2*x))**(1/2),x)","\int \sqrt{\tan{\left(x \right)} \tan{\left(2 x \right)}}\, dx"," ",0,"Integral(sqrt(tan(x)*tan(2*x)), x)","F",0
457,0,0,0,0.000000," ","integrate((cot(2*x)/cot(x))**(1/2),x)","\int \sqrt{\frac{\cot{\left(2 x \right)}}{\cot{\left(x \right)}}}\, dx"," ",0,"Integral(sqrt(cot(2*x)/cot(x)), x)","F",0
458,1,24,0,0.118140," ","integrate(1/x**5/(x**2+5),x)","\frac{\log{\left(x \right)}}{125} - \frac{\log{\left(x^{2} + 5 \right)}}{250} + \frac{2 x^{2} - 5}{100 x^{4}}"," ",0,"log(x)/125 - log(x**2 + 5)/250 + (2*x**2 - 5)/(100*x**4)","A",0
459,1,32,0,0.133233," ","integrate(1/x**6/(x**2+5),x)","- \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} \right)}}{625} + \frac{- 3 x^{4} + 5 x^{2} - 15}{375 x^{5}}"," ",0,"-sqrt(5)*atan(sqrt(5)*x/5)/625 + (-3*x**4 + 5*x**2 - 15)/(375*x**5)","A",0
460,1,41,0,0.158367," ","integrate(1/x/(x**2-4)**4,x)","\frac{- 3 x^{4} + 30 x^{2} - 88}{384 x^{6} - 4608 x^{4} + 18432 x^{2} - 24576} + \frac{\log{\left(x \right)}}{256} - \frac{\log{\left(x^{2} - 4 \right)}}{512}"," ",0,"(-3*x**4 + 30*x**2 - 88)/(384*x**6 - 4608*x**4 + 18432*x**2 - 24576) + log(x)/256 - log(x**2 - 4)/512","A",0
461,1,986,0,3.827019," ","integrate(1/x/(x**2-2)**(5/2),x)","\begin{cases} - \frac{6 i x^{4} \log{\left(x \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{3 i x^{4} \log{\left(x^{2} \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{6 x^{4} \operatorname{asin}{\left(\frac{\sqrt{2}}{x} \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{6 \sqrt{2} x^{2} \sqrt{x^{2} - 2}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{24 i x^{2} \log{\left(x \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{12 i x^{2} \log{\left(x^{2} \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{24 x^{2} \operatorname{asin}{\left(\frac{\sqrt{2}}{x} \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{16 \sqrt{2} \sqrt{x^{2} - 2}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{24 i \log{\left(x \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{12 i \log{\left(x^{2} \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{24 \operatorname{asin}{\left(\frac{\sqrt{2}}{x} \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} & \text{for}\: \frac{\left|{x^{2}}\right|}{2} > 1 \\\frac{3 i x^{4} \log{\left(x^{2} \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{6 i x^{4} \log{\left(\sqrt{1 - \frac{x^{2}}{2}} + 1 \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{3 \pi x^{4}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{3 i x^{4} \log{\left(2 \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{6 \sqrt{2} i x^{2} \sqrt{2 - x^{2}}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{12 i x^{2} \log{\left(x^{2} \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{24 i x^{2} \log{\left(\sqrt{1 - \frac{x^{2}}{2}} + 1 \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{12 \pi x^{2}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{12 i x^{2} \log{\left(2 \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{16 \sqrt{2} i \sqrt{2 - x^{2}}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{12 i \log{\left(x^{2} \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{24 i \log{\left(\sqrt{1 - \frac{x^{2}}{2}} + 1 \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} + \frac{12 \pi}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} - \frac{12 i \log{\left(2 \right)}}{- 24 \sqrt{2} x^{4} + 96 \sqrt{2} x^{2} - 96 \sqrt{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*I*x**4*log(x)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 3*I*x**4*log(x**2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 6*x**4*asin(sqrt(2)/x)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 6*sqrt(2)*x**2*sqrt(x**2 - 2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 24*I*x**2*log(x)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 12*I*x**2*log(x**2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 24*x**2*asin(sqrt(2)/x)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 16*sqrt(2)*sqrt(x**2 - 2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 24*I*log(x)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 12*I*log(x**2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 24*asin(sqrt(2)/x)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)), Abs(x**2)/2 > 1), (3*I*x**4*log(x**2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 6*I*x**4*log(sqrt(1 - x**2/2) + 1)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 3*pi*x**4/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 3*I*x**4*log(2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 6*sqrt(2)*I*x**2*sqrt(2 - x**2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 12*I*x**2*log(x**2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 24*I*x**2*log(sqrt(1 - x**2/2) + 1)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 12*pi*x**2/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 12*I*x**2*log(2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 16*sqrt(2)*I*sqrt(2 - x**2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 12*I*log(x**2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 24*I*log(sqrt(1 - x**2/2) + 1)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) + 12*pi/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)) - 12*I*log(2)/(-24*sqrt(2)*x**4 + 96*sqrt(2)*x**2 - 96*sqrt(2)), True))","C",0
462,1,167,0,5.545397," ","integrate((x**2-10)**(5/2)/x,x)","\begin{cases} \frac{x^{4} \sqrt{x^{2} - 10}}{5} - \frac{22 x^{2} \sqrt{x^{2} - 10}}{3} + \frac{460 \sqrt{x^{2} - 10}}{3} - 100 \sqrt{10} i \log{\left(x \right)} + 50 \sqrt{10} i \log{\left(x^{2} \right)} + 100 \sqrt{10} \operatorname{asin}{\left(\frac{\sqrt{10}}{x} \right)} & \text{for}\: \frac{\left|{x^{2}}\right|}{10} > 1 \\\frac{i x^{4} \sqrt{10 - x^{2}}}{5} - \frac{22 i x^{2} \sqrt{10 - x^{2}}}{3} + \frac{460 i \sqrt{10 - x^{2}}}{3} + 50 \sqrt{10} i \log{\left(x^{2} \right)} - 100 \sqrt{10} i \log{\left(\sqrt{1 - \frac{x^{2}}{10}} + 1 \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**4*sqrt(x**2 - 10)/5 - 22*x**2*sqrt(x**2 - 10)/3 + 460*sqrt(x**2 - 10)/3 - 100*sqrt(10)*I*log(x) + 50*sqrt(10)*I*log(x**2) + 100*sqrt(10)*asin(sqrt(10)/x), Abs(x**2)/10 > 1), (I*x**4*sqrt(10 - x**2)/5 - 22*I*x**2*sqrt(10 - x**2)/3 + 460*I*sqrt(10 - x**2)/3 + 50*sqrt(10)*I*log(x**2) - 100*sqrt(10)*I*log(sqrt(1 - x**2/10) + 1), True))","C",0
463,1,19,0,0.061132," ","integrate(x**(1+2*n),x)","\begin{cases} \frac{x^{2 n + 2}}{2 n + 2} & \text{for}\: 2 n + 1 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**(2*n + 2)/(2*n + 2), Ne(2*n + 1, -1)), (log(x), True))","A",0
464,1,32,0,0.117682," ","integrate(x**7/(x**2-5)**3,x)","\frac{x^{2}}{2} + \frac{625 - 150 x^{2}}{4 x^{4} - 40 x^{2} + 100} + \frac{15 \log{\left(x^{2} - 5 \right)}}{2}"," ",0,"x**2/2 + (625 - 150*x**2)/(4*x**4 - 40*x**2 + 100) + 15*log(x**2 - 5)/2","A",0
465,1,32,0,0.134632," ","integrate((3*x**5-4*x**3)/(x**2-1)**5,x)","\frac{- 18 x^{4} + 28 x^{2} - 7}{24 x^{8} - 96 x^{6} + 144 x^{4} - 96 x^{2} + 24}"," ",0,"(-18*x**4 + 28*x**2 - 7)/(24*x**8 - 96*x**6 + 144*x**4 - 96*x**2 + 24)","A",0
466,1,41,0,5.541794," ","integrate(x**3*(x**2+1)**(9/14),x)","\frac{7 x^{4} \left(x^{2} + 1\right)^{\frac{9}{14}}}{37} + \frac{63 x^{2} \left(x^{2} + 1\right)^{\frac{9}{14}}}{851} - \frac{98 \left(x^{2} + 1\right)^{\frac{9}{14}}}{851}"," ",0,"7*x**4*(x**2 + 1)**(9/14)/37 + 63*x**2*(x**2 + 1)**(9/14)/851 - 98*(x**2 + 1)**(9/14)/851","A",0
467,1,82,0,5.063153," ","integrate(x**5/(x**2-4)**(13/6),x)","\frac{21 x^{4}}{35 x^{2} \sqrt[6]{x^{2} - 4} - 140 \sqrt[6]{x^{2} - 4}} - \frac{1008 x^{2}}{35 x^{2} \sqrt[6]{x^{2} - 4} - 140 \sqrt[6]{x^{2} - 4}} + \frac{3456}{35 x^{2} \sqrt[6]{x^{2} - 4} - 140 \sqrt[6]{x^{2} - 4}}"," ",0,"21*x**4/(35*x**2*(x**2 - 4)**(1/6) - 140*(x**2 - 4)**(1/6)) - 1008*x**2/(35*x**2*(x**2 - 4)**(1/6) - 140*(x**2 - 4)**(1/6)) + 3456/(35*x**2*(x**2 - 4)**(1/6) - 140*(x**2 - 4)**(1/6))","B",0
468,1,61,0,2.401301," ","integrate(1/(2*x**2+1)**(5/2),x)","\frac{4 x^{3}}{6 x^{2} \sqrt{2 x^{2} + 1} + 3 \sqrt{2 x^{2} + 1}} + \frac{3 x}{6 x^{2} \sqrt{2 x^{2} + 1} + 3 \sqrt{2 x^{2} + 1}}"," ",0,"4*x**3/(6*x**2*sqrt(2*x**2 + 1) + 3*sqrt(2*x**2 + 1)) + 3*x/(6*x**2*sqrt(2*x**2 + 1) + 3*sqrt(2*x**2 + 1))","B",0
469,0,0,0,0.000000," ","integrate(1/(x**2-2*x-1)**(5/2),x)","\int \frac{1}{\left(x^{2} - 2 x - 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((x**2 - 2*x - 1)**(-5/2), x)","F",0
470,1,151,0,2.667598," ","integrate(1/x**4/(x**2-8)**(3/2),x)","\begin{cases} - \frac{i x^{4} \sqrt{-1 + \frac{8}{x^{2}}}}{192 x^{4} - 1536 x^{2}} + \frac{4 i x^{2} \sqrt{-1 + \frac{8}{x^{2}}}}{192 x^{4} - 1536 x^{2}} + \frac{8 i \sqrt{-1 + \frac{8}{x^{2}}}}{192 x^{4} - 1536 x^{2}} & \text{for}\: \frac{8}{\left|{x^{2}}\right|} > 1 \\- \frac{x^{4} \sqrt{1 - \frac{8}{x^{2}}}}{192 x^{4} - 1536 x^{2}} + \frac{4 x^{2} \sqrt{1 - \frac{8}{x^{2}}}}{192 x^{4} - 1536 x^{2}} + \frac{8 \sqrt{1 - \frac{8}{x^{2}}}}{192 x^{4} - 1536 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x**4*sqrt(-1 + 8/x**2)/(192*x**4 - 1536*x**2) + 4*I*x**2*sqrt(-1 + 8/x**2)/(192*x**4 - 1536*x**2) + 8*I*sqrt(-1 + 8/x**2)/(192*x**4 - 1536*x**2), 8/Abs(x**2) > 1), (-x**4*sqrt(1 - 8/x**2)/(192*x**4 - 1536*x**2) + 4*x**2*sqrt(1 - 8/x**2)/(192*x**4 - 1536*x**2) + 8*sqrt(1 - 8/x**2)/(192*x**4 - 1536*x**2), True))","A",0
471,1,24,0,7.848529," ","integrate((x**2+5)**2/x**(13/3),x)","\frac{3 x^{\frac{2}{3}}}{2} - \frac{15}{2 x^{\frac{4}{3}}} - \frac{15}{2 x^{\frac{10}{3}}}"," ",0,"3*x**(2/3)/2 - 15/(2*x**(4/3)) - 15/(2*x**(10/3))","A",0
472,1,49,0,0.169563," ","integrate(1/x**7/(x**2+1)**3,x)","- 10 \log{\left(x \right)} + 5 \log{\left(x^{2} + 1 \right)} + \frac{- 60 x^{8} - 90 x^{6} - 20 x^{4} + 5 x^{2} - 2}{12 x^{10} + 24 x^{8} + 12 x^{6}}"," ",0,"-10*log(x) + 5*log(x**2 + 1) + (-60*x**8 - 90*x**6 - 20*x**4 + 5*x**2 - 2)/(12*x**10 + 24*x**8 + 12*x**6)","A",0
473,-1,0,0,0.000000," ","integrate(((x**2+2)/x**2)**(7/9)/(x**2+2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-1,0,0,0.000000," ","integrate(x**4/(-x**2+10**(1/2))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,1,49,0,0.534749," ","integrate(x**2/(-x**2+3)**(3/2),x)","- \frac{x^{2} \operatorname{asin}{\left(\frac{\sqrt{3} x}{3} \right)}}{x^{2} - 3} - \frac{x \sqrt{3 - x^{2}}}{x^{2} - 3} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{3} x}{3} \right)}}{x^{2} - 3}"," ",0,"-x**2*asin(sqrt(3)*x/3)/(x**2 - 3) - x*sqrt(3 - x**2)/(x**2 - 3) + 3*asin(sqrt(3)*x/3)/(x**2 - 3)","B",0
476,1,32,0,2.234770," ","integrate((-x**2+25)**(3/2)/x**4,x)","\operatorname{asin}{\left(\frac{x}{5} \right)} + \frac{4 \sqrt{25 - x^{2}}}{3 x} - \frac{25 \sqrt{25 - x^{2}}}{3 x^{3}}"," ",0,"asin(x/5) + 4*sqrt(25 - x**2)/(3*x) - 25*sqrt(25 - x**2)/(3*x**3)","A",0
477,1,291,0,12.347318," ","integrate(1/(-2*x**2+1)**(7/2),x)","\begin{cases} - \frac{32 i x^{5}}{60 x^{4} \sqrt{2 x^{2} - 1} - 60 x^{2} \sqrt{2 x^{2} - 1} + 15 \sqrt{2 x^{2} - 1}} + \frac{40 i x^{3}}{60 x^{4} \sqrt{2 x^{2} - 1} - 60 x^{2} \sqrt{2 x^{2} - 1} + 15 \sqrt{2 x^{2} - 1}} - \frac{15 i x}{60 x^{4} \sqrt{2 x^{2} - 1} - 60 x^{2} \sqrt{2 x^{2} - 1} + 15 \sqrt{2 x^{2} - 1}} & \text{for}\: 2 \left|{x^{2}}\right| > 1 \\\frac{32 x^{5}}{60 x^{4} \sqrt{1 - 2 x^{2}} - 60 x^{2} \sqrt{1 - 2 x^{2}} + 15 \sqrt{1 - 2 x^{2}}} - \frac{40 x^{3}}{60 x^{4} \sqrt{1 - 2 x^{2}} - 60 x^{2} \sqrt{1 - 2 x^{2}} + 15 \sqrt{1 - 2 x^{2}}} + \frac{15 x}{60 x^{4} \sqrt{1 - 2 x^{2}} - 60 x^{2} \sqrt{1 - 2 x^{2}} + 15 \sqrt{1 - 2 x^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*I*x**5/(60*x**4*sqrt(2*x**2 - 1) - 60*x**2*sqrt(2*x**2 - 1) + 15*sqrt(2*x**2 - 1)) + 40*I*x**3/(60*x**4*sqrt(2*x**2 - 1) - 60*x**2*sqrt(2*x**2 - 1) + 15*sqrt(2*x**2 - 1)) - 15*I*x/(60*x**4*sqrt(2*x**2 - 1) - 60*x**2*sqrt(2*x**2 - 1) + 15*sqrt(2*x**2 - 1)), 2*Abs(x**2) > 1), (32*x**5/(60*x**4*sqrt(1 - 2*x**2) - 60*x**2*sqrt(1 - 2*x**2) + 15*sqrt(1 - 2*x**2)) - 40*x**3/(60*x**4*sqrt(1 - 2*x**2) - 60*x**2*sqrt(1 - 2*x**2) + 15*sqrt(1 - 2*x**2)) + 15*x/(60*x**4*sqrt(1 - 2*x**2) - 60*x**2*sqrt(1 - 2*x**2) + 15*sqrt(1 - 2*x**2)), True))","B",0
478,0,0,0,0.000000," ","integrate(1/(-x**2+6*x-7)**(5/2),x)","\int \frac{1}{\left(- x^{2} + 6 x - 7\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-x**2 + 6*x - 7)**(-5/2), x)","F",0
479,1,34,0,0.060702," ","integrate((-2*x**2-2*x+1)**3,x)","- \frac{8 x^{7}}{7} - 4 x^{6} - \frac{12 x^{5}}{5} + 4 x^{4} + 2 x^{3} - 3 x^{2} + x"," ",0,"-8*x**7/7 - 4*x**6 - 12*x**5/5 + 4*x**4 + 2*x**3 - 3*x**2 + x","A",0
480,1,34,0,0.064481," ","integrate((-1+5*x)*(x**2-x-1)**2,x)","\frac{5 x^{6}}{6} - \frac{11 x^{5}}{5} - \frac{3 x^{4}}{4} + \frac{11 x^{3}}{3} + \frac{3 x^{2}}{2} - x"," ",0,"5*x**6/6 - 11*x**5/5 - 3*x**4/4 + 11*x**3/3 + 3*x**2/2 - x","A",0
481,0,0,0,0.000000," ","integrate((1+3*x)/(2*x**2-8*x+1)**(5/2),x)","\int \frac{3 x + 1}{\left(2 x^{2} - 8 x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((3*x + 1)/(2*x**2 - 8*x + 1)**(5/2), x)","F",0
482,0,0,0,0.000000," ","integrate((8*x**3-8*x-1)/(-4*x**2+2*x+1)**(5/2),x)","\int \frac{8 x^{3} - 8 x - 1}{\left(- 4 x^{2} + 2 x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((8*x**3 - 8*x - 1)/(-4*x**2 + 2*x + 1)**(5/2), x)","F",0
483,1,112,0,3.486156," ","integrate(x**2*cos(x)**5,x)","\frac{8 x^{2} \sin^{5}{\left(x \right)}}{15} + \frac{4 x^{2} \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{3} + x^{2} \sin{\left(x \right)} \cos^{4}{\left(x \right)} + \frac{16 x \sin^{4}{\left(x \right)} \cos{\left(x \right)}}{15} + \frac{104 x \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{45} + \frac{298 x \cos^{5}{\left(x \right)}}{225} - \frac{4144 \sin^{5}{\left(x \right)}}{3375} - \frac{1712 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{675} - \frac{298 \sin{\left(x \right)} \cos^{4}{\left(x \right)}}{225}"," ",0,"8*x**2*sin(x)**5/15 + 4*x**2*sin(x)**3*cos(x)**2/3 + x**2*sin(x)*cos(x)**4 + 16*x*sin(x)**4*cos(x)/15 + 104*x*sin(x)**2*cos(x)**3/45 + 298*x*cos(x)**5/225 - 4144*sin(x)**5/3375 - 1712*sin(x)**3*cos(x)**2/675 - 298*sin(x)*cos(x)**4/225","A",0
484,1,92,0,2.044965," ","integrate(x**3*sin(x)**3,x)","- x^{3} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{2 x^{3} \cos^{3}{\left(x \right)}}{3} + \frac{7 x^{2} \sin^{3}{\left(x \right)}}{3} + 2 x^{2} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{14 x \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{3} + \frac{40 x \cos^{3}{\left(x \right)}}{9} - \frac{122 \sin^{3}{\left(x \right)}}{27} - \frac{40 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{9}"," ",0,"-x**3*sin(x)**2*cos(x) - 2*x**3*cos(x)**3/3 + 7*x**2*sin(x)**3/3 + 2*x**2*sin(x)*cos(x)**2 + 14*x*sin(x)**2*cos(x)/3 + 40*x*cos(x)**3/9 - 122*sin(x)**3/27 - 40*sin(x)*cos(x)**2/9","A",0
485,1,192,0,5.898125," ","integrate(x**2*sin(x)**6,x)","\frac{5 x^{3} \sin^{6}{\left(x \right)}}{48} + \frac{5 x^{3} \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} + \frac{5 x^{3} \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{16} + \frac{5 x^{3} \cos^{6}{\left(x \right)}}{48} - \frac{11 x^{2} \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{16} - \frac{5 x^{2} \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{6} - \frac{5 x^{2} \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{16} + \frac{299 x \sin^{6}{\left(x \right)}}{1152} + \frac{35 x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{384} - \frac{125 x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{384} - \frac{245 x \cos^{6}{\left(x \right)}}{1152} + \frac{299 \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{1152} + \frac{25 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{54} + \frac{245 \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{1152}"," ",0,"5*x**3*sin(x)**6/48 + 5*x**3*sin(x)**4*cos(x)**2/16 + 5*x**3*sin(x)**2*cos(x)**4/16 + 5*x**3*cos(x)**6/48 - 11*x**2*sin(x)**5*cos(x)/16 - 5*x**2*sin(x)**3*cos(x)**3/6 - 5*x**2*sin(x)*cos(x)**5/16 + 299*x*sin(x)**6/1152 + 35*x*sin(x)**4*cos(x)**2/384 - 125*x*sin(x)**2*cos(x)**4/384 - 245*x*cos(x)**6/1152 + 299*sin(x)**5*cos(x)/1152 + 25*sin(x)**3*cos(x)**3/54 + 245*sin(x)*cos(x)**5/1152","A",0
486,1,53,0,1.227319," ","integrate(x**2*cos(x)*sin(x)**2,x)","\frac{x^{2} \sin^{3}{\left(x \right)}}{3} + \frac{2 x \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{3} + \frac{4 x \cos^{3}{\left(x \right)}}{9} - \frac{14 \sin^{3}{\left(x \right)}}{27} - \frac{4 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{9}"," ",0,"x**2*sin(x)**3/3 + 2*x*sin(x)**2*cos(x)/3 + 4*x*cos(x)**3/9 - 14*sin(x)**3/27 - 4*sin(x)*cos(x)**2/9","A",0
487,1,507,0,2.011806," ","integrate(x*cos(x)**4/sin(x)**2,x)","- \frac{3 x^{2} \tan^{5}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} - \frac{6 x^{2} \tan^{3}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} - \frac{3 x^{2} \tan{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} + \frac{2 x \tan^{6}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} + \frac{6 x \tan^{4}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} - \frac{6 x \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} - \frac{2 x}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} - \frac{4 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{5}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} - \frac{8 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} - \frac{4 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} + \frac{4 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan^{5}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} + \frac{8 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} + \frac{4 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}} + \frac{4 \tan^{3}{\left(\frac{x}{2} \right)}}{4 \tan^{5}{\left(\frac{x}{2} \right)} + 8 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)}}"," ",0,"-3*x**2*tan(x/2)**5/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) - 6*x**2*tan(x/2)**3/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) - 3*x**2*tan(x/2)/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) + 2*x*tan(x/2)**6/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) + 6*x*tan(x/2)**4/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) - 6*x*tan(x/2)**2/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) - 2*x/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) - 4*log(tan(x/2)**2 + 1)*tan(x/2)**5/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) - 8*log(tan(x/2)**2 + 1)*tan(x/2)**3/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) - 4*log(tan(x/2)**2 + 1)*tan(x/2)/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) + 4*log(tan(x/2))*tan(x/2)**5/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) + 8*log(tan(x/2))*tan(x/2)**3/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) + 4*log(tan(x/2))*tan(x/2)/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2)) + 4*tan(x/2)**3/(4*tan(x/2)**5 + 8*tan(x/2)**3 + 4*tan(x/2))","B",0
488,1,551,0,1.691323," ","integrate(x*sin(x)**3/cos(x)**4,x)","\frac{4 x \tan^{6}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} - \frac{12 x \tan^{4}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} - \frac{12 x \tan^{2}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} + \frac{4 x}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} - \frac{5 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{6}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} + \frac{15 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} - \frac{15 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} + \frac{5 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} + \frac{5 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} - \frac{15 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} + \frac{15 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} - \frac{5 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} - \frac{2 \tan^{5}{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{6 \tan^{6}{\left(\frac{x}{2} \right)} - 18 \tan^{4}{\left(\frac{x}{2} \right)} + 18 \tan^{2}{\left(\frac{x}{2} \right)} - 6}"," ",0,"4*x*tan(x/2)**6/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) - 12*x*tan(x/2)**4/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) - 12*x*tan(x/2)**2/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) + 4*x/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) - 5*log(tan(x/2) - 1)*tan(x/2)**6/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) + 15*log(tan(x/2) - 1)*tan(x/2)**4/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) - 15*log(tan(x/2) - 1)*tan(x/2)**2/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) + 5*log(tan(x/2) - 1)/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) + 5*log(tan(x/2) + 1)*tan(x/2)**6/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) - 15*log(tan(x/2) + 1)*tan(x/2)**4/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) + 15*log(tan(x/2) + 1)*tan(x/2)**2/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) - 5*log(tan(x/2) + 1)/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) - 2*tan(x/2)**5/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6) + 2*tan(x/2)/(6*tan(x/2)**6 - 18*tan(x/2)**4 + 18*tan(x/2)**2 - 6)","B",0
489,1,128,0,1.033625," ","integrate(x*sin(x)/cos(x)**3,x)","\frac{x \tan^{4}{\left(\frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2} + \frac{2 x \tan^{2}{\left(\frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2} + \frac{x}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2} + \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{2} \right)} - 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2}"," ",0,"x*tan(x/2)**4/(2*tan(x/2)**4 - 4*tan(x/2)**2 + 2) + 2*x*tan(x/2)**2/(2*tan(x/2)**4 - 4*tan(x/2)**2 + 2) + x/(2*tan(x/2)**4 - 4*tan(x/2)**2 + 2) + 2*tan(x/2)**3/(2*tan(x/2)**4 - 4*tan(x/2)**2 + 2) - 2*tan(x/2)/(2*tan(x/2)**4 - 4*tan(x/2)**2 + 2)","B",0
490,0,0,0,0.000000," ","integrate(x*sin(x)**3/cos(x),x)","\int \frac{x \sin^{3}{\left(x \right)}}{\cos{\left(x \right)}}\, dx"," ",0,"Integral(x*sin(x)**3/cos(x), x)","F",0
491,0,0,0,0.000000," ","integrate(x*sin(x)**3/cos(x)**3,x)","\int \frac{x \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}}\, dx"," ",0,"Integral(x*sin(x)**3/cos(x)**3, x)","F",0
492,0,0,0,0.000000," ","integrate((2*x+sin(2*x))/(cos(x)+x*sin(x))**2,x)","\int \frac{2 x + \sin{\left(2 x \right)}}{\left(x \sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((2*x + sin(2*x))/(x*sin(x) + cos(x))**2, x)","F",0
493,1,66,0,1.474222," ","integrate(x**2/(x*cos(x)-sin(x))**2,x)","- \frac{2 x \tan{\left(\frac{x}{2} \right)}}{x \tan^{2}{\left(\frac{x}{2} \right)} - x + 2 \tan{\left(\frac{x}{2} \right)}} + \frac{\tan^{2}{\left(\frac{x}{2} \right)}}{x \tan^{2}{\left(\frac{x}{2} \right)} - x + 2 \tan{\left(\frac{x}{2} \right)}} - \frac{1}{x \tan^{2}{\left(\frac{x}{2} \right)} - x + 2 \tan{\left(\frac{x}{2} \right)}}"," ",0,"-2*x*tan(x/2)/(x*tan(x/2)**2 - x + 2*tan(x/2)) + tan(x/2)**2/(x*tan(x/2)**2 - x + 2*tan(x/2)) - 1/(x*tan(x/2)**2 - x + 2*tan(x/2))","B",0
494,1,42,0,0.701710," ","integrate(a**(m*x)*b**(n*x),x)","\begin{cases} \frac{a^{m x} b^{n x}}{m \log{\left(a \right)} + n \log{\left(b \right)}} & \text{for}\: m \neq - \frac{n \log{\left(b \right)}}{\log{\left(a \right)}} \\b^{n x} x e^{- n x \log{\left(b \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(m*x)*b**(n*x)/(m*log(a) + n*log(b)), Ne(m, -n*log(b)/log(a))), (b**(n*x)*x*exp(-n*x*log(b)), True))","A",0
495,-2,0,0,0.000000," ","integrate((a**x-b**x)**2/(a**x)/(b**x),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
496,1,7,0,0.086383," ","integrate(-1/exp(x)+exp(x),x)","e^{x} + e^{- x}"," ",0,"exp(x) + exp(-x)","A",0
497,1,17,0,0.107790," ","integrate((-1/exp(x)+exp(x))**2,x)","- 2 x + \frac{e^{2 x}}{2} - \frac{e^{- 2 x}}{2}"," ",0,"-2*x + exp(2*x)/2 - exp(-2*x)/2","A",0
498,1,24,0,0.128336," ","integrate((-1/exp(x)+exp(x))**3,x)","\frac{e^{3 x}}{3} - 3 e^{x} - 3 e^{- x} + \frac{e^{- 3 x}}{3}"," ",0,"exp(3*x)/3 - 3*exp(x) - 3*exp(-x) + exp(-3*x)/3","A",0
499,1,31,0,0.144021," ","integrate((-1/exp(x)+exp(x))**4,x)","6 x + \frac{e^{4 x}}{4} - 2 e^{2 x} + 2 e^{- 2 x} - \frac{e^{- 4 x}}{4}"," ",0,"6*x + exp(4*x)/4 - 2*exp(2*x) + 2*exp(-2*x) - exp(-4*x)/4","A",0
500,0,0,0,0.000000," ","integrate((-1/exp(x)+exp(x))**n,x)","\int \left(e^{x} - e^{- x}\right)^{n}\, dx"," ",0,"Integral((exp(x) - exp(-x))**n, x)","F",0
501,1,54,0,0.222577," ","integrate((1/(a**(4*x))-a**(2*x))**3,x)","3 x + \begin{cases} \frac{- 24 a^{6 x} \log{\left(a \right)}^{2} + 72 a^{- 6 x} \log{\left(a \right)}^{2} - 12 a^{- 12 x} \log{\left(a \right)}^{2}}{144 \log{\left(a \right)}^{3}} & \text{for}\: 144 \log{\left(a \right)}^{3} \neq 0 \\- 3 x & \text{otherwise} \end{cases}"," ",0,"3*x + Piecewise(((-24*a**(6*x)*log(a)**2 + 72*a**(-6*x)*log(a)**2 - 12*a**(-12*x)*log(a)**2)/(144*log(a)**3), Ne(144*log(a)**3, 0)), (-3*x, True))","A",0
502,1,29,0,0.263767," ","integrate(a**(k*x)+a**(l*x),x)","\begin{cases} \frac{a^{k x}}{k \log{\left(a \right)}} & \text{for}\: k \log{\left(a \right)} \neq 0 \\x & \text{otherwise} \end{cases} + \begin{cases} \frac{a^{l x}}{l \log{\left(a \right)}} & \text{for}\: l \log{\left(a \right)} \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(k*x)/(k*log(a)), Ne(k*log(a), 0)), (x, True)) + Piecewise((a**(l*x)/(l*log(a)), Ne(l*log(a), 0)), (x, True))","A",0
503,1,250,0,2.067750," ","integrate((a**(k*x)+a**(l*x))**2,x)","\begin{cases} 4 x & \text{for}\: a = 1 \wedge \left(a = 1 \vee k = 0\right) \wedge \left(a = 1 \vee l = 0\right) \\\frac{a^{2 l x}}{2 l \log{\left(a \right)}} + \frac{2 a^{l x}}{l \log{\left(a \right)}} + x & \text{for}\: k = 0 \\\frac{a^{2 l x}}{2 l \log{\left(a \right)}} + 2 x - \frac{a^{- 2 l x}}{2 l \log{\left(a \right)}} & \text{for}\: k = - l \\\frac{a^{2 k x}}{2 k \log{\left(a \right)}} + \frac{2 a^{k x}}{k \log{\left(a \right)}} + x & \text{for}\: l = 0 \\\frac{a^{2 k x} k l}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} + \frac{a^{2 k x} l^{2}}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} + \frac{4 a^{k x} a^{l x} k l}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} + \frac{a^{2 l x} k^{2}}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} + \frac{a^{2 l x} k l}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*x, Eq(a, 1) & (Eq(a, 1) | Eq(k, 0)) & (Eq(a, 1) | Eq(l, 0))), (a**(2*l*x)/(2*l*log(a)) + 2*a**(l*x)/(l*log(a)) + x, Eq(k, 0)), (a**(2*l*x)/(2*l*log(a)) + 2*x - a**(-2*l*x)/(2*l*log(a)), Eq(k, -l)), (a**(2*k*x)/(2*k*log(a)) + 2*a**(k*x)/(k*log(a)) + x, Eq(l, 0)), (a**(2*k*x)*k*l/(2*k**2*l*log(a) + 2*k*l**2*log(a)) + a**(2*k*x)*l**2/(2*k**2*l*log(a) + 2*k*l**2*log(a)) + 4*a**(k*x)*a**(l*x)*k*l/(2*k**2*l*log(a) + 2*k*l**2*log(a)) + a**(2*l*x)*k**2/(2*k**2*l*log(a) + 2*k*l**2*log(a)) + a**(2*l*x)*k*l/(2*k**2*l*log(a) + 2*k*l**2*log(a)), True))","A",0
504,1,665,0,23.435203," ","integrate((a**(k*x)+a**(l*x))**3,x)","\begin{cases} 8 x & \text{for}\: a = 1 \wedge \left(a = 1 \vee k = 0\right) \wedge \left(a = 1 \vee l = 0\right) \\\frac{a^{3 l x}}{3 l \log{\left(a \right)}} + \frac{3 a^{2 l x}}{2 l \log{\left(a \right)}} + \frac{3 a^{l x}}{l \log{\left(a \right)}} + x & \text{for}\: k = 0 \\\frac{a^{3 l x}}{3 l \log{\left(a \right)}} + 3 x - \frac{a^{- 3 l x}}{l \log{\left(a \right)}} - \frac{a^{- 6 l x}}{6 l \log{\left(a \right)}} & \text{for}\: k = - 2 l \\\frac{2 a^{\frac{3 l x}{2}}}{l \log{\left(a \right)}} + \frac{a^{3 l x}}{3 l \log{\left(a \right)}} + 3 x - \frac{2 a^{- \frac{3 l x}{2}}}{3 l \log{\left(a \right)}} & \text{for}\: k = - \frac{l}{2} \\\frac{a^{3 k x}}{3 k \log{\left(a \right)}} + \frac{3 a^{2 k x}}{2 k \log{\left(a \right)}} + \frac{3 a^{k x}}{k \log{\left(a \right)}} + x & \text{for}\: l = 0 \\\frac{2 a^{3 k x} k^{2} l}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{5 a^{3 k x} k l^{2}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{2 a^{3 k x} l^{3}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{9 a^{2 k x} a^{l x} k^{2} l}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{18 a^{2 k x} a^{l x} k l^{2}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{18 a^{k x} a^{2 l x} k^{2} l}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{9 a^{k x} a^{2 l x} k l^{2}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{2 a^{3 l x} k^{3}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{5 a^{3 l x} k^{2} l}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{2 a^{3 l x} k l^{2}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*x, Eq(a, 1) & (Eq(a, 1) | Eq(k, 0)) & (Eq(a, 1) | Eq(l, 0))), (a**(3*l*x)/(3*l*log(a)) + 3*a**(2*l*x)/(2*l*log(a)) + 3*a**(l*x)/(l*log(a)) + x, Eq(k, 0)), (a**(3*l*x)/(3*l*log(a)) + 3*x - a**(-3*l*x)/(l*log(a)) - a**(-6*l*x)/(6*l*log(a)), Eq(k, -2*l)), (2*a**(3*l*x/2)/(l*log(a)) + a**(3*l*x)/(3*l*log(a)) + 3*x - 2*a**(-3*l*x/2)/(3*l*log(a)), Eq(k, -l/2)), (a**(3*k*x)/(3*k*log(a)) + 3*a**(2*k*x)/(2*k*log(a)) + 3*a**(k*x)/(k*log(a)) + x, Eq(l, 0)), (2*a**(3*k*x)*k**2*l/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 5*a**(3*k*x)*k*l**2/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 2*a**(3*k*x)*l**3/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 9*a**(2*k*x)*a**(l*x)*k**2*l/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 18*a**(2*k*x)*a**(l*x)*k*l**2/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 18*a**(k*x)*a**(2*l*x)*k**2*l/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 9*a**(k*x)*a**(2*l*x)*k*l**2/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 2*a**(3*l*x)*k**3/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 5*a**(3*l*x)*k**2*l/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 2*a**(3*l*x)*k*l**2/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)), True))","A",0
505,-1,0,0,0.000000," ","integrate((a**(k*x)+a**(l*x))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,0,0,0,0.000000," ","integrate((a**(k*x)+a**(l*x))**n,x)","\int \left(a^{k x} + a^{l x}\right)^{n}\, dx"," ",0,"Integral((a**(k*x) + a**(l*x))**n, x)","F",0
507,1,29,0,0.266591," ","integrate(a**(k*x)-a**(l*x),x)","\begin{cases} \frac{a^{k x}}{k \log{\left(a \right)}} & \text{for}\: k \log{\left(a \right)} \neq 0 \\x & \text{otherwise} \end{cases} - \begin{cases} \frac{a^{l x}}{l \log{\left(a \right)}} & \text{for}\: l \log{\left(a \right)} \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(k*x)/(k*log(a)), Ne(k*log(a), 0)), (x, True)) - Piecewise((a**(l*x)/(l*log(a)), Ne(l*log(a), 0)), (x, True))","A",0
508,1,248,0,1.984846," ","integrate((a**(k*x)-a**(l*x))**2,x)","\begin{cases} 0 & \text{for}\: a = 1 \wedge \left(a = 1 \vee k = 0\right) \wedge \left(a = 1 \vee l = 0\right) \\\frac{a^{2 l x}}{2 l \log{\left(a \right)}} - \frac{2 a^{l x}}{l \log{\left(a \right)}} + x & \text{for}\: k = 0 \\\frac{a^{2 l x}}{2 l \log{\left(a \right)}} - 2 x - \frac{a^{- 2 l x}}{2 l \log{\left(a \right)}} & \text{for}\: k = - l \\\frac{a^{2 k x}}{2 k \log{\left(a \right)}} - \frac{2 a^{k x}}{k \log{\left(a \right)}} + x & \text{for}\: l = 0 \\\frac{a^{2 k x} k l}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} + \frac{a^{2 k x} l^{2}}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} - \frac{4 a^{k x} a^{l x} k l}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} + \frac{a^{2 l x} k^{2}}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} + \frac{a^{2 l x} k l}{2 k^{2} l \log{\left(a \right)} + 2 k l^{2} \log{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, Eq(a, 1) & (Eq(a, 1) | Eq(k, 0)) & (Eq(a, 1) | Eq(l, 0))), (a**(2*l*x)/(2*l*log(a)) - 2*a**(l*x)/(l*log(a)) + x, Eq(k, 0)), (a**(2*l*x)/(2*l*log(a)) - 2*x - a**(-2*l*x)/(2*l*log(a)), Eq(k, -l)), (a**(2*k*x)/(2*k*log(a)) - 2*a**(k*x)/(k*log(a)) + x, Eq(l, 0)), (a**(2*k*x)*k*l/(2*k**2*l*log(a) + 2*k*l**2*log(a)) + a**(2*k*x)*l**2/(2*k**2*l*log(a) + 2*k*l**2*log(a)) - 4*a**(k*x)*a**(l*x)*k*l/(2*k**2*l*log(a) + 2*k*l**2*log(a)) + a**(2*l*x)*k**2/(2*k**2*l*log(a) + 2*k*l**2*log(a)) + a**(2*l*x)*k*l/(2*k**2*l*log(a) + 2*k*l**2*log(a)), True))","A",0
509,1,663,0,23.592967," ","integrate((a**(k*x)-a**(l*x))**3,x)","\begin{cases} 0 & \text{for}\: a = 1 \wedge \left(a = 1 \vee k = 0\right) \wedge \left(a = 1 \vee l = 0\right) \\- \frac{a^{3 l x}}{3 l \log{\left(a \right)}} + \frac{3 a^{2 l x}}{2 l \log{\left(a \right)}} - \frac{3 a^{l x}}{l \log{\left(a \right)}} + x & \text{for}\: k = 0 \\- \frac{a^{3 l x}}{3 l \log{\left(a \right)}} + 3 x + \frac{a^{- 3 l x}}{l \log{\left(a \right)}} - \frac{a^{- 6 l x}}{6 l \log{\left(a \right)}} & \text{for}\: k = - 2 l \\\frac{2 a^{\frac{3 l x}{2}}}{l \log{\left(a \right)}} - \frac{a^{3 l x}}{3 l \log{\left(a \right)}} - 3 x - \frac{2 a^{- \frac{3 l x}{2}}}{3 l \log{\left(a \right)}} & \text{for}\: k = - \frac{l}{2} \\\frac{a^{3 k x}}{3 k \log{\left(a \right)}} - \frac{3 a^{2 k x}}{2 k \log{\left(a \right)}} + \frac{3 a^{k x}}{k \log{\left(a \right)}} - x & \text{for}\: l = 0 \\\frac{2 a^{3 k x} k^{2} l}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{5 a^{3 k x} k l^{2}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{2 a^{3 k x} l^{3}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} - \frac{9 a^{2 k x} a^{l x} k^{2} l}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} - \frac{18 a^{2 k x} a^{l x} k l^{2}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{18 a^{k x} a^{2 l x} k^{2} l}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} + \frac{9 a^{k x} a^{2 l x} k l^{2}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} - \frac{2 a^{3 l x} k^{3}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} - \frac{5 a^{3 l x} k^{2} l}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} - \frac{2 a^{3 l x} k l^{2}}{6 k^{3} l \log{\left(a \right)} + 15 k^{2} l^{2} \log{\left(a \right)} + 6 k l^{3} \log{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, Eq(a, 1) & (Eq(a, 1) | Eq(k, 0)) & (Eq(a, 1) | Eq(l, 0))), (-a**(3*l*x)/(3*l*log(a)) + 3*a**(2*l*x)/(2*l*log(a)) - 3*a**(l*x)/(l*log(a)) + x, Eq(k, 0)), (-a**(3*l*x)/(3*l*log(a)) + 3*x + a**(-3*l*x)/(l*log(a)) - a**(-6*l*x)/(6*l*log(a)), Eq(k, -2*l)), (2*a**(3*l*x/2)/(l*log(a)) - a**(3*l*x)/(3*l*log(a)) - 3*x - 2*a**(-3*l*x/2)/(3*l*log(a)), Eq(k, -l/2)), (a**(3*k*x)/(3*k*log(a)) - 3*a**(2*k*x)/(2*k*log(a)) + 3*a**(k*x)/(k*log(a)) - x, Eq(l, 0)), (2*a**(3*k*x)*k**2*l/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 5*a**(3*k*x)*k*l**2/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 2*a**(3*k*x)*l**3/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) - 9*a**(2*k*x)*a**(l*x)*k**2*l/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) - 18*a**(2*k*x)*a**(l*x)*k*l**2/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 18*a**(k*x)*a**(2*l*x)*k**2*l/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) + 9*a**(k*x)*a**(2*l*x)*k*l**2/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) - 2*a**(3*l*x)*k**3/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) - 5*a**(3*l*x)*k**2*l/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)) - 2*a**(3*l*x)*k*l**2/(6*k**3*l*log(a) + 15*k**2*l**2*log(a) + 6*k*l**3*log(a)), True))","A",0
510,-1,0,0,0.000000," ","integrate((a**(k*x)-a**(l*x))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,0,0,0,0.000000," ","integrate((a**(k*x)-a**(l*x))**n,x)","\int \left(a^{k x} - a^{l x}\right)^{n}\, dx"," ",0,"Integral((a**(k*x) - a**(l*x))**n, x)","F",0
512,1,15,0,0.090482," ","integrate(1+a**(m*x),x)","x + \begin{cases} \frac{a^{m x}}{m \log{\left(a \right)}} & \text{for}\: m \log{\left(a \right)} \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"x + Piecewise((a**(m*x)/(m*log(a)), Ne(m*log(a), 0)), (x, True))","A",0
513,1,46,0,0.117741," ","integrate((1+a**(m*x))**2,x)","x + \begin{cases} \frac{a^{2 m x} m \log{\left(a \right)} + 4 a^{m x} m \log{\left(a \right)}}{2 m^{2} \log{\left(a \right)}^{2}} & \text{for}\: 2 m^{2} \log{\left(a \right)}^{2} \neq 0 \\3 x & \text{otherwise} \end{cases}"," ",0,"x + Piecewise(((a**(2*m*x)*m*log(a) + 4*a**(m*x)*m*log(a))/(2*m**2*log(a)**2), Ne(2*m**2*log(a)**2, 0)), (3*x, True))","A",0
514,1,71,0,0.137590," ","integrate((1+a**(m*x))**3,x)","x + \begin{cases} \frac{2 a^{3 m x} m^{2} \log{\left(a \right)}^{2} + 9 a^{2 m x} m^{2} \log{\left(a \right)}^{2} + 18 a^{m x} m^{2} \log{\left(a \right)}^{2}}{6 m^{3} \log{\left(a \right)}^{3}} & \text{for}\: 6 m^{3} \log{\left(a \right)}^{3} \neq 0 \\7 x & \text{otherwise} \end{cases}"," ",0,"x + Piecewise(((2*a**(3*m*x)*m**2*log(a)**2 + 9*a**(2*m*x)*m**2*log(a)**2 + 18*a**(m*x)*m**2*log(a)**2)/(6*m**3*log(a)**3), Ne(6*m**3*log(a)**3, 0)), (7*x, True))","A",0
515,1,88,0,0.157773," ","integrate((1+a**(m*x))**4,x)","x + \begin{cases} \frac{3 a^{4 m x} m^{3} \log{\left(a \right)}^{3} + 16 a^{3 m x} m^{3} \log{\left(a \right)}^{3} + 36 a^{2 m x} m^{3} \log{\left(a \right)}^{3} + 48 a^{m x} m^{3} \log{\left(a \right)}^{3}}{12 m^{4} \log{\left(a \right)}^{4}} & \text{for}\: 12 m^{4} \log{\left(a \right)}^{4} \neq 0 \\15 x & \text{otherwise} \end{cases}"," ",0,"x + Piecewise(((3*a**(4*m*x)*m**3*log(a)**3 + 16*a**(3*m*x)*m**3*log(a)**3 + 36*a**(2*m*x)*m**3*log(a)**3 + 48*a**(m*x)*m**3*log(a)**3)/(12*m**4*log(a)**4), Ne(12*m**4*log(a)**4, 0)), (15*x, True))","A",0
516,0,0,0,0.000000," ","integrate((1+a**(m*x))**n,x)","\int \left(a^{m x} + 1\right)^{n}\, dx"," ",0,"Integral((a**(m*x) + 1)**n, x)","F",0
517,1,19,0,0.095386," ","integrate(1-a**(m*x),x)","x + \begin{cases} - \frac{a^{m x}}{m \log{\left(a \right)}} & \text{for}\: m \log{\left(a \right)} \neq 0 \\- x & \text{otherwise} \end{cases}"," ",0,"x + Piecewise((-a**(m*x)/(m*log(a)), Ne(m*log(a), 0)), (-x, True))","A",0
518,1,46,0,0.117458," ","integrate((1-a**(m*x))**2,x)","x + \begin{cases} \frac{a^{2 m x} m \log{\left(a \right)} - 4 a^{m x} m \log{\left(a \right)}}{2 m^{2} \log{\left(a \right)}^{2}} & \text{for}\: 2 m^{2} \log{\left(a \right)}^{2} \neq 0 \\- x & \text{otherwise} \end{cases}"," ",0,"x + Piecewise(((a**(2*m*x)*m*log(a) - 4*a**(m*x)*m*log(a))/(2*m**2*log(a)**2), Ne(2*m**2*log(a)**2, 0)), (-x, True))","A",0
519,1,71,0,0.142760," ","integrate((1-a**(m*x))**3,x)","x + \begin{cases} \frac{- 2 a^{3 m x} m^{2} \log{\left(a \right)}^{2} + 9 a^{2 m x} m^{2} \log{\left(a \right)}^{2} - 18 a^{m x} m^{2} \log{\left(a \right)}^{2}}{6 m^{3} \log{\left(a \right)}^{3}} & \text{for}\: 6 m^{3} \log{\left(a \right)}^{3} \neq 0 \\- x & \text{otherwise} \end{cases}"," ",0,"x + Piecewise(((-2*a**(3*m*x)*m**2*log(a)**2 + 9*a**(2*m*x)*m**2*log(a)**2 - 18*a**(m*x)*m**2*log(a)**2)/(6*m**3*log(a)**3), Ne(6*m**3*log(a)**3, 0)), (-x, True))","A",0
520,1,88,0,0.162356," ","integrate((1-a**(m*x))**4,x)","x + \begin{cases} \frac{3 a^{4 m x} m^{3} \log{\left(a \right)}^{3} - 16 a^{3 m x} m^{3} \log{\left(a \right)}^{3} + 36 a^{2 m x} m^{3} \log{\left(a \right)}^{3} - 48 a^{m x} m^{3} \log{\left(a \right)}^{3}}{12 m^{4} \log{\left(a \right)}^{4}} & \text{for}\: 12 m^{4} \log{\left(a \right)}^{4} \neq 0 \\- x & \text{otherwise} \end{cases}"," ",0,"x + Piecewise(((3*a**(4*m*x)*m**3*log(a)**3 - 16*a**(3*m*x)*m**3*log(a)**3 + 36*a**(2*m*x)*m**3*log(a)**3 - 48*a**(m*x)*m**3*log(a)**3)/(12*m**4*log(a)**4), Ne(12*m**4*log(a)**4, 0)), (-x, True))","A",0
521,0,0,0,0.000000," ","integrate((1-a**(m*x))**n,x)","\int \left(1 - a^{m x}\right)^{n}\, dx"," ",0,"Integral((1 - a**(m*x))**n, x)","F",0
522,1,15,0,0.122923," ","integrate(1/(b+a*exp(n*x)),x)","\frac{x}{b} - \frac{\log{\left(e^{n x} + \frac{b}{a} \right)}}{b n}"," ",0,"x/b - log(exp(n*x) + b/a)/(b*n)","A",0
523,1,22,0,0.174929," ","integrate(exp(x)/(b+a*exp(3*x)),x)","\operatorname{RootSum} {\left(27 z^{3} a b^{2} - 1, \left( i \mapsto i \log{\left(3 i b + e^{x} \right)} \right)\right)}"," ",0,"RootSum(27*_z**3*a*b**2 - 1, Lambda(_i, _i*log(3*_i*b + exp(x))))","A",0
524,1,8,0,0.080787," ","integrate((-1+exp(x))/(1+exp(x)),x)","- x + 2 \log{\left(e^{x} + 1 \right)}"," ",0,"-x + 2*log(exp(x) + 1)","A",0
525,1,22,0,0.144106," ","integrate(exp(4*x)/(1-2*exp(2*x)+3*exp(4*x)),x)","\operatorname{RootSum} {\left(96 z^{2} - 16 z + 1, \left( i \mapsto i \log{\left(8 i + e^{2 x} - 1 \right)} \right)\right)}"," ",0,"RootSum(96*_z**2 - 16*_z + 1, Lambda(_i, _i*log(8*_i + exp(2*x) - 1)))","A",0
526,1,48,0,0.205687," ","integrate((exp(x)+exp(5*x))/(-1+exp(x)-exp(2*x)+exp(3*x)),x)","\frac{e^{2 x}}{2} + e^{x} + \log{\left(e^{x} - 1 \right)} + \operatorname{RootSum} {\left(2 z^{2} + 2 z + 1, \left( i \mapsto i \log{\left(\frac{4 i^{2}}{5} - \frac{6 i}{5} + e^{x} - \frac{3}{5} \right)} \right)\right)}"," ",0,"exp(2*x)/2 + exp(x) + log(exp(x) - 1) + RootSum(2*_z**2 + 2*_z + 1, Lambda(_i, _i*log(4*_i**2/5 - 6*_i/5 + exp(x) - 3/5)))","A",0
527,1,94,0,1.318476," ","integrate(exp(n*x)*(a+b*exp(n*x))**(r/s),x)","\begin{cases} \frac{x}{a} & \text{for}\: b = 0 \wedge n = 0 \wedge r = - s \\\frac{a^{\frac{r}{s}} e^{n x}}{n} & \text{for}\: b = 0 \\x \left(a + b\right)^{\frac{r}{s}} & \text{for}\: n = 0 \\\frac{\log{\left(\frac{a}{b} + e^{n x} \right)}}{b n} & \text{for}\: r = - s \\\frac{a s \left(a + b e^{n x}\right)^{\frac{r}{s}}}{b n r + b n s} + \frac{b s \left(a + b e^{n x}\right)^{\frac{r}{s}} e^{n x}}{b n r + b n s} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a, Eq(b, 0) & Eq(n, 0) & Eq(r, -s)), (a**(r/s)*exp(n*x)/n, Eq(b, 0)), (x*(a + b)**(r/s), Eq(n, 0)), (log(a/b + exp(n*x))/(b*n), Eq(r, -s)), (a*s*(a + b*exp(n*x))**(r/s)/(b*n*r + b*n*s) + b*s*(a + b*exp(n*x))**(r/s)*exp(n*x)/(b*n*r + b*n*s), True))","A",0
528,0,0,0,0.000000," ","integrate((1-2*exp(1/3*x))**(1/4),x)","\int \sqrt[4]{1 - 2 e^{\frac{x}{3}}}\, dx"," ",0,"Integral((1 - 2*exp(x/3))**(1/4), x)","F",0
529,0,0,0,0.000000," ","integrate((a+b*exp(n*x))**(r/s),x)","\int \left(a + b e^{n x}\right)^{\frac{r}{s}}\, dx"," ",0,"Integral((a + b*exp(n*x))**(r/s), x)","F",0
530,1,31,0,0.727874," ","integrate(exp(x)/(a**2+exp(2*x))**(1/2),x)","\begin{cases} \operatorname{asinh}{\left(\sqrt{\frac{1}{a^{2}}} e^{x} \right)} & \text{for}\: a^{2} > 0 \\\operatorname{acosh}{\left(\sqrt{- \frac{1}{a^{2}}} e^{x} \right)} & \text{for}\: a^{2} < 0 \end{cases}"," ",0,"Piecewise((asinh(sqrt(a**(-2))*exp(x)), a**2 > 0), (acosh(sqrt(-1/a**2)*exp(x)), a**2 < 0))","A",0
531,1,31,0,0.727607," ","integrate(exp(x)/(-a**2+exp(2*x))**(1/2),x)","\begin{cases} \operatorname{asinh}{\left(\sqrt{- \frac{1}{a^{2}}} e^{x} \right)} & \text{for}\: a^{2} < 0 \\\operatorname{acosh}{\left(\sqrt{\frac{1}{a^{2}}} e^{x} \right)} & \text{for}\: a^{2} > 0 \end{cases}"," ",0,"Piecewise((asinh(sqrt(-1/a**2)*exp(x)), a**2 < 0), (acosh(sqrt(a**(-2))*exp(x)), a**2 > 0))","A",0
532,0,0,0,0.000000," ","integrate(exp(3/4*x)/(-2+exp(3/4*x))/(-2+exp(3/4*x)+exp(3/2*x))**(1/2),x)","\int \frac{e^{\frac{3 x}{4}}}{\left(e^{\frac{3 x}{4}} - 2\right) \sqrt{e^{\frac{3 x}{4}} + e^{\frac{3 x}{2}} - 2}}\, dx"," ",0,"Integral(exp(3*x/4)/((exp(3*x/4) - 2)*sqrt(exp(3*x/4) + exp(3*x/2) - 2)), x)","F",0
533,0,0,0,0.000000," ","integrate((-3+exp(7*x))**(2/3)/exp(2*x),x)","\int \left(e^{7 x} - 3\right)^{\frac{2}{3}} e^{- 2 x}\, dx"," ",0,"Integral((exp(7*x) - 3)**(2/3)*exp(-2*x), x)","F",0
534,0,0,0,0.000000," ","integrate(exp(2*x)/(3-exp(1/2*x))**(3/4),x)","\int \frac{e^{2 x}}{\left(3 - e^{\frac{x}{2}}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(exp(2*x)/(3 - exp(x/2))**(3/4), x)","F",0
535,1,20,0,0.090342," ","integrate(x**3/exp(1/2*x),x)","\left(- 2 x^{3} - 12 x^{2} - 48 x - 96\right) e^{- \frac{x}{2}}"," ",0,"(-2*x**3 - 12*x**2 - 48*x - 96)*exp(-x/2)","A",0
536,1,32,0,1.340400," ","integrate(1/exp(1/2*x)/x**3,x)","\frac{\operatorname{Ei}{\left(\frac{x e^{i \pi}}{2} \right)}}{8} + \frac{e^{- \frac{x}{2}}}{4 x} - \frac{e^{- \frac{x}{2}}}{2 x^{2}}"," ",0,"Ei(x*exp_polar(I*pi)/2)/8 + exp(-x/2)/(4*x) - exp(-x/2)/(2*x**2)","C",0
537,1,39,0,0.114733," ","integrate(a**(3*x)*x**2,x)","\begin{cases} \frac{a^{3 x} \left(9 x^{2} \log{\left(a \right)}^{2} - 6 x \log{\left(a \right)} + 2\right)}{27 \log{\left(a \right)}^{3}} & \text{for}\: 27 \log{\left(a \right)}^{3} \neq 0 \\\frac{x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(3*x)*(9*x**2*log(a)**2 - 6*x*log(a) + 2)/(27*log(a)**3), Ne(27*log(a)**3, 0)), (x**3/3, True))","A",0
538,1,8,0,0.091436," ","integrate(exp(x**2)*x*(x**2+1),x)","\frac{x^{2} e^{x^{2}}}{2}"," ",0,"x**2*exp(x**2)/2","A",0
539,1,22,0,0.106163," ","integrate(x/(exp(-x)+exp(x))**2,x)","\frac{x}{2} - \frac{x}{2 e^{2 x} + 2} - \frac{\log{\left(e^{2 x} + 1 \right)}}{4}"," ",0,"x/2 - x/(2*exp(2*x) + 2) - log(exp(2*x) + 1)/4","A",0
540,0,0,0,0.000000," ","integrate(exp(x)*(-x**2-x+1)/(-x**2+1)**(1/2),x)","- \int \left(- \frac{e^{x}}{\sqrt{1 - x^{2}}}\right)\, dx - \int \frac{x e^{x}}{\sqrt{1 - x^{2}}}\, dx - \int \frac{x^{2} e^{x}}{\sqrt{1 - x^{2}}}\, dx"," ",0,"-Integral(-exp(x)/sqrt(1 - x**2), x) - Integral(x*exp(x)/sqrt(1 - x**2), x) - Integral(x**2*exp(x)/sqrt(1 - x**2), x)","F",0
541,1,26,0,0.470467," ","integrate(cos(2*x)/exp(3*x),x)","\frac{2 e^{- 3 x} \sin{\left(2 x \right)}}{13} - \frac{3 e^{- 3 x} \cos{\left(2 x \right)}}{13}"," ",0,"2*exp(-3*x)*sin(2*x)/13 - 3*exp(-3*x)*cos(2*x)/13","A",0
542,1,29,0,0.845943," ","integrate((cos(1/2*x)+sin(1/2*x))/exp(x)**(1/3),x)","\frac{6 \sin{\left(\frac{x}{2} \right)}}{13 \sqrt[3]{e^{x}}} - \frac{30 \cos{\left(\frac{x}{2} \right)}}{13 \sqrt[3]{e^{x}}}"," ",0,"6*sin(x/2)/(13*exp(x)**(1/3)) - 30*cos(x/2)/(13*exp(x)**(1/3))","A",0
543,1,70,0,2.453809," ","integrate(cos(3/2*x)/(3**(3*x))**(1/4),x)","\frac{8 \sin{\left(\frac{3 x}{2} \right)}}{3 \sqrt[4]{3^{3 x}} \log{\left(3 \right)}^{2} + 12 \sqrt[4]{3^{3 x}}} - \frac{4 \log{\left(3 \right)} \cos{\left(\frac{3 x}{2} \right)}}{3 \sqrt[4]{3^{3 x}} \log{\left(3 \right)}^{2} + 12 \sqrt[4]{3^{3 x}}}"," ",0,"8*sin(3*x/2)/(3*(3**(3*x))**(1/4)*log(3)**2 + 12*(3**(3*x))**(1/4)) - 4*log(3)*cos(3*x/2)/(3*(3**(3*x))**(1/4)*log(3)**2 + 12*(3**(3*x))**(1/4))","A",0
544,1,265,0,2.813157," ","integrate(exp(m*x)*cos(x)**2,x)","\begin{cases} \frac{x \sin^{2}{\left(x \right)}}{2} + \frac{x \cos^{2}{\left(x \right)}}{2} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} & \text{for}\: m = 0 \\- \frac{x e^{- 2 i x} \sin^{2}{\left(x \right)}}{4} + \frac{i x e^{- 2 i x} \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{x e^{- 2 i x} \cos^{2}{\left(x \right)}}{4} - \frac{e^{- 2 i x} \sin{\left(x \right)} \cos{\left(x \right)}}{4} + \frac{i e^{- 2 i x} \cos^{2}{\left(x \right)}}{2} & \text{for}\: m = - 2 i \\- \frac{x e^{2 i x} \sin^{2}{\left(x \right)}}{4} - \frac{i x e^{2 i x} \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{x e^{2 i x} \cos^{2}{\left(x \right)}}{4} - \frac{e^{2 i x} \sin{\left(x \right)} \cos{\left(x \right)}}{4} - \frac{i e^{2 i x} \cos^{2}{\left(x \right)}}{2} & \text{for}\: m = 2 i \\\frac{m^{2} e^{m x} \cos^{2}{\left(x \right)}}{m^{3} + 4 m} + \frac{2 m e^{m x} \sin{\left(x \right)} \cos{\left(x \right)}}{m^{3} + 4 m} + \frac{2 e^{m x} \sin^{2}{\left(x \right)}}{m^{3} + 4 m} + \frac{2 e^{m x} \cos^{2}{\left(x \right)}}{m^{3} + 4 m} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(x)**2/2 + x*cos(x)**2/2 + sin(x)*cos(x)/2, Eq(m, 0)), (-x*exp(-2*I*x)*sin(x)**2/4 + I*x*exp(-2*I*x)*sin(x)*cos(x)/2 + x*exp(-2*I*x)*cos(x)**2/4 - exp(-2*I*x)*sin(x)*cos(x)/4 + I*exp(-2*I*x)*cos(x)**2/2, Eq(m, -2*I)), (-x*exp(2*I*x)*sin(x)**2/4 - I*x*exp(2*I*x)*sin(x)*cos(x)/2 + x*exp(2*I*x)*cos(x)**2/4 - exp(2*I*x)*sin(x)*cos(x)/4 - I*exp(2*I*x)*cos(x)**2/2, Eq(m, 2*I)), (m**2*exp(m*x)*cos(x)**2/(m**3 + 4*m) + 2*m*exp(m*x)*sin(x)*cos(x)/(m**3 + 4*m) + 2*exp(m*x)*sin(x)**2/(m**3 + 4*m) + 2*exp(m*x)*cos(x)**2/(m**3 + 4*m), True))","A",0
545,1,638,0,11.650916," ","integrate(exp(m*x)*sin(x)**3,x)","\begin{cases} \frac{x e^{- 3 i x} \sin^{3}{\left(x \right)}}{8} - \frac{3 i x e^{- 3 i x} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{3 x e^{- 3 i x} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{8} + \frac{i x e^{- 3 i x} \cos^{3}{\left(x \right)}}{8} + \frac{7 i e^{- 3 i x} \sin^{3}{\left(x \right)}}{24} + \frac{i e^{- 3 i x} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{e^{- 3 i x} \cos^{3}{\left(x \right)}}{8} & \text{for}\: m = - 3 i \\\frac{3 x e^{- i x} \sin^{3}{\left(x \right)}}{8} - \frac{3 i x e^{- i x} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{3 x e^{- i x} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{8} - \frac{3 i x e^{- i x} \cos^{3}{\left(x \right)}}{8} + \frac{5 i e^{- i x} \sin^{3}{\left(x \right)}}{8} + \frac{3 i e^{- i x} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{3 e^{- i x} \cos^{3}{\left(x \right)}}{8} & \text{for}\: m = - i \\\frac{3 x e^{i x} \sin^{3}{\left(x \right)}}{8} + \frac{3 i x e^{i x} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{3 x e^{i x} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{8} + \frac{3 i x e^{i x} \cos^{3}{\left(x \right)}}{8} - \frac{5 i e^{i x} \sin^{3}{\left(x \right)}}{8} - \frac{3 i e^{i x} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{3 e^{i x} \cos^{3}{\left(x \right)}}{8} & \text{for}\: m = i \\\frac{x e^{3 i x} \sin^{3}{\left(x \right)}}{8} + \frac{3 i x e^{3 i x} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{3 x e^{3 i x} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{8} - \frac{i x e^{3 i x} \cos^{3}{\left(x \right)}}{8} - \frac{7 i e^{3 i x} \sin^{3}{\left(x \right)}}{24} - \frac{i e^{3 i x} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{e^{3 i x} \cos^{3}{\left(x \right)}}{8} & \text{for}\: m = 3 i \\\frac{m^{3} e^{m x} \sin^{3}{\left(x \right)}}{m^{4} + 10 m^{2} + 9} - \frac{3 m^{2} e^{m x} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{m^{4} + 10 m^{2} + 9} + \frac{7 m e^{m x} \sin^{3}{\left(x \right)}}{m^{4} + 10 m^{2} + 9} + \frac{6 m e^{m x} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{m^{4} + 10 m^{2} + 9} - \frac{9 e^{m x} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{m^{4} + 10 m^{2} + 9} - \frac{6 e^{m x} \cos^{3}{\left(x \right)}}{m^{4} + 10 m^{2} + 9} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(-3*I*x)*sin(x)**3/8 - 3*I*x*exp(-3*I*x)*sin(x)**2*cos(x)/8 - 3*x*exp(-3*I*x)*sin(x)*cos(x)**2/8 + I*x*exp(-3*I*x)*cos(x)**3/8 + 7*I*exp(-3*I*x)*sin(x)**3/24 + I*exp(-3*I*x)*sin(x)*cos(x)**2/4 + exp(-3*I*x)*cos(x)**3/8, Eq(m, -3*I)), (3*x*exp(-I*x)*sin(x)**3/8 - 3*I*x*exp(-I*x)*sin(x)**2*cos(x)/8 + 3*x*exp(-I*x)*sin(x)*cos(x)**2/8 - 3*I*x*exp(-I*x)*cos(x)**3/8 + 5*I*exp(-I*x)*sin(x)**3/8 + 3*I*exp(-I*x)*sin(x)*cos(x)**2/4 + 3*exp(-I*x)*cos(x)**3/8, Eq(m, -I)), (3*x*exp(I*x)*sin(x)**3/8 + 3*I*x*exp(I*x)*sin(x)**2*cos(x)/8 + 3*x*exp(I*x)*sin(x)*cos(x)**2/8 + 3*I*x*exp(I*x)*cos(x)**3/8 - 5*I*exp(I*x)*sin(x)**3/8 - 3*I*exp(I*x)*sin(x)*cos(x)**2/4 + 3*exp(I*x)*cos(x)**3/8, Eq(m, I)), (x*exp(3*I*x)*sin(x)**3/8 + 3*I*x*exp(3*I*x)*sin(x)**2*cos(x)/8 - 3*x*exp(3*I*x)*sin(x)*cos(x)**2/8 - I*x*exp(3*I*x)*cos(x)**3/8 - 7*I*exp(3*I*x)*sin(x)**3/24 - I*exp(3*I*x)*sin(x)*cos(x)**2/4 + exp(3*I*x)*cos(x)**3/8, Eq(m, 3*I)), (m**3*exp(m*x)*sin(x)**3/(m**4 + 10*m**2 + 9) - 3*m**2*exp(m*x)*sin(x)**2*cos(x)/(m**4 + 10*m**2 + 9) + 7*m*exp(m*x)*sin(x)**3/(m**4 + 10*m**2 + 9) + 6*m*exp(m*x)*sin(x)*cos(x)**2/(m**4 + 10*m**2 + 9) - 9*exp(m*x)*sin(x)**2*cos(x)/(m**4 + 10*m**2 + 9) - 6*exp(m*x)*cos(x)**3/(m**4 + 10*m**2 + 9), True))","A",0
546,1,76,0,2.469784," ","integrate(cos(1/3*x)**3/exp(x)**(1/2),x)","\frac{32 \sin^{3}{\left(\frac{x}{3} \right)}}{65 \sqrt{e^{x}}} - \frac{48 \sin^{2}{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)}}{65 \sqrt{e^{x}}} + \frac{84 \sin{\left(\frac{x}{3} \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{65 \sqrt{e^{x}}} - \frac{74 \cos^{3}{\left(\frac{x}{3} \right)}}{65 \sqrt{e^{x}}}"," ",0,"32*sin(x/3)**3/(65*sqrt(exp(x))) - 48*sin(x/3)**2*cos(x/3)/(65*sqrt(exp(x))) + 84*sin(x/3)*cos(x/3)**2/(65*sqrt(exp(x))) - 74*cos(x/3)**3/(65*sqrt(exp(x)))","A",0
547,1,70,0,5.059197," ","integrate(exp(2*x)*cos(x)**2*sin(x)**2,x)","\frac{e^{2 x} \sin^{4}{\left(x \right)}}{20} + \frac{e^{2 x} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{10} + \frac{e^{2 x} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{5} - \frac{e^{2 x} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{10} + \frac{e^{2 x} \cos^{4}{\left(x \right)}}{20}"," ",0,"exp(2*x)*sin(x)**4/20 + exp(2*x)*sin(x)**3*cos(x)/10 + exp(2*x)*sin(x)**2*cos(x)**2/5 - exp(2*x)*sin(x)*cos(x)**3/10 + exp(2*x)*cos(x)**4/20","B",0
548,1,99,0,4.865583," ","integrate(exp(3*x)*cos(3/2*x)**2*sin(3/2*x)**2,x)","\frac{e^{3 x} \sin^{4}{\left(\frac{3 x}{2} \right)}}{30} + \frac{e^{3 x} \sin^{3}{\left(\frac{3 x}{2} \right)} \cos{\left(\frac{3 x}{2} \right)}}{15} + \frac{2 e^{3 x} \sin^{2}{\left(\frac{3 x}{2} \right)} \cos^{2}{\left(\frac{3 x}{2} \right)}}{15} - \frac{e^{3 x} \sin{\left(\frac{3 x}{2} \right)} \cos^{3}{\left(\frac{3 x}{2} \right)}}{15} + \frac{e^{3 x} \cos^{4}{\left(\frac{3 x}{2} \right)}}{30}"," ",0,"exp(3*x)*sin(3*x/2)**4/30 + exp(3*x)*sin(3*x/2)**3*cos(3*x/2)/15 + 2*exp(3*x)*sin(3*x/2)**2*cos(3*x/2)**2/15 - exp(3*x)*sin(3*x/2)*cos(3*x/2)**3/15 + exp(3*x)*cos(3*x/2)**4/30","B",0
549,0,0,0,0.000000," ","integrate(exp(m*x)*tan(x)**2,x)","\int e^{m x} \tan^{2}{\left(x \right)}\, dx"," ",0,"Integral(exp(m*x)*tan(x)**2, x)","F",0
550,0,0,0,0.000000," ","integrate(exp(m*x)/sin(x)**2,x)","\int \frac{e^{m x}}{\sin^{2}{\left(x \right)}}\, dx"," ",0,"Integral(exp(m*x)/sin(x)**2, x)","F",0
551,0,0,0,0.000000," ","integrate(exp(m*x)/cos(x)**3,x)","\int \frac{e^{m x}}{\cos^{3}{\left(x \right)}}\, dx"," ",0,"Integral(exp(m*x)/cos(x)**3, x)","F",0
552,0,0,0,0.000000," ","integrate(exp(x)/(1+cos(x)),x)","\int \frac{e^{x}}{\cos{\left(x \right)} + 1}\, dx"," ",0,"Integral(exp(x)/(cos(x) + 1), x)","F",0
553,0,0,0,0.000000," ","integrate(exp(x)/(1-cos(x)),x)","- \int \frac{e^{x}}{\cos{\left(x \right)} - 1}\, dx"," ",0,"-Integral(exp(x)/(cos(x) - 1), x)","F",0
554,0,0,0,0.000000," ","integrate(exp(x)/(1+sin(x)),x)","\int \frac{e^{x}}{\sin{\left(x \right)} + 1}\, dx"," ",0,"Integral(exp(x)/(sin(x) + 1), x)","F",0
555,0,0,0,0.000000," ","integrate(exp(x)/(1-sin(x)),x)","- \int \frac{e^{x}}{\sin{\left(x \right)} - 1}\, dx"," ",0,"-Integral(exp(x)/(sin(x) - 1), x)","F",0
556,0,0,0,0.000000," ","integrate(exp(x)*(1-sin(x))/(1-cos(x)),x)","\int \frac{\left(\sin{\left(x \right)} - 1\right) e^{x}}{\cos{\left(x \right)} - 1}\, dx"," ",0,"Integral((sin(x) - 1)*exp(x)/(cos(x) - 1), x)","F",0
557,0,0,0,0.000000," ","integrate(exp(x)*(1+sin(x))/(1-cos(x)),x)","- \int \frac{e^{x}}{\cos{\left(x \right)} - 1}\, dx - \int \frac{e^{x} \sin{\left(x \right)}}{\cos{\left(x \right)} - 1}\, dx"," ",0,"-Integral(exp(x)/(cos(x) - 1), x) - Integral(exp(x)*sin(x)/(cos(x) - 1), x)","F",0
558,0,0,0,0.000000," ","integrate(exp(x)*(1+sin(x))/(1+cos(x)),x)","\int \frac{\left(\sin{\left(x \right)} + 1\right) e^{x}}{\cos{\left(x \right)} + 1}\, dx"," ",0,"Integral((sin(x) + 1)*exp(x)/(cos(x) + 1), x)","F",0
559,0,0,0,0.000000," ","integrate(exp(x)*(1-sin(x))/(1+cos(x)),x)","- \int \left(- \frac{e^{x}}{\cos{\left(x \right)} + 1}\right)\, dx - \int \frac{e^{x} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx"," ",0,"-Integral(-exp(x)/(cos(x) + 1), x) - Integral(exp(x)*sin(x)/(cos(x) + 1), x)","F",0
560,0,0,0,0.000000," ","integrate(exp(x)*(1-cos(x))/(1-sin(x)),x)","\int \frac{\left(\cos{\left(x \right)} - 1\right) e^{x}}{\sin{\left(x \right)} - 1}\, dx"," ",0,"Integral((cos(x) - 1)*exp(x)/(sin(x) - 1), x)","F",0
561,0,0,0,0.000000," ","integrate(exp(x)*(1+cos(x))/(1-sin(x)),x)","- \int \frac{e^{x}}{\sin{\left(x \right)} - 1}\, dx - \int \frac{e^{x} \cos{\left(x \right)}}{\sin{\left(x \right)} - 1}\, dx"," ",0,"-Integral(exp(x)/(sin(x) - 1), x) - Integral(exp(x)*cos(x)/(sin(x) - 1), x)","F",0
562,0,0,0,0.000000," ","integrate(exp(x)*(1+cos(x))/(1+sin(x)),x)","\int \frac{\left(\cos{\left(x \right)} + 1\right) e^{x}}{\sin{\left(x \right)} + 1}\, dx"," ",0,"Integral((cos(x) + 1)*exp(x)/(sin(x) + 1), x)","F",0
563,0,0,0,0.000000," ","integrate(exp(x)*(1-cos(x))/(1+sin(x)),x)","- \int \left(- \frac{e^{x}}{\sin{\left(x \right)} + 1}\right)\, dx - \int \frac{e^{x} \cos{\left(x \right)}}{\sin{\left(x \right)} + 1}\, dx"," ",0,"-Integral(-exp(x)/(sin(x) + 1), x) - Integral(exp(x)*cos(x)/(sin(x) + 1), x)","F",0
564,1,27,0,0.829248," ","integrate(exp(x)*x*cos(x),x)","\frac{x e^{x} \sin{\left(x \right)}}{2} + \frac{x e^{x} \cos{\left(x \right)}}{2} - \frac{e^{x} \sin{\left(x \right)}}{2}"," ",0,"x*exp(x)*sin(x)/2 + x*exp(x)*cos(x)/2 - exp(x)*sin(x)/2","A",0
565,1,48,0,2.058483," ","integrate(exp(x)*x**2*sin(x),x)","\frac{x^{2} e^{x} \sin{\left(x \right)}}{2} - \frac{x^{2} e^{x} \cos{\left(x \right)}}{2} + x e^{x} \cos{\left(x \right)} - \frac{e^{x} \sin{\left(x \right)}}{2} - \frac{e^{x} \cos{\left(x \right)}}{2}"," ",0,"x**2*exp(x)*sin(x)/2 - x**2*exp(x)*cos(x)/2 + x*exp(x)*cos(x) - exp(x)*sin(x)/2 - exp(x)*cos(x)/2","A",0
566,1,80,0,2.283994," ","integrate(x**2*sin(x)/exp(3*x),x)","- \frac{3 x^{2} e^{- 3 x} \sin{\left(x \right)}}{10} - \frac{x^{2} e^{- 3 x} \cos{\left(x \right)}}{10} - \frac{4 x e^{- 3 x} \sin{\left(x \right)}}{25} - \frac{3 x e^{- 3 x} \cos{\left(x \right)}}{25} - \frac{9 e^{- 3 x} \sin{\left(x \right)}}{250} - \frac{13 e^{- 3 x} \cos{\left(x \right)}}{250}"," ",0,"-3*x**2*exp(-3*x)*sin(x)/10 - x**2*exp(-3*x)*cos(x)/10 - 4*x*exp(-3*x)*sin(x)/25 - 3*x*exp(-3*x)*cos(x)/25 - 9*exp(-3*x)*sin(x)/250 - 13*exp(-3*x)*cos(x)/250","A",0
567,1,202,0,11.766122," ","integrate(exp(1/2*x)*x**2*cos(x)**3,x)","\frac{96 x^{2} e^{\frac{x}{2}} \sin^{3}{\left(x \right)}}{185} + \frac{48 x^{2} e^{\frac{x}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{185} + \frac{156 x^{2} e^{\frac{x}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{185} + \frac{58 x^{2} e^{\frac{x}{2}} \cos^{3}{\left(x \right)}}{185} - \frac{32256 x e^{\frac{x}{2}} \sin^{3}{\left(x \right)}}{34225} + \frac{19392 x e^{\frac{x}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{34225} - \frac{34656 x e^{\frac{x}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{34225} + \frac{26392 x e^{\frac{x}{2}} \cos^{3}{\left(x \right)}}{34225} - \frac{1116672 e^{\frac{x}{2}} \sin^{3}{\left(x \right)}}{6331625} - \frac{6525696 e^{\frac{x}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{6331625} - \frac{1512672 e^{\frac{x}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{6331625} - \frac{6739696 e^{\frac{x}{2}} \cos^{3}{\left(x \right)}}{6331625}"," ",0,"96*x**2*exp(x/2)*sin(x)**3/185 + 48*x**2*exp(x/2)*sin(x)**2*cos(x)/185 + 156*x**2*exp(x/2)*sin(x)*cos(x)**2/185 + 58*x**2*exp(x/2)*cos(x)**3/185 - 32256*x*exp(x/2)*sin(x)**3/34225 + 19392*x*exp(x/2)*sin(x)**2*cos(x)/34225 - 34656*x*exp(x/2)*sin(x)*cos(x)**2/34225 + 26392*x*exp(x/2)*cos(x)**3/34225 - 1116672*exp(x/2)*sin(x)**3/6331625 - 6525696*exp(x/2)*sin(x)**2*cos(x)/6331625 - 1512672*exp(x/2)*sin(x)*cos(x)**2/6331625 - 6739696*exp(x/2)*cos(x)**3/6331625","A",0
568,1,85,0,2.110713," ","integrate(exp(2*x)*x**2*sin(4*x),x)","\frac{x^{2} e^{2 x} \sin{\left(4 x \right)}}{10} - \frac{x^{2} e^{2 x} \cos{\left(4 x \right)}}{5} + \frac{3 x e^{2 x} \sin{\left(4 x \right)}}{50} + \frac{2 x e^{2 x} \cos{\left(4 x \right)}}{25} - \frac{11 e^{2 x} \sin{\left(4 x \right)}}{500} + \frac{e^{2 x} \cos{\left(4 x \right)}}{250}"," ",0,"x**2*exp(2*x)*sin(4*x)/10 - x**2*exp(2*x)*cos(4*x)/5 + 3*x*exp(2*x)*sin(4*x)/50 + 2*x*exp(2*x)*cos(4*x)/25 - 11*exp(2*x)*sin(4*x)/500 + exp(2*x)*cos(4*x)/250","A",0
569,1,202,0,11.806939," ","integrate(exp(1/2*x)*x**2*cos(x)*sin(x)**2,x)","\frac{52 x^{2} e^{\frac{x}{2}} \sin^{3}{\left(x \right)}}{185} + \frac{26 x^{2} e^{\frac{x}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{185} - \frac{8 x^{2} e^{\frac{x}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{185} + \frac{16 x^{2} e^{\frac{x}{2}} \cos^{3}{\left(x \right)}}{185} - \frac{11552 x e^{\frac{x}{2}} \sin^{3}{\left(x \right)}}{34225} + \frac{13464 x e^{\frac{x}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{34225} - \frac{9152 x e^{\frac{x}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{34225} + \frac{6464 x e^{\frac{x}{2}} \cos^{3}{\left(x \right)}}{34225} - \frac{504224 e^{\frac{x}{2}} \sin^{3}{\left(x \right)}}{6331625} - \frac{2389232 e^{\frac{x}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{6331625} - \frac{108224 e^{\frac{x}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{6331625} - \frac{2175232 e^{\frac{x}{2}} \cos^{3}{\left(x \right)}}{6331625}"," ",0,"52*x**2*exp(x/2)*sin(x)**3/185 + 26*x**2*exp(x/2)*sin(x)**2*cos(x)/185 - 8*x**2*exp(x/2)*sin(x)*cos(x)**2/185 + 16*x**2*exp(x/2)*cos(x)**3/185 - 11552*x*exp(x/2)*sin(x)**3/34225 + 13464*x*exp(x/2)*sin(x)**2*cos(x)/34225 - 9152*x*exp(x/2)*sin(x)*cos(x)**2/34225 + 6464*x*exp(x/2)*cos(x)**3/34225 - 504224*exp(x/2)*sin(x)**3/6331625 - 2389232*exp(x/2)*sin(x)**2*cos(x)/6331625 - 108224*exp(x/2)*sin(x)*cos(x)**2/6331625 - 2175232*exp(x/2)*cos(x)**3/6331625","A",0
570,1,2,0,0.125530," ","integrate(cosh(x),x)","\sinh{\left(x \right)}"," ",0,"sinh(x)","A",0
571,1,2,0,0.126019," ","integrate(sinh(x),x)","\cosh{\left(x \right)}"," ",0,"cosh(x)","A",0
572,1,7,0,0.129025," ","integrate(tanh(x),x)","x - \log{\left(\tanh{\left(x \right)} + 1 \right)}"," ",0,"x - log(tanh(x) + 1)","B",0
573,1,12,0,0.309889," ","integrate(coth(x),x)","x - \log{\left(\tanh{\left(x \right)} + 1 \right)} + \log{\left(\tanh{\left(x \right)} \right)}"," ",0,"x - log(tanh(x) + 1) + log(tanh(x))","B",0
574,0,0,0,0.000000," ","integrate(sech(x),x)","\int \operatorname{sech}{\left(x \right)}\, dx"," ",0,"Integral(sech(x), x)","F",0
575,0,0,0,0.000000," ","integrate(csch(x),x)","\int \operatorname{csch}{\left(x \right)}\, dx"," ",0,"Integral(csch(x), x)","F",0
576,1,24,0,0.195923," ","integrate(cosh(x)**2,x)","- \frac{x \sinh^{2}{\left(x \right)}}{2} + \frac{x \cosh^{2}{\left(x \right)}}{2} + \frac{\sinh{\left(x \right)} \cosh{\left(x \right)}}{2}"," ",0,"-x*sinh(x)**2/2 + x*cosh(x)**2/2 + sinh(x)*cosh(x)/2","B",0
577,1,29,0,1.120609," ","integrate(sinh(x)**5,x)","\sinh^{4}{\left(x \right)} \cosh{\left(x \right)} - \frac{4 \sinh^{2}{\left(x \right)} \cosh^{3}{\left(x \right)}}{3} + \frac{8 \cosh^{5}{\left(x \right)}}{15}"," ",0,"sinh(x)**4*cosh(x) - 4*sinh(x)**2*cosh(x)**3/3 + 8*cosh(x)**5/15","A",0
578,1,10,0,0.227821," ","integrate(tanh(x)**4,x)","x - \frac{\tanh^{3}{\left(x \right)}}{3} - \tanh{\left(x \right)}"," ",0,"x - tanh(x)**3/3 - tanh(x)","A",0
579,0,0,0,0.000000," ","integrate(csch(x)**3,x)","\int \operatorname{csch}^{3}{\left(x \right)}\, dx"," ",0,"Integral(csch(x)**3, x)","F",0
580,1,422,0,2.829619," ","integrate(1/cosh(x)**5,x)","\frac{3 \tanh^{8}{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{4 \tanh^{8}{\left(\frac{x}{2} \right)} + 16 \tanh^{6}{\left(\frac{x}{2} \right)} + 24 \tanh^{4}{\left(\frac{x}{2} \right)} + 16 \tanh^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{5 \tanh^{7}{\left(\frac{x}{2} \right)}}{4 \tanh^{8}{\left(\frac{x}{2} \right)} + 16 \tanh^{6}{\left(\frac{x}{2} \right)} + 24 \tanh^{4}{\left(\frac{x}{2} \right)} + 16 \tanh^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{12 \tanh^{6}{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{4 \tanh^{8}{\left(\frac{x}{2} \right)} + 16 \tanh^{6}{\left(\frac{x}{2} \right)} + 24 \tanh^{4}{\left(\frac{x}{2} \right)} + 16 \tanh^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{3 \tanh^{5}{\left(\frac{x}{2} \right)}}{4 \tanh^{8}{\left(\frac{x}{2} \right)} + 16 \tanh^{6}{\left(\frac{x}{2} \right)} + 24 \tanh^{4}{\left(\frac{x}{2} \right)} + 16 \tanh^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{18 \tanh^{4}{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{4 \tanh^{8}{\left(\frac{x}{2} \right)} + 16 \tanh^{6}{\left(\frac{x}{2} \right)} + 24 \tanh^{4}{\left(\frac{x}{2} \right)} + 16 \tanh^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{3 \tanh^{3}{\left(\frac{x}{2} \right)}}{4 \tanh^{8}{\left(\frac{x}{2} \right)} + 16 \tanh^{6}{\left(\frac{x}{2} \right)} + 24 \tanh^{4}{\left(\frac{x}{2} \right)} + 16 \tanh^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{12 \tanh^{2}{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{4 \tanh^{8}{\left(\frac{x}{2} \right)} + 16 \tanh^{6}{\left(\frac{x}{2} \right)} + 24 \tanh^{4}{\left(\frac{x}{2} \right)} + 16 \tanh^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{5 \tanh{\left(\frac{x}{2} \right)}}{4 \tanh^{8}{\left(\frac{x}{2} \right)} + 16 \tanh^{6}{\left(\frac{x}{2} \right)} + 24 \tanh^{4}{\left(\frac{x}{2} \right)} + 16 \tanh^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{3 \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{4 \tanh^{8}{\left(\frac{x}{2} \right)} + 16 \tanh^{6}{\left(\frac{x}{2} \right)} + 24 \tanh^{4}{\left(\frac{x}{2} \right)} + 16 \tanh^{2}{\left(\frac{x}{2} \right)} + 4}"," ",0,"3*tanh(x/2)**8*atan(tanh(x/2))/(4*tanh(x/2)**8 + 16*tanh(x/2)**6 + 24*tanh(x/2)**4 + 16*tanh(x/2)**2 + 4) - 5*tanh(x/2)**7/(4*tanh(x/2)**8 + 16*tanh(x/2)**6 + 24*tanh(x/2)**4 + 16*tanh(x/2)**2 + 4) + 12*tanh(x/2)**6*atan(tanh(x/2))/(4*tanh(x/2)**8 + 16*tanh(x/2)**6 + 24*tanh(x/2)**4 + 16*tanh(x/2)**2 + 4) + 3*tanh(x/2)**5/(4*tanh(x/2)**8 + 16*tanh(x/2)**6 + 24*tanh(x/2)**4 + 16*tanh(x/2)**2 + 4) + 18*tanh(x/2)**4*atan(tanh(x/2))/(4*tanh(x/2)**8 + 16*tanh(x/2)**6 + 24*tanh(x/2)**4 + 16*tanh(x/2)**2 + 4) - 3*tanh(x/2)**3/(4*tanh(x/2)**8 + 16*tanh(x/2)**6 + 24*tanh(x/2)**4 + 16*tanh(x/2)**2 + 4) + 12*tanh(x/2)**2*atan(tanh(x/2))/(4*tanh(x/2)**8 + 16*tanh(x/2)**6 + 24*tanh(x/2)**4 + 16*tanh(x/2)**2 + 4) + 5*tanh(x/2)/(4*tanh(x/2)**8 + 16*tanh(x/2)**6 + 24*tanh(x/2)**4 + 16*tanh(x/2)**2 + 4) + 3*atan(tanh(x/2))/(4*tanh(x/2)**8 + 16*tanh(x/2)**6 + 24*tanh(x/2)**4 + 16*tanh(x/2)**2 + 4)","B",0
581,0,0,0,0.000000," ","integrate(tanh(x)**5/sech(x)**4,x)","\int \frac{\tanh^{5}{\left(x \right)}}{\operatorname{sech}^{4}{\left(x \right)}}\, dx"," ",0,"Integral(tanh(x)**5/sech(x)**4, x)","F",0
582,-1,0,0,0.000000," ","integrate(sech(x)**(3/4)*tanh(x)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,1,126,0,4.413937," ","integrate(1/(a+b*cosh(x)),x)","\begin{cases} \tilde{\infty} \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{b \tanh{\left(\frac{x}{2} \right)}} & \text{for}\: a = - b \\\frac{\tanh{\left(\frac{x}{2} \right)}}{b} & \text{for}\: a = b \\- \frac{\log{\left(- \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{a \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} - b \sqrt{\frac{a}{a - b} + \frac{b}{a - b}}} + \frac{\log{\left(\sqrt{\frac{a}{a - b} + \frac{b}{a - b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{a \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} - b \sqrt{\frac{a}{a - b} + \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*atan(tanh(x/2)), Eq(a, 0) & Eq(b, 0)), (-1/(b*tanh(x/2)), Eq(a, -b)), (tanh(x/2)/b, Eq(a, b)), (-log(-sqrt(a/(a - b) + b/(a - b)) + tanh(x/2))/(a*sqrt(a/(a - b) + b/(a - b)) - b*sqrt(a/(a - b) + b/(a - b))) + log(sqrt(a/(a - b) + b/(a - b)) + tanh(x/2))/(a*sqrt(a/(a - b) + b/(a - b)) - b*sqrt(a/(a - b) + b/(a - b))), True))","A",0
584,1,14,0,0.384710," ","integrate(1/(1+cosh(x))**2,x)","- \frac{\tanh^{3}{\left(\frac{x}{2} \right)}}{6} + \frac{\tanh{\left(\frac{x}{2} \right)}}{2}"," ",0,"-tanh(x/2)**3/6 + tanh(x/2)/2","A",0
585,1,146,0,0.613755," ","integrate(1/(a+b*tanh(x)),x)","\begin{cases} \tilde{\infty} \left(x - \log{\left(\tanh{\left(x \right)} + 1 \right)} + \log{\left(\tanh{\left(x \right)} \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{x}{a} & \text{for}\: b = 0 \\- \frac{x \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} - 2 b} + \frac{x}{2 b \tanh{\left(x \right)} - 2 b} + \frac{1}{2 b \tanh{\left(x \right)} - 2 b} & \text{for}\: a = - b \\\frac{x \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} + 2 b} + \frac{x}{2 b \tanh{\left(x \right)} + 2 b} - \frac{1}{2 b \tanh{\left(x \right)} + 2 b} & \text{for}\: a = b \\\frac{a x}{a^{2} - b^{2}} - \frac{b x}{a^{2} - b^{2}} - \frac{b \log{\left(\frac{a}{b} + \tanh{\left(x \right)} \right)}}{a^{2} - b^{2}} + \frac{b \log{\left(\tanh{\left(x \right)} + 1 \right)}}{a^{2} - b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(x - log(tanh(x) + 1) + log(tanh(x))), Eq(a, 0) & Eq(b, 0)), (x/a, Eq(b, 0)), (-x*tanh(x)/(2*b*tanh(x) - 2*b) + x/(2*b*tanh(x) - 2*b) + 1/(2*b*tanh(x) - 2*b), Eq(a, -b)), (x*tanh(x)/(2*b*tanh(x) + 2*b) + x/(2*b*tanh(x) + 2*b) - 1/(2*b*tanh(x) + 2*b), Eq(a, b)), (a*x/(a**2 - b**2) - b*x/(a**2 - b**2) - b*log(a/b + tanh(x))/(a**2 - b**2) + b*log(tanh(x) + 1)/(a**2 - b**2), True))","A",0
586,1,605,0,46.111870," ","integrate(1/(a**2+b**2*cosh(x)**2),x)","\begin{cases} \frac{\tilde{\infty} \tanh{\left(\frac{x}{2} \right)}}{\tanh^{2}{\left(\frac{x}{2} \right)} + 1} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{\tanh{\left(\frac{x}{2} \right)}}{2 b^{2}} - \frac{1}{2 b^{2} \tanh{\left(\frac{x}{2} \right)}} & \text{for}\: a = - i b \vee a = i b \\\frac{2 \tanh{\left(\frac{x}{2} \right)}}{b^{2} \left(\tanh^{2}{\left(\frac{x}{2} \right)} + 1\right)} & \text{for}\: a = 0 \\\frac{a \log{\left(- \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{- 2 a^{3} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} - 2 a b^{2} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}}} - \frac{a \log{\left(\sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{- 2 a^{3} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} - 2 a b^{2} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}}} - \frac{i b \log{\left(- \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{- 2 a^{3} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} - 2 a b^{2} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}}} + \frac{i b \log{\left(\sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{- 2 a^{3} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} - 2 a b^{2} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}}} + \frac{\sqrt{\frac{a}{a - i b} + \frac{i b}{a - i b}} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} \log{\left(- \sqrt{\frac{a}{a - i b} + \frac{i b}{a - i b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{- 2 a^{2} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} - 2 i a b \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}}} - \frac{\sqrt{\frac{a}{a - i b} + \frac{i b}{a - i b}} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} \log{\left(\sqrt{\frac{a}{a - i b} + \frac{i b}{a - i b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{- 2 a^{2} \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}} - 2 i a b \sqrt{\frac{a}{a + i b} - \frac{i b}{a + i b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*tanh(x/2)/(tanh(x/2)**2 + 1), Eq(a, 0) & Eq(b, 0)), (-tanh(x/2)/(2*b**2) - 1/(2*b**2*tanh(x/2)), Eq(a, I*b) | Eq(a, -I*b)), (2*tanh(x/2)/(b**2*(tanh(x/2)**2 + 1)), Eq(a, 0)), (a*log(-sqrt(a/(a + I*b) - I*b/(a + I*b)) + tanh(x/2))/(-2*a**3*sqrt(a/(a + I*b) - I*b/(a + I*b)) - 2*a*b**2*sqrt(a/(a + I*b) - I*b/(a + I*b))) - a*log(sqrt(a/(a + I*b) - I*b/(a + I*b)) + tanh(x/2))/(-2*a**3*sqrt(a/(a + I*b) - I*b/(a + I*b)) - 2*a*b**2*sqrt(a/(a + I*b) - I*b/(a + I*b))) - I*b*log(-sqrt(a/(a + I*b) - I*b/(a + I*b)) + tanh(x/2))/(-2*a**3*sqrt(a/(a + I*b) - I*b/(a + I*b)) - 2*a*b**2*sqrt(a/(a + I*b) - I*b/(a + I*b))) + I*b*log(sqrt(a/(a + I*b) - I*b/(a + I*b)) + tanh(x/2))/(-2*a**3*sqrt(a/(a + I*b) - I*b/(a + I*b)) - 2*a*b**2*sqrt(a/(a + I*b) - I*b/(a + I*b))) + sqrt(a/(a - I*b) + I*b/(a - I*b))*sqrt(a/(a + I*b) - I*b/(a + I*b))*log(-sqrt(a/(a - I*b) + I*b/(a - I*b)) + tanh(x/2))/(-2*a**2*sqrt(a/(a + I*b) - I*b/(a + I*b)) - 2*I*a*b*sqrt(a/(a + I*b) - I*b/(a + I*b))) - sqrt(a/(a - I*b) + I*b/(a - I*b))*sqrt(a/(a + I*b) - I*b/(a + I*b))*log(sqrt(a/(a - I*b) + I*b/(a - I*b)) + tanh(x/2))/(-2*a**2*sqrt(a/(a + I*b) - I*b/(a + I*b)) - 2*I*a*b*sqrt(a/(a + I*b) - I*b/(a + I*b))), True))","A",0
587,1,892,0,40.604290," ","integrate(1/(a**2-b**2*cosh(x)**2),x)","\begin{cases} \frac{\tilde{\infty} \tanh{\left(\frac{x}{2} \right)}}{\tanh^{2}{\left(\frac{x}{2} \right)} + 1} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\tanh{\left(\frac{x}{2} \right)}}{2 b^{2}} + \frac{1}{2 b^{2} \tanh{\left(\frac{x}{2} \right)}} & \text{for}\: a = b \\- \frac{2 \tanh{\left(\frac{x}{2} \right)}}{b^{2} \left(\tanh^{2}{\left(\frac{x}{2} \right)} + 1\right)} & \text{for}\: a = 0 \\\frac{\tanh{\left(\frac{x}{2} \right)}}{2 b^{2}} + \frac{1}{2 b^{2} \tanh{\left(\frac{x}{2} \right)}} & \text{for}\: a = - b \\- \frac{a \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \log{\left(- \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{2 a^{3} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} - 2 a b^{2} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}}} + \frac{a \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \log{\left(\sqrt{\frac{a}{a + b} - \frac{b}{a + b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{2 a^{3} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} - 2 a b^{2} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}}} - \frac{a \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} \log{\left(- \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{2 a^{3} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} - 2 a b^{2} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}}} + \frac{a \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} \log{\left(\sqrt{\frac{a}{a - b} + \frac{b}{a - b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{2 a^{3} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} - 2 a b^{2} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}}} + \frac{b \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \log{\left(- \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{2 a^{3} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} - 2 a b^{2} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}}} - \frac{b \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \log{\left(\sqrt{\frac{a}{a + b} - \frac{b}{a + b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{2 a^{3} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} - 2 a b^{2} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}}} - \frac{b \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} \log{\left(- \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{2 a^{3} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} - 2 a b^{2} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}}} + \frac{b \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} \log{\left(\sqrt{\frac{a}{a - b} + \frac{b}{a - b}} + \tanh{\left(\frac{x}{2} \right)} \right)}}{2 a^{3} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}} - 2 a b^{2} \sqrt{\frac{a}{a - b} + \frac{b}{a - b}} \sqrt{\frac{a}{a + b} - \frac{b}{a + b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*tanh(x/2)/(tanh(x/2)**2 + 1), Eq(a, 0) & Eq(b, 0)), (tanh(x/2)/(2*b**2) + 1/(2*b**2*tanh(x/2)), Eq(a, b)), (-2*tanh(x/2)/(b**2*(tanh(x/2)**2 + 1)), Eq(a, 0)), (tanh(x/2)/(2*b**2) + 1/(2*b**2*tanh(x/2)), Eq(a, -b)), (-a*sqrt(a/(a - b) + b/(a - b))*log(-sqrt(a/(a + b) - b/(a + b)) + tanh(x/2))/(2*a**3*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b)) - 2*a*b**2*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b))) + a*sqrt(a/(a - b) + b/(a - b))*log(sqrt(a/(a + b) - b/(a + b)) + tanh(x/2))/(2*a**3*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b)) - 2*a*b**2*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b))) - a*sqrt(a/(a + b) - b/(a + b))*log(-sqrt(a/(a - b) + b/(a - b)) + tanh(x/2))/(2*a**3*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b)) - 2*a*b**2*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b))) + a*sqrt(a/(a + b) - b/(a + b))*log(sqrt(a/(a - b) + b/(a - b)) + tanh(x/2))/(2*a**3*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b)) - 2*a*b**2*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b))) + b*sqrt(a/(a - b) + b/(a - b))*log(-sqrt(a/(a + b) - b/(a + b)) + tanh(x/2))/(2*a**3*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b)) - 2*a*b**2*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b))) - b*sqrt(a/(a - b) + b/(a - b))*log(sqrt(a/(a + b) - b/(a + b)) + tanh(x/2))/(2*a**3*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b)) - 2*a*b**2*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b))) - b*sqrt(a/(a + b) - b/(a + b))*log(-sqrt(a/(a - b) + b/(a - b)) + tanh(x/2))/(2*a**3*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b)) - 2*a*b**2*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b))) + b*sqrt(a/(a + b) - b/(a + b))*log(sqrt(a/(a - b) + b/(a - b)) + tanh(x/2))/(2*a**3*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b)) - 2*a*b**2*sqrt(a/(a - b) + b/(a - b))*sqrt(a/(a + b) - b/(a + b))), True))","A",0
588,1,908,0,7.436383," ","integrate(1/(1-sinh(x)**4),x)","\frac{3064704 \log{\left(\tanh{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} + \frac{2167073 \sqrt{2} \log{\left(\tanh{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} + \frac{3064704 \log{\left(\tanh{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} + \frac{2167073 \sqrt{2} \log{\left(\tanh{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} + \frac{3064704 \log{\left(\tanh{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} + \frac{2167073 \sqrt{2} \log{\left(\tanh{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} + \frac{3064704 \log{\left(\tanh{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} + \frac{2167073 \sqrt{2} \log{\left(\tanh{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} - \frac{2167073 \sqrt{2} \log{\left(\tanh{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} - \frac{3064704 \log{\left(\tanh{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} - \frac{2167073 \sqrt{2} \log{\left(\tanh{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} - \frac{3064704 \log{\left(\tanh{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} - \frac{2167073 \sqrt{2} \log{\left(\tanh{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} - \frac{3064704 \log{\left(\tanh{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} - \frac{2167073 \sqrt{2} \log{\left(\tanh{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} - \frac{3064704 \log{\left(\tanh{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} + \frac{12258816 \sqrt{2} \tanh{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584} + \frac{17336584 \tanh{\left(\frac{x}{2} \right)}}{12258816 \sqrt{2} \tanh^{2}{\left(\frac{x}{2} \right)} + 17336584 \tanh^{2}{\left(\frac{x}{2} \right)} + 12258816 \sqrt{2} + 17336584}"," ",0,"3064704*log(tanh(x/2) - 1 + sqrt(2))*tanh(x/2)**2/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) + 2167073*sqrt(2)*log(tanh(x/2) - 1 + sqrt(2))*tanh(x/2)**2/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) + 3064704*log(tanh(x/2) - 1 + sqrt(2))/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) + 2167073*sqrt(2)*log(tanh(x/2) - 1 + sqrt(2))/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) + 3064704*log(tanh(x/2) + 1 + sqrt(2))*tanh(x/2)**2/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) + 2167073*sqrt(2)*log(tanh(x/2) + 1 + sqrt(2))*tanh(x/2)**2/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) + 3064704*log(tanh(x/2) + 1 + sqrt(2))/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) + 2167073*sqrt(2)*log(tanh(x/2) + 1 + sqrt(2))/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) - 2167073*sqrt(2)*log(tanh(x/2) - sqrt(2) - 1)*tanh(x/2)**2/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) - 3064704*log(tanh(x/2) - sqrt(2) - 1)*tanh(x/2)**2/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) - 2167073*sqrt(2)*log(tanh(x/2) - sqrt(2) - 1)/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) - 3064704*log(tanh(x/2) - sqrt(2) - 1)/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) - 2167073*sqrt(2)*log(tanh(x/2) - sqrt(2) + 1)*tanh(x/2)**2/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) - 3064704*log(tanh(x/2) - sqrt(2) + 1)*tanh(x/2)**2/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) - 2167073*sqrt(2)*log(tanh(x/2) - sqrt(2) + 1)/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) - 3064704*log(tanh(x/2) - sqrt(2) + 1)/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) + 12258816*sqrt(2)*tanh(x/2)/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584) + 17336584*tanh(x/2)/(12258816*sqrt(2)*tanh(x/2)**2 + 17336584*tanh(x/2)**2 + 12258816*sqrt(2) + 17336584)","B",0
589,1,102,0,1.825099," ","integrate((cosh(x)**3-sinh(x)**3)/(cosh(x)**3+sinh(x)**3),x)","\frac{4 \sqrt{3} \sinh{\left(x \right)} \operatorname{atan}{\left(\frac{2 \sqrt{3} \sinh{\left(x \right)}}{3 \cosh{\left(x \right)}} - \frac{\sqrt{3}}{3} \right)}}{9 \sinh{\left(x \right)} + 9 \cosh{\left(x \right)}} + \frac{3 \sinh{\left(x \right)}}{9 \sinh{\left(x \right)} + 9 \cosh{\left(x \right)}} + \frac{4 \sqrt{3} \cosh{\left(x \right)} \operatorname{atan}{\left(\frac{2 \sqrt{3} \sinh{\left(x \right)}}{3 \cosh{\left(x \right)}} - \frac{\sqrt{3}}{3} \right)}}{9 \sinh{\left(x \right)} + 9 \cosh{\left(x \right)}}"," ",0,"4*sqrt(3)*sinh(x)*atan(2*sqrt(3)*sinh(x)/(3*cosh(x)) - sqrt(3)/3)/(9*sinh(x) + 9*cosh(x)) + 3*sinh(x)/(9*sinh(x) + 9*cosh(x)) + 4*sqrt(3)*cosh(x)*atan(2*sqrt(3)*sinh(x)/(3*cosh(x)) - sqrt(3)/3)/(9*sinh(x) + 9*cosh(x))","B",0
590,1,116,0,13.118502," ","integrate(cosh(x)*cosh(2*x)*cosh(3*x),x)","\frac{x \sinh{\left(x \right)} \sinh{\left(2 x \right)} \cosh{\left(3 x \right)}}{4} - \frac{x \sinh{\left(x \right)} \sinh{\left(3 x \right)} \cosh{\left(2 x \right)}}{4} - \frac{x \sinh{\left(2 x \right)} \sinh{\left(3 x \right)} \cosh{\left(x \right)}}{4} + \frac{x \cosh{\left(x \right)} \cosh{\left(2 x \right)} \cosh{\left(3 x \right)}}{4} - \frac{3 \sinh{\left(x \right)} \sinh{\left(2 x \right)} \sinh{\left(3 x \right)}}{8} + \frac{\sinh{\left(x \right)} \cosh{\left(2 x \right)} \cosh{\left(3 x \right)}}{3} + \frac{5 \sinh{\left(2 x \right)} \cosh{\left(x \right)} \cosh{\left(3 x \right)}}{24}"," ",0,"x*sinh(x)*sinh(2*x)*cosh(3*x)/4 - x*sinh(x)*sinh(3*x)*cosh(2*x)/4 - x*sinh(2*x)*sinh(3*x)*cosh(x)/4 + x*cosh(x)*cosh(2*x)*cosh(3*x)/4 - 3*sinh(x)*sinh(2*x)*sinh(3*x)/8 + sinh(x)*cosh(2*x)*cosh(3*x)/3 + 5*sinh(2*x)*cosh(x)*cosh(3*x)/24","B",0
591,1,138,0,12.144736," ","integrate(cosh(3/2*x)*sinh(x)*sinh(5/2*x),x)","- \frac{x \sinh{\left(x \right)} \sinh{\left(\frac{3 x}{2} \right)} \cosh{\left(\frac{5 x}{2} \right)}}{4} + \frac{x \sinh{\left(x \right)} \sinh{\left(\frac{5 x}{2} \right)} \cosh{\left(\frac{3 x}{2} \right)}}{4} + \frac{x \sinh{\left(\frac{3 x}{2} \right)} \sinh{\left(\frac{5 x}{2} \right)} \cosh{\left(x \right)}}{4} - \frac{x \cosh{\left(x \right)} \cosh{\left(\frac{3 x}{2} \right)} \cosh{\left(\frac{5 x}{2} \right)}}{4} - \frac{\sinh{\left(x \right)} \sinh{\left(\frac{3 x}{2} \right)} \sinh{\left(\frac{5 x}{2} \right)}}{12} + \frac{7 \sinh{\left(x \right)} \cosh{\left(\frac{3 x}{2} \right)} \cosh{\left(\frac{5 x}{2} \right)}}{20} - \frac{\sinh{\left(\frac{3 x}{2} \right)} \cosh{\left(x \right)} \cosh{\left(\frac{5 x}{2} \right)}}{15}"," ",0,"-x*sinh(x)*sinh(3*x/2)*cosh(5*x/2)/4 + x*sinh(x)*sinh(5*x/2)*cosh(3*x/2)/4 + x*sinh(3*x/2)*sinh(5*x/2)*cosh(x)/4 - x*cosh(x)*cosh(3*x/2)*cosh(5*x/2)/4 - sinh(x)*sinh(3*x/2)*sinh(5*x/2)/12 + 7*sinh(x)*cosh(3*x/2)*cosh(5*x/2)/20 - sinh(3*x/2)*cosh(x)*cosh(5*x/2)/15","B",0
592,0,0,0,0.000000," ","integrate(cosh(x)*(-cosh(2*x)+tanh(x))/(sinh(x)**2+sinh(2*x))/sinh(2*x)**(1/2),x)","- \int \frac{\cosh{\left(x \right)} \cosh{\left(2 x \right)}}{\sinh^{2}{\left(x \right)} \sqrt{\sinh{\left(2 x \right)}} + \sinh^{\frac{3}{2}}{\left(2 x \right)}}\, dx - \int \left(- \frac{\cosh{\left(x \right)} \tanh{\left(x \right)}}{\sinh^{2}{\left(x \right)} \sqrt{\sinh{\left(2 x \right)}} + \sinh^{\frac{3}{2}}{\left(2 x \right)}}\right)\, dx"," ",0,"-Integral(cosh(x)*cosh(2*x)/(sinh(x)**2*sqrt(sinh(2*x)) + sinh(2*x)**(3/2)), x) - Integral(-cosh(x)*tanh(x)/(sinh(x)**2*sqrt(sinh(2*x)) + sinh(2*x)**(3/2)), x)","F",0
593,-1,0,0,0.000000," ","integrate(sinh(x)/(-9+4*cosh(x)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,0,0,0,0.000000," ","integrate(sinh(x)**2*sinh(2*x)/(1-sinh(x)**2)**(3/2),x)","\int \frac{\sinh^{2}{\left(x \right)} \sinh{\left(2 x \right)}}{\left(- \left(\sinh{\left(x \right)} - 1\right) \left(\sinh{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sinh(x)**2*sinh(2*x)/(-(sinh(x) - 1)*(sinh(x) + 1))**(3/2), x)","F",0
595,0,0,0,0.000000," ","integrate(cosh(x)/cosh(2*x)**(1/2),x)","\int \frac{\cosh{\left(x \right)}}{\sqrt{\cosh{\left(2 x \right)}}}\, dx"," ",0,"Integral(cosh(x)/sqrt(cosh(2*x)), x)","F",0
596,1,17,0,0.194836," ","integrate(x*tanh(x)**2,x)","\frac{x^{2}}{2} - x \tanh{\left(x \right)} + x - \log{\left(\tanh{\left(x \right)} + 1 \right)}"," ",0,"x**2/2 - x*tanh(x) + x - log(tanh(x) + 1)","A",0
597,1,22,0,0.663252," ","integrate(x*coth(x)**2,x)","\frac{x^{2}}{2} + x - \frac{x}{\tanh{\left(x \right)}} - \log{\left(\tanh{\left(x \right)} + 1 \right)} + \log{\left(\tanh{\left(x \right)} \right)}"," ",0,"x**2/2 + x - x/tanh(x) - log(tanh(x) + 1) + log(tanh(x))","A",0
598,1,26,0,0.417048," ","integrate((x+cosh(x)+sinh(x))/(cosh(x)-sinh(x)),x)","\frac{x}{- \sinh{\left(x \right)} + \cosh{\left(x \right)}} + \frac{\sinh{\left(x \right)}}{- \sinh{\left(x \right)} + \cosh{\left(x \right)}} - \frac{1}{- \sinh{\left(x \right)} + \cosh{\left(x \right)}}"," ",0,"x/(-sinh(x) + cosh(x)) + sinh(x)/(-sinh(x) + cosh(x)) - 1/(-sinh(x) + cosh(x))","A",0
599,1,12,0,0.465285," ","integrate((x+cosh(x)+sinh(x))/(1+cosh(x)),x)","x \tanh{\left(\frac{x}{2} \right)} + x - \tanh{\left(\frac{x}{2} \right)}"," ",0,"x*tanh(x/2) + x - tanh(x/2)","A",0
600,0,0,0,0.000000," ","integrate(exp(2*x)/sinh(x)**4,x)","\int \frac{e^{2 x}}{\sinh^{4}{\left(x \right)}}\, dx"," ",0,"Integral(exp(2*x)/sinh(x)**4, x)","F",0
601,0,0,0,0.000000," ","integrate(1/exp(2*x)/cosh(x)**4,x)","\int \frac{e^{- 2 x}}{\cosh^{4}{\left(x \right)}}\, dx"," ",0,"Integral(exp(-2*x)/cosh(x)**4, x)","F",0
602,1,12,0,0.485757," ","integrate(exp(x)/(cosh(x)-sinh(x)),x)","\frac{e^{x}}{- 2 \sinh{\left(x \right)} + 2 \cosh{\left(x \right)}}"," ",0,"exp(x)/(-2*sinh(x) + 2*cosh(x))","B",0
603,1,32,0,0.561283," ","integrate(exp(m*x)/(cosh(x)+sinh(x)),x)","\begin{cases} \frac{e^{m x}}{m \sinh{\left(x \right)} + m \cosh{\left(x \right)} - \sinh{\left(x \right)} - \cosh{\left(x \right)}} & \text{for}\: m \neq 1 \\\frac{x e^{x}}{\sinh{\left(x \right)} + \cosh{\left(x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((exp(m*x)/(m*sinh(x) + m*cosh(x) - sinh(x) - cosh(x)), Ne(m, 1)), (x*exp(x)/(sinh(x) + cosh(x)), True))","A",0
604,1,10,0,0.413195," ","integrate(exp(x)/(cosh(x)+sinh(x)),x)","\frac{x e^{x}}{\sinh{\left(x \right)} + \cosh{\left(x \right)}}"," ",0,"x*exp(x)/(sinh(x) + cosh(x))","B",0
605,0,0,0,0.000000," ","integrate(exp(x)/(1-cosh(x)),x)","- \int \frac{e^{x}}{\cosh{\left(x \right)} - 1}\, dx"," ",0,"-Integral(exp(x)/(cosh(x) - 1), x)","F",0
606,0,0,0,0.000000," ","integrate(exp(x)*(1+sinh(x))/(1+cosh(x)),x)","\int \frac{\left(\sinh{\left(x \right)} + 1\right) e^{x}}{\cosh{\left(x \right)} + 1}\, dx"," ",0,"Integral((sinh(x) + 1)*exp(x)/(cosh(x) + 1), x)","F",0
607,0,0,0,0.000000," ","integrate(exp(x)*(1-sinh(x))/(1-cosh(x)),x)","\int \frac{\left(\sinh{\left(x \right)} - 1\right) e^{x}}{\cosh{\left(x \right)} - 1}\, dx"," ",0,"Integral((sinh(x) - 1)*exp(x)/(cosh(x) - 1), x)","F",0
608,1,56,0,0.756433," ","integrate(x**m*ln(x),x)","\begin{cases} \frac{m x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} + \frac{x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} - \frac{x x^{m}}{m^{2} + 2 m + 1} & \text{for}\: m \neq -1 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((m*x*x**m*log(x)/(m**2 + 2*m + 1) + x*x**m*log(x)/(m**2 + 2*m + 1) - x*x**m/(m**2 + 2*m + 1), Ne(m, -1)), (log(x)**2/2, True))","A",0
609,1,155,0,1.571977," ","integrate(x**m*ln(x)**2,x)","\begin{cases} \frac{m^{2} x x^{m} \log{\left(x \right)}^{2}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 m x x^{m} \log{\left(x \right)}^{2}}{m^{3} + 3 m^{2} + 3 m + 1} - \frac{2 m x x^{m} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{x x^{m} \log{\left(x \right)}^{2}}{m^{3} + 3 m^{2} + 3 m + 1} - \frac{2 x x^{m} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 x x^{m}}{m^{3} + 3 m^{2} + 3 m + 1} & \text{for}\: m \neq -1 \\\frac{\log{\left(x \right)}^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((m**2*x*x**m*log(x)**2/(m**3 + 3*m**2 + 3*m + 1) + 2*m*x*x**m*log(x)**2/(m**3 + 3*m**2 + 3*m + 1) - 2*m*x*x**m*log(x)/(m**3 + 3*m**2 + 3*m + 1) + x*x**m*log(x)**2/(m**3 + 3*m**2 + 3*m + 1) - 2*x*x**m*log(x)/(m**3 + 3*m**2 + 3*m + 1) + 2*x*x**m/(m**3 + 3*m**2 + 3*m + 1), Ne(m, -1)), (log(x)**3/3, True))","A",0
610,1,34,0,6.088155," ","integrate(ln(x)**2/x**(5/2),x)","- \frac{2 \log{\left(x \right)}^{2}}{3 x^{\frac{3}{2}}} - \frac{8 \log{\left(x \right)}}{9 x^{\frac{3}{2}}} - \frac{16}{27 x^{\frac{3}{2}}}"," ",0,"-2*log(x)**2/(3*x**(3/2)) - 8*log(x)/(9*x**(3/2)) - 16/(27*x**(3/2))","A",0
611,1,22,0,0.112827," ","integrate((b*x+a)*ln(x),x)","- a x - \frac{b x^{2}}{4} + \left(a x + \frac{b x^{2}}{2}\right) \log{\left(x \right)}"," ",0,"-a*x - b*x**2/4 + (a*x + b*x**2/2)*log(x)","A",0
612,1,71,0,0.153917," ","integrate((b*x+a)**3*ln(x),x)","- a^{3} x - \frac{3 a^{2} b x^{2}}{4} - \frac{a b^{2} x^{3}}{3} - \frac{b^{3} x^{4}}{16} + \left(a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}\right) \log{\left(x \right)}"," ",0,"-a**3*x - 3*a**2*b*x**2/4 - a*b**2*x**3/3 - b**3*x**4/16 + (a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4)*log(x)","A",0
613,1,26,0,0.108064," ","integrate(-1-8*ln(x)**2+3*ln(x)**3,x)","3 x \log{\left(x \right)}^{3} - 17 x \log{\left(x \right)}^{2} + 34 x \log{\left(x \right)} - 35 x"," ",0,"3*x*log(x)**3 - 17*x*log(x)**2 + 34*x*log(x) - 35*x","A",0
614,1,51,0,0.155748," ","integrate((x**4+1)*(1-2*ln(x)+ln(x)**3),x)","\frac{169 x^{5}}{625} - 3 x + \left(- \frac{44 x^{5}}{125} + 4 x\right) \log{\left(x \right)} + \left(- \frac{3 x^{5}}{25} - 3 x\right) \log{\left(x \right)}^{2} + \left(\frac{x^{5}}{5} + x\right) \log{\left(x \right)}^{3}"," ",0,"169*x**5/625 - 3*x + (-44*x**5/125 + 4*x)*log(x) + (-3*x**5/25 - 3*x)*log(x)**2 + (x**5/5 + x)*log(x)**3","A",0
615,1,32,0,0.716189," ","integrate(1/x**3/ln(x)**4,x)","- \frac{4 \operatorname{Ei}{\left(- 2 \log{\left(x \right)} \right)}}{3} + \frac{- 2 \log{\left(x \right)}^{2} + \log{\left(x \right)} - 1}{3 x^{2} \log{\left(x \right)}^{3}}"," ",0,"-4*Ei(-2*log(x))/3 + (-2*log(x)**2 + log(x) - 1)/(3*x**2*log(x)**3)","A",0
616,1,151,0,6.441712," ","integrate(ln(x)/(b*x+a),x)","\begin{cases} \frac{\log{\left(\frac{a}{b} \right)} \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{i \pi \log{\left(\frac{a}{b} + x \right)}}{b} - \frac{\operatorname{Li}_{2}\left(\frac{b \left(\frac{a}{b} + x\right)}{a}\right)}{b} & \text{for}\: \left|{\frac{a}{b} + x}\right| < 1 \\- \frac{\log{\left(\frac{a}{b} \right)} \log{\left(\frac{1}{\frac{a}{b} + x} \right)}}{b} - \frac{i \pi \log{\left(\frac{1}{\frac{a}{b} + x} \right)}}{b} - \frac{\operatorname{Li}_{2}\left(\frac{b \left(\frac{a}{b} + x\right)}{a}\right)}{b} & \text{for}\: \frac{1}{\left|{\frac{a}{b} + x}\right|} < 1 \\- \frac{{G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {\frac{a}{b} + x} \right)} \log{\left(\frac{a}{b} \right)}}{b} - \frac{i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {\frac{a}{b} + x} \right)}}{b} + \frac{{G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)} \log{\left(\frac{a}{b} \right)}}{b} + \frac{i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)}}{b} - \frac{\operatorname{Li}_{2}\left(\frac{b \left(\frac{a}{b} + x\right)}{a}\right)}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(a/b)*log(a/b + x)/b + I*pi*log(a/b + x)/b - polylog(2, b*(a/b + x)/a)/b, Abs(a/b + x) < 1), (-log(a/b)*log(1/(a/b + x))/b - I*pi*log(1/(a/b + x))/b - polylog(2, b*(a/b + x)/a)/b, 1/Abs(a/b + x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), a/b + x)*log(a/b)/b - I*pi*meijerg(((), (1, 1)), ((0, 0), ()), a/b + x)/b + meijerg(((1, 1), ()), ((), (0, 0)), a/b + x)*log(a/b)/b + I*pi*meijerg(((1, 1), ()), ((), (0, 0)), a/b + x)/b - polylog(2, b*(a/b + x)/a)/b, True))","C",0
617,1,24,0,0.354991," ","integrate(ln(x)/(b*x+a)**2,x)","- \frac{\log{\left(x \right)}}{a b + b^{2} x} + \frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a b}"," ",0,"-log(x)/(a*b + b**2*x) + (log(x) - log(a/b + x))/(a*b)","A",0
618,1,15,0,0.890599," ","integrate(ln(x)**n/x,x)","\begin{cases} \frac{\log{\left(x \right)}^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left(\log{\left(x \right)} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)**(n + 1)/(n + 1), Ne(n, -1)), (log(log(x)), True))","A",0
619,1,36,0,1.267354," ","integrate((a+b*ln(x))**n/x,x)","- \begin{cases} - a^{n} \log{\left(x \right)} & \text{for}\: b = 0 \\- \frac{\begin{cases} \frac{\left(a + b \log{\left(x \right)}\right)^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left(a + b \log{\left(x \right)} \right)} & \text{otherwise} \end{cases}}{b} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((-a**n*log(x), Eq(b, 0)), (-Piecewise(((a + b*log(x))**(n + 1)/(n + 1), Ne(n, -1)), (log(a + b*log(x)), True))/b, True))","A",0
620,1,8,0,0.125894," ","integrate(1/x/(a+b*ln(x)),x)","\frac{\log{\left(\frac{a}{b} + \log{\left(x \right)} \right)}}{b}"," ",0,"log(a/b + log(x))/b","A",0
621,1,71,0,20.647530," ","integrate(1/x/((a+b*ln(x))**n),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 1 \\a^{- n} \log{\left(x \right)} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + \log{\left(x \right)} \right)}}{b} & \text{for}\: n = 1 \\- \frac{a}{b n \left(a + b \log{\left(x \right)}\right)^{n} - b \left(a + b \log{\left(x \right)}\right)^{n}} - \frac{b \log{\left(x \right)}}{b n \left(a + b \log{\left(x \right)}\right)^{n} - b \left(a + b \log{\left(x \right)}\right)^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 1)), (a**(-n)*log(x), Eq(b, 0)), (log(a/b + log(x))/b, Eq(n, 1)), (-a/(b*n*(a + b*log(x))**n - b*(a + b*log(x))**n) - b*log(x)/(b*n*(a + b*log(x))**n - b*(a + b*log(x))**n), True))","A",0
622,0,0,0,0.000000," ","integrate(1/x/(a**2+ln(x)**2)**(1/2),x)","\int \frac{1}{x \sqrt{a^{2} + \log{\left(x \right)}^{2}}}\, dx"," ",0,"Integral(1/(x*sqrt(a**2 + log(x)**2)), x)","F",0
623,0,0,0,0.000000," ","integrate(1/x/(-a**2+ln(x)**2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(a - \log{\left(x \right)}\right) \left(a + \log{\left(x \right)}\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(-(a - log(x))*(a + log(x)))), x)","F",0
624,0,0,0,0.000000," ","integrate(1/x/(a**2-ln(x)**2)**(1/2),x)","\int \frac{1}{x \sqrt{\left(a - \log{\left(x \right)}\right) \left(a + \log{\left(x \right)}\right)}}\, dx"," ",0,"Integral(1/(x*sqrt((a - log(x))*(a + log(x)))), x)","F",0
625,0,0,0,0.000000," ","integrate(1/x/ln(x)/(a**2+ln(x)**2)**(1/2),x)","\int \frac{1}{x \sqrt{a^{2} + \log{\left(x \right)}^{2}} \log{\left(x \right)}}\, dx"," ",0,"Integral(1/(x*sqrt(a**2 + log(x)**2)*log(x)), x)","F",0
626,0,0,0,0.000000," ","integrate(1/x/ln(x)/(a**2-ln(x)**2)**(1/2),x)","\int \frac{1}{x \sqrt{\left(a - \log{\left(x \right)}\right) \left(a + \log{\left(x \right)}\right)} \log{\left(x \right)}}\, dx"," ",0,"Integral(1/(x*sqrt((a - log(x))*(a + log(x)))*log(x)), x)","F",0
627,0,0,0,0.000000," ","integrate(1/x/ln(x)/(-a**2+ln(x)**2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(a - \log{\left(x \right)}\right) \left(a + \log{\left(x \right)}\right)} \log{\left(x \right)}}\, dx"," ",0,"Integral(1/(x*sqrt(-(a - log(x))*(a + log(x)))*log(x)), x)","F",0
628,1,10,0,0.257379," ","integrate(ln(ln(x))/x,x)","\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} - \log{\left(x \right)}"," ",0,"log(x)*log(log(x)) - log(x)","A",0
629,1,24,0,0.305219," ","integrate(ln(ln(x))**2/x,x)","\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{2} - 2 \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + 2 \log{\left(x \right)}"," ",0,"log(x)*log(log(x))**2 - 2*log(x)*log(log(x)) + 2*log(x)","A",0
630,1,36,0,0.349156," ","integrate(ln(ln(x))**3/x,x)","\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{3} - 3 \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{2} + 6 \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} - 6 \log{\left(x \right)}"," ",0,"log(x)*log(log(x))**3 - 3*log(x)*log(log(x))**2 + 6*log(x)*log(log(x)) - 6*log(x)","A",0
631,1,48,0,0.393835," ","integrate(ln(ln(x))**4/x,x)","\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{4} - 4 \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{3} + 12 \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}^{2} - 24 \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + 24 \log{\left(x \right)}"," ",0,"log(x)*log(log(x))**4 - 4*log(x)*log(log(x))**3 + 12*log(x)*log(log(x))**2 - 24*log(x)*log(log(x)) + 24*log(x)","A",0
632,1,24,0,1.849733," ","integrate(ln(ln(x))**n/x,x)","\left(- \log{\left(\log{\left(x \right)} \right)}\right)^{- n} \log{\left(\log{\left(x \right)} \right)}^{n} \Gamma\left(n + 1, - \log{\left(\log{\left(x \right)} \right)}\right)"," ",0,"(-log(log(x)))**(-n)*log(log(x))**n*uppergamma(n + 1, -log(log(x)))","A",0
633,0,0,0,0.000000," ","integrate(cot(x)/ln(sin(x)),x)","\int \frac{\cot{\left(x \right)}}{\log{\left(\sin{\left(x \right)} \right)}}\, dx"," ",0,"Integral(cot(x)/log(sin(x)), x)","F",0
634,1,7,0,1.730473," ","integrate((1/cos(x)+cos(x))*tan(x),x)","- \cos{\left(x \right)} + \frac{1}{\cos{\left(x \right)}}"," ",0,"-cos(x) + 1/cos(x)","A",0
635,1,10,0,0.945063," ","integrate(ln(cosh(x))*sinh(x),x)","\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} - \cosh{\left(x \right)}"," ",0,"log(cosh(x))*cosh(x) - cosh(x)","A",0
636,0,0,0,0.000000," ","integrate(ln(cosh(x))*tanh(x),x)","\int \log{\left(\cosh{\left(x \right)} \right)} \tanh{\left(x \right)}\, dx"," ",0,"Integral(log(cosh(x))*tanh(x), x)","F",0
637,1,20,0,6.260925," ","integrate(ln(x-(x**2+1)**(1/2)),x)","x \log{\left(x - \sqrt{x^{2} + 1} \right)} + \sqrt{x^{2} + 1}"," ",0,"x*log(x - sqrt(x**2 + 1)) + sqrt(x**2 + 1)","A",0
638,1,26,0,0.143391," ","integrate(ln(-1+x)/x**3,x)","- \frac{\log{\left(x \right)}}{2} + \frac{\log{\left(x - 1 \right)}}{2} + \frac{1}{2 x} - \frac{\log{\left(x - 1 \right)}}{2 x^{2}}"," ",0,"-log(x)/2 + log(x - 1)/2 + 1/(2*x) - log(x - 1)/(2*x**2)","A",0
639,-2,0,0,0.000000," ","integrate((-1/exp(x)+exp(x))*ln(1+exp(2*x)),x)","\text{Exception raised: ShapeError}"," ",0,"Exception raised: ShapeError","F(-2)",0
640,-1,0,0,0.000000," ","integrate(exp(3/2*x)*ln(-1+exp(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,1,42,0,5.236058," ","integrate(cos(x)**3*ln(sin(x)),x)","\frac{2 \log{\left(\sin{\left(x \right)} \right)} \sin^{3}{\left(x \right)}}{3} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{8 \sin^{3}{\left(x \right)}}{9} - \sin{\left(x \right)} \cos^{2}{\left(x \right)}"," ",0,"2*log(sin(x))*sin(x)**3/3 + log(sin(x))*sin(x)*cos(x)**2 - 8*sin(x)**3/9 - sin(x)*cos(x)**2","A",0
642,1,46,0,20.460688," ","integrate(ln(tan(x))/cos(x)**4,x)","\frac{\log{\left(\tan{\left(x \right)} \right)} \tan^{3}{\left(x \right)}}{3} + \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)} - \frac{\sin^{3}{\left(x \right)}}{9 \cos^{3}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{3 \cos{\left(x \right)}} - \frac{4 \tan{\left(x \right)}}{3}"," ",0,"log(tan(x))*tan(x)**3/3 + log(tan(x))*tan(x) - sin(x)**3/(9*cos(x)**3) + sin(x)/(3*cos(x)) - 4*tan(x)/3","A",0
643,0,0,0,0.000000," ","integrate(ln(cos(1/2*x))/(1+cos(x)),x)","\int \frac{\log{\left(\cos{\left(\frac{x}{2} \right)} \right)}}{\cos{\left(x \right)} + 1}\, dx"," ",0,"Integral(log(cos(x/2))/(cos(x) + 1), x)","F",0
644,1,107,0,7.995285," ","integrate(cos(x)*ln(sin(x))/(1+cos(x))**2,x)","- \frac{2 x}{3} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{6} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan{\left(\frac{x}{2} \right)}}{2} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{6} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{2} - \frac{\log{\left(2 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{6} - \frac{\tan^{3}{\left(\frac{x}{2} \right)}}{18} + \frac{\log{\left(2 \right)} \tan{\left(\frac{x}{2} \right)}}{2} + \frac{5 \tan{\left(\frac{x}{2} \right)}}{6}"," ",0,"-2*x/3 + log(tan(x/2)**2 + 1)*tan(x/2)**3/6 - log(tan(x/2)**2 + 1)*tan(x/2)/2 - log(tan(x/2))*tan(x/2)**3/6 + log(tan(x/2))*tan(x/2)/2 - log(2)*tan(x/2)**3/6 - tan(x/2)**3/18 + log(2)*tan(x/2)/2 + 5*tan(x/2)/6","A",0
645,0,0,0,0.000000," ","integrate(acos(x)**2/x**5,x)","\int \frac{\operatorname{acos}^{2}{\left(x \right)}}{x^{5}}\, dx"," ",0,"Integral(acos(x)**2/x**5, x)","F",0
646,1,54,0,0.655811," ","integrate(x**2*asin(x)**2,x)","\frac{x^{3} \operatorname{asin}^{2}{\left(x \right)}}{3} - \frac{2 x^{3}}{27} + \frac{2 x^{2} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{9} - \frac{4 x}{9} + \frac{4 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{9}"," ",0,"x**3*asin(x)**2/3 - 2*x**3/27 + 2*x**2*sqrt(1 - x**2)*asin(x)/9 - 4*x/9 + 4*sqrt(1 - x**2)*asin(x)/9","A",0
647,1,44,0,0.624923," ","integrate(x**3*atan(x)**2,x)","\frac{x^{4} \operatorname{atan}^{2}{\left(x \right)}}{4} - \frac{x^{3} \operatorname{atan}{\left(x \right)}}{6} + \frac{x^{2}}{12} + \frac{x \operatorname{atan}{\left(x \right)}}{2} - \frac{\log{\left(x^{2} + 1 \right)}}{3} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{4}"," ",0,"x**4*atan(x)**2/4 - x**3*atan(x)/6 + x**2/12 + x*atan(x)/2 - log(x**2 + 1)/3 - atan(x)**2/4","A",0
648,1,53,0,0.875003," ","integrate(atan(x)**2/x**5,x)","- \frac{2 \log{\left(x \right)}}{3} + \frac{\log{\left(x^{2} + 1 \right)}}{3} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{4} + \frac{\operatorname{atan}{\left(x \right)}}{2 x} - \frac{1}{12 x^{2}} - \frac{\operatorname{atan}{\left(x \right)}}{6 x^{3}} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{4 x^{4}}"," ",0,"-2*log(x)/3 + log(x**2 + 1)/3 + atan(x)**2/4 + atan(x)/(2*x) - 1/(12*x**2) - atan(x)/(6*x**3) - atan(x)**2/(4*x**4)","A",0
649,0,0,0,0.000000," ","integrate(x**3*acsc(x)**2,x)","\int x^{3} \operatorname{acsc}^{2}{\left(x \right)}\, dx"," ",0,"Integral(x**3*acsc(x)**2, x)","F",0
650,0,0,0,0.000000," ","integrate(asec(x)**4/x**5,x)","\int \frac{\operatorname{asec}^{4}{\left(x \right)}}{x^{5}}\, dx"," ",0,"Integral(asec(x)**4/x**5, x)","F",0
651,1,48,0,24.118814," ","integrate(asin(x)*(-x**2+1)**(1/2),x)","\left(\begin{cases} \frac{x \sqrt{1 - x^{2}}}{2} + \frac{\operatorname{asin}{\left(x \right)}}{2} & \text{for}\: x > -1 \wedge x < 1 \end{cases}\right) \operatorname{asin}{\left(x \right)} - \begin{cases} \text{NaN} & \text{for}\: x < -1 \\\frac{x^{2}}{4} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{4} - \frac{\pi^{2}}{16} - \frac{1}{4} & \text{for}\: x < 1 \\\text{NaN} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sqrt(1 - x**2)/2 + asin(x)/2, (x > -1) & (x < 1)))*asin(x) - Piecewise((nan, x < -1), (x**2/4 + asin(x)**2/4 - pi**2/16 - 1/4, x < 1), (nan, True))","A",0
652,1,48,0,24.579311," ","integrate(acos(x)*(-x**2+1)**(1/2),x)","\left(\begin{cases} \frac{x \sqrt{1 - x^{2}}}{2} + \frac{\operatorname{asin}{\left(x \right)}}{2} & \text{for}\: x > -1 \wedge x < 1 \end{cases}\right) \operatorname{acos}{\left(x \right)} + \begin{cases} \text{NaN} & \text{for}\: x < -1 \\\frac{x^{2}}{4} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{4} - \frac{\pi^{2}}{16} - \frac{1}{4} & \text{for}\: x < 1 \\\text{NaN} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sqrt(1 - x**2)/2 + asin(x)/2, (x > -1) & (x < 1)))*acos(x) + Piecewise((nan, x < -1), (x**2/4 + asin(x)**2/4 - pi**2/16 - 1/4, x < 1), (nan, True))","A",0
653,1,37,0,1.059104," ","integrate(x*acos(x)*(-x**2+1)**(1/2),x)","\frac{x^{3}}{9} + \frac{x^{2} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}{3} - \frac{x}{3} - \frac{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}{3}"," ",0,"x**3/9 + x**2*sqrt(1 - x**2)*acos(x)/3 - x/3 - sqrt(1 - x**2)*acos(x)/3","A",0
654,1,53,0,2.077824," ","integrate((-x**2+1)**(3/2)*asin(x),x)","\frac{x^{4}}{16} - \frac{x^{3} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{4} - \frac{5 x^{2}}{16} + \frac{5 x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{8} + \frac{3 \operatorname{asin}^{2}{\left(x \right)}}{16}"," ",0,"x**4/16 - x**3*sqrt(1 - x**2)*asin(x)/4 - 5*x**2/16 + 5*x*sqrt(1 - x**2)*asin(x)/8 + 3*asin(x)**2/16","A",0
655,1,63,0,3.453833," ","integrate(x*(-x**2+1)**(3/2)*asin(x),x)","\frac{x^{5}}{25} - \frac{x^{4} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{5} - \frac{2 x^{3}}{15} + \frac{2 x^{2} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{5} + \frac{x}{5} - \frac{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{5}"," ",0,"x**5/25 - x**4*sqrt(1 - x**2)*asin(x)/5 - 2*x**3/15 + 2*x**2*sqrt(1 - x**2)*asin(x)/5 + x/5 - sqrt(1 - x**2)*asin(x)/5","B",0
656,1,88,0,162.011090," ","integrate(x**3*(-x**2+1)**(3/2)*acos(x),x)","- \frac{x^{7}}{49} - \frac{x^{6} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}{7} + \frac{8 x^{5}}{175} + \frac{8 x^{4} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}{35} - \frac{x^{3}}{105} - \frac{x^{2} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}{35} - \frac{2 x}{35} - \frac{2 \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}{35}"," ",0,"-x**7/49 - x**6*sqrt(1 - x**2)*acos(x)/7 + 8*x**5/175 + 8*x**4*sqrt(1 - x**2)*acos(x)/35 - x**3/105 - x**2*sqrt(1 - x**2)*acos(x)/35 - 2*x/35 - 2*sqrt(1 - x**2)*acos(x)/35","A",0
657,-1,0,0,0.000000," ","integrate((-x**2+1)**(3/2)*acos(x)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
658,0,0,0,0.000000," ","integrate((-x**2+1)**(3/2)*asin(x)/x**6,x)","\int \frac{\left(- \left(x - 1\right) \left(x + 1\right)\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}}{x^{6}}\, dx"," ",0,"Integral((-(x - 1)*(x + 1))**(3/2)*asin(x)/x**6, x)","F",0
659,1,26,0,0.371802," ","integrate(x**2*asin(x)/(-x**2+1)**(1/2),x)","\frac{x^{2}}{4} - \frac{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{2} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{4}"," ",0,"x**2/4 - x*sqrt(1 - x**2)*asin(x)/2 + asin(x)**2/4","A",0
660,1,53,0,1.318491," ","integrate(x**4*asin(x)/(-x**2+1)**(1/2),x)","\frac{x^{4}}{16} - \frac{x^{3} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{4} + \frac{3 x^{2}}{16} - \frac{3 x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{8} + \frac{3 \operatorname{asin}^{2}{\left(x \right)}}{16}"," ",0,"x**4/16 - x**3*sqrt(1 - x**2)*asin(x)/4 + 3*x**2/16 - 3*x*sqrt(1 - x**2)*asin(x)/8 + 3*asin(x)**2/16","A",0
661,1,20,0,11.287616," ","integrate(x*asin(x)/(-x**2+1)**(3/2),x)","- \begin{cases} \operatorname{acoth}{\left(x \right)} & \text{for}\: x^{2} > 1 \\\operatorname{atanh}{\left(x \right)} & \text{for}\: x^{2} < 1 \end{cases} + \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}"," ",0,"-Piecewise((acoth(x), x**2 > 1), (atanh(x), x**2 < 1)) + asin(x)/sqrt(1 - x**2)","A",0
662,1,20,0,11.909754," ","integrate(x*acos(x)/(-x**2+1)**(3/2),x)","\begin{cases} \operatorname{acoth}{\left(x \right)} & \text{for}\: x^{2} > 1 \\\operatorname{atanh}{\left(x \right)} & \text{for}\: x^{2} < 1 \end{cases} + \frac{\operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}}}"," ",0,"Piecewise((acoth(x), x**2 > 1), (atanh(x), x**2 < 1)) + acos(x)/sqrt(1 - x**2)","A",0
663,-1,0,0,0.000000," ","integrate(asin(x)/(-x**2+1)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
664,1,37,0,18.477166," ","integrate(x**3*asin(x)/(-x**2+1)**(3/2),x)","- x - \left(- \sqrt{1 - x^{2}} - \frac{1}{\sqrt{1 - x^{2}}}\right) \operatorname{asin}{\left(x \right)} + \frac{\log{\left(x - 1 \right)}}{2} - \frac{\log{\left(x + 1 \right)}}{2}"," ",0,"-x - (-sqrt(1 - x**2) - 1/sqrt(1 - x**2))*asin(x) + log(x - 1)/2 - log(x + 1)/2","A",0
665,0,0,0,0.000000," ","integrate(asin(x)/x/(-x**2+1)**(3/2),x)","\int \frac{\operatorname{asin}{\left(x \right)}}{x \left(- \left(x - 1\right) \left(x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asin(x)/(x*(-(x - 1)*(x + 1))**(3/2)), x)","F",0
666,1,60,0,139.931964," ","integrate(acos(x)/x**4/(-x**2+1)**(1/2),x)","\left(\begin{cases} - \frac{\sqrt{1 - x^{2}}}{x} - \frac{\left(1 - x^{2}\right)^{\frac{3}{2}}}{3 x^{3}} & \text{for}\: x > -1 \wedge x < 1 \end{cases}\right) \operatorname{acos}{\left(x \right)} + \begin{cases} \text{NaN} & \text{for}\: x < -1 \\- \frac{2 \log{\left(x \right)}}{3} - \frac{1}{6} + \frac{2 i \pi}{3} + \frac{1}{6 x^{2}} & \text{for}\: x < 1 \\\text{NaN} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(1 - x**2)/x - (1 - x**2)**(3/2)/(3*x**3), (x > -1) & (x < 1)))*acos(x) + Piecewise((nan, x < -1), (-2*log(x)/3 - 1/6 + 2*I*pi/3 + 1/(6*x**2), x < 1), (nan, True))","A",0
667,1,78,0,3.039301," ","integrate(x*acos(x)**2*(-x**2+1)**(1/2),x)","\frac{2 x^{3} \operatorname{acos}{\left(x \right)}}{9} + \frac{x^{2} \sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}{3} - \frac{2 x^{2} \sqrt{1 - x^{2}}}{27} - \frac{2 x \operatorname{acos}{\left(x \right)}}{3} - \frac{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}{3} + \frac{14 \sqrt{1 - x^{2}}}{27}"," ",0,"2*x**3*acos(x)/9 + x**2*sqrt(1 - x**2)*acos(x)**2/3 - 2*x**2*sqrt(1 - x**2)/27 - 2*x*acos(x)/3 - sqrt(1 - x**2)*acos(x)**2/3 + 14*sqrt(1 - x**2)/27","A",0
668,1,66,0,1.315273," ","integrate(x**2*asin(x)**3/(-x**2+1)**(1/2),x)","\frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{4} - \frac{3 x^{2}}{8} - \frac{x \sqrt{1 - x^{2}} \operatorname{asin}^{3}{\left(x \right)}}{2} + \frac{3 x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{4} + \frac{\operatorname{asin}^{4}{\left(x \right)}}{8} - \frac{3 \operatorname{asin}^{2}{\left(x \right)}}{8}"," ",0,"3*x**2*asin(x)**2/4 - 3*x**2/8 - x*sqrt(1 - x**2)*asin(x)**3/2 + 3*x*sqrt(1 - x**2)*asin(x)/4 + asin(x)**4/8 - 3*asin(x)**2/8","A",0
669,1,31,0,0.637851," ","integrate(x*atan(x)/(x**2+1)**2,x)","\frac{x^{2} \operatorname{atan}{\left(x \right)}}{4 x^{2} + 4} + \frac{x}{4 x^{2} + 4} - \frac{\operatorname{atan}{\left(x \right)}}{4 x^{2} + 4}"," ",0,"x**2*atan(x)/(4*x**2 + 4) + x/(4*x**2 + 4) - atan(x)/(4*x**2 + 4)","A",0
670,1,88,0,1.073040," ","integrate(x*atan(x)/(x**2+1)**3,x)","\frac{3 x^{4} \operatorname{atan}{\left(x \right)}}{32 x^{4} + 64 x^{2} + 32} + \frac{3 x^{3}}{32 x^{4} + 64 x^{2} + 32} + \frac{6 x^{2} \operatorname{atan}{\left(x \right)}}{32 x^{4} + 64 x^{2} + 32} + \frac{5 x}{32 x^{4} + 64 x^{2} + 32} - \frac{5 \operatorname{atan}{\left(x \right)}}{32 x^{4} + 64 x^{2} + 32}"," ",0,"3*x**4*atan(x)/(32*x**4 + 64*x**2 + 32) + 3*x**3/(32*x**4 + 64*x**2 + 32) + 6*x**2*atan(x)/(32*x**4 + 64*x**2 + 32) + 5*x/(32*x**4 + 64*x**2 + 32) - 5*atan(x)/(32*x**4 + 64*x**2 + 32)","B",0
671,1,19,0,0.384470," ","integrate(x**2*atan(x)/(x**2+1),x)","x \operatorname{atan}{\left(x \right)} - \frac{\log{\left(x^{2} + 1 \right)}}{2} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{2}"," ",0,"x*atan(x) - log(x**2 + 1)/2 - atan(x)**2/2","A",0
672,0,0,0,0.000000," ","integrate(x**3*atan(x)/(x**2+1),x)","\int \frac{x^{3} \operatorname{atan}{\left(x \right)}}{x^{2} + 1}\, dx"," ",0,"Integral(x**3*atan(x)/(x**2 + 1), x)","F",0
673,-2,0,0,0.000000," ","integrate(x**2*atan(x)/(x**2+1)**2,x)","\text{Exception raised: RecursionError}"," ",0,"Exception raised: RecursionError","F(-2)",0
674,-2,0,0,0.000000," ","integrate(x**3*atan(x)/(x**2+1)**2,x)","\text{Exception raised: RecursionError}"," ",0,"Exception raised: RecursionError","F(-2)",0
675,-2,0,0,0.000000," ","integrate(x**5*atan(x)/(x**2+1)**2,x)","\text{Exception raised: RecursionError}"," ",0,"Exception raised: RecursionError","F(-2)",0
676,1,19,0,0.373431," ","integrate((x**2+1)*atan(x)/x**2,x)","x \operatorname{atan}{\left(x \right)} + \log{\left(x \right)} - \log{\left(x^{2} + 1 \right)} - \frac{\operatorname{atan}{\left(x \right)}}{x}"," ",0,"x*atan(x) + log(x) - log(x**2 + 1) - atan(x)/x","A",0
677,1,34,0,0.835698," ","integrate((x**2+1)*atan(x)/x**5,x)","- \frac{\operatorname{atan}{\left(x \right)}}{4} - \frac{1}{4 x} - \frac{\operatorname{atan}{\left(x \right)}}{2 x^{2}} - \frac{1}{12 x^{3}} - \frac{\operatorname{atan}{\left(x \right)}}{4 x^{4}}"," ",0,"-atan(x)/4 - 1/(4*x) - atan(x)/(2*x**2) - 1/(12*x**3) - atan(x)/(4*x**4)","A",0
678,0,0,0,0.000000," ","integrate((x**2+1)**2*atan(x)/x**5,x)","\int \frac{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}}{x^{5}}\, dx"," ",0,"Integral((x**2 + 1)**2*atan(x)/x**5, x)","F",0
679,1,22,0,0.573294," ","integrate(atan(x)/x**2/(x**2+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{2} + 1 \right)}}{2} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{2} - \frac{\operatorname{atan}{\left(x \right)}}{x}"," ",0,"log(x) - log(x**2 + 1)/2 - atan(x)**2/2 - atan(x)/x","A",0
680,1,32,0,0.529774," ","integrate(atan(x)**2/x**3,x)","\log{\left(x \right)} - \frac{\log{\left(x^{2} + 1 \right)}}{2} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{2} - \frac{\operatorname{atan}{\left(x \right)}}{x} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{2 x^{2}}"," ",0,"log(x) - log(x**2 + 1)/2 - atan(x)**2/2 - atan(x)/x - atan(x)**2/(2*x**2)","A",0
681,1,61,0,0.896858," ","integrate((x**2+1)*atan(x)**2/x**5,x)","\frac{\log{\left(x \right)}}{3} - \frac{\log{\left(x^{2} + 1 \right)}}{6} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{4} - \frac{\operatorname{atan}{\left(x \right)}}{2 x} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{2 x^{2}} - \frac{1}{12 x^{2}} - \frac{\operatorname{atan}{\left(x \right)}}{6 x^{3}} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{4 x^{4}}"," ",0,"log(x)/3 - log(x**2 + 1)/6 - atan(x)**2/4 - atan(x)/(2*x) - atan(x)**2/(2*x**2) - 1/(12*x**2) - atan(x)/(6*x**3) - atan(x)**2/(4*x**4)","A",0
682,0,0,0,0.000000," ","integrate(x**3*atan(x)**2/(x**2+1)**3,x)","\int \frac{x^{3} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}}\, dx"," ",0,"Integral(x**3*atan(x)**2/(x**2 + 1)**3, x)","F",0
683,0,0,0,0.000000," ","integrate(asec(x)*(x**2-1)**(1/2)/x**2,x)","\int \frac{\sqrt{\left(x - 1\right) \left(x + 1\right)} \operatorname{asec}{\left(x \right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt((x - 1)*(x + 1))*asec(x)/x**2, x)","F",0
684,-1,0,0,0.000000," ","integrate((x**2-1)**(5/2)*acsc(x)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
685,-1,0,0,0.000000," ","integrate(asec(x)*(x**2-1)**(1/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
686,-1,0,0,0.000000," ","integrate(asec(x)/(x**2-1)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
687,-1,0,0,0.000000," ","integrate(x**2*asec(x)/(x**2-1)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
688,-1,0,0,0.000000," ","integrate(x**3*asec(x)/(x**2-1)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
689,-1,0,0,0.000000," ","integrate(x**6*asec(x)/(x**2-1)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
690,0,0,0,0.000000," ","integrate(asec(x)/x**2/(x**2-1)**(1/2),x)","\int \frac{\operatorname{asec}{\left(x \right)}}{x^{2} \sqrt{\left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral(asec(x)/(x**2*sqrt((x - 1)*(x + 1))), x)","F",0
691,-1,0,0,0.000000," ","integrate(acsc(x)/x**2/(x**2-1)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,0,0,0,0.000000," ","integrate(acsc(x)**4/x**2/(x**2-1)**(1/2),x)","\int \frac{\operatorname{acsc}^{4}{\left(x \right)}}{x^{2} \sqrt{\left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral(acsc(x)**4/(x**2*sqrt((x - 1)*(x + 1))), x)","F",0
693,-1,0,0,0.000000," ","integrate((x**2-1)**(3/2)*asec(x)**2/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,0,0,0,0.000000," ","integrate(asec(x)**3*(x**2-1)**(1/2)/x**4,x)","\int \frac{\sqrt{\left(x - 1\right) \left(x + 1\right)} \operatorname{asec}^{3}{\left(x \right)}}{x^{4}}\, dx"," ",0,"Integral(sqrt((x - 1)*(x + 1))*asec(x)**3/x**4, x)","F",0
695,0,0,0,0.000000," ","integrate(asin(((-a+x)/(a+x))**(1/2)),x)","\int \operatorname{asin}{\left(\sqrt{\frac{- a + x}{a + x}} \right)}\, dx"," ",0,"Integral(asin(sqrt((-a + x)/(a + x))), x)","F",0
696,0,0,0,0.000000," ","integrate(atan(((-a+x)/(a+x))**(1/2)),x)","\int \operatorname{atan}{\left(\sqrt{\frac{- a + x}{a + x}} \right)}\, dx"," ",0,"Integral(atan(sqrt((-a + x)/(a + x))), x)","F",0
697,1,153,0,0.636749," ","integrate(atan(x)/(1+x)**3,x)","\frac{2 x^{2} \log{\left(x + 1 \right)}}{8 x^{2} + 16 x + 8} - \frac{x^{2} \log{\left(x^{2} + 1 \right)}}{8 x^{2} + 16 x + 8} + \frac{4 x \log{\left(x + 1 \right)}}{8 x^{2} + 16 x + 8} - \frac{2 x \log{\left(x^{2} + 1 \right)}}{8 x^{2} + 16 x + 8} - \frac{2 x}{8 x^{2} + 16 x + 8} + \frac{2 \log{\left(x + 1 \right)}}{8 x^{2} + 16 x + 8} - \frac{\log{\left(x^{2} + 1 \right)}}{8 x^{2} + 16 x + 8} - \frac{4 \operatorname{atan}{\left(x \right)}}{8 x^{2} + 16 x + 8} - \frac{2}{8 x^{2} + 16 x + 8}"," ",0,"2*x**2*log(x + 1)/(8*x**2 + 16*x + 8) - x**2*log(x**2 + 1)/(8*x**2 + 16*x + 8) + 4*x*log(x + 1)/(8*x**2 + 16*x + 8) - 2*x*log(x**2 + 1)/(8*x**2 + 16*x + 8) - 2*x/(8*x**2 + 16*x + 8) + 2*log(x + 1)/(8*x**2 + 16*x + 8) - log(x**2 + 1)/(8*x**2 + 16*x + 8) - 4*atan(x)/(8*x**2 + 16*x + 8) - 2/(8*x**2 + 16*x + 8)","B",0
698,0,0,0,0.000000," ","integrate(-atan(a-x)/(a+x),x)","- \int \frac{\operatorname{atan}{\left(a - x \right)}}{a + x}\, dx"," ",0,"-Integral(atan(a - x)/(a + x), x)","F",0
699,1,22,0,2.564408," ","integrate(asin((-x**2+1)**(1/2))/(-x**2+1)**(1/2),x)","- \frac{\sqrt{x^{2}} \operatorname{asin}^{2}{\left(\sqrt{1 - x^{2}} \right)}}{2 x}"," ",0,"-sqrt(x**2)*asin(sqrt(1 - x**2))**2/(2*x)","A",0
700,1,26,0,2.416252," ","integrate(x*atan((x**2+1)**(1/2))/(x**2+1)**(1/2),x)","\sqrt{x^{2} + 1} \operatorname{atan}{\left(\sqrt{x^{2} + 1} \right)} - \frac{\log{\left(x^{2} + 2 \right)}}{2}"," ",0,"sqrt(x**2 + 1)*atan(sqrt(x**2 + 1)) - log(x**2 + 2)/2","A",0
701,0,0,0,0.000000," ","integrate(asin(x)/(1-x)**(5/2),x)","\int \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(asin(x)/(1 - x)**(5/2), x)","F",0
702,-1,0,0,0.000000," ","integrate((-1+x)**(5/2)*acsc(x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
703,0,0,0,0.000000," ","integrate(asin(sinh(x))*sech(x)**4,x)","\int \operatorname{asin}{\left(\sinh{\left(x \right)} \right)} \operatorname{sech}^{4}{\left(x \right)}\, dx"," ",0,"Integral(asin(sinh(x))*sech(x)**4, x)","F",0
704,-1,0,0,0.000000," ","integrate(acot(cosh(x))*cosh(x)/sinh(x)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,0,0,0,0.000000," ","integrate(exp(x)*asin(tanh(x)),x)","\int e^{x} \operatorname{asin}{\left(\tanh{\left(x \right)} \right)}\, dx"," ",0,"Integral(exp(x)*asin(tanh(x)), x)","F",0
