1,1,10,0,0.053264," ","integrate(x**2+x+1,x)","\frac{x^{3}}{3} + \frac{x^{2}}{2} + x"," ",0,"x**3/3 + x**2/2 + x","A",0
2,1,17,0,0.057616," ","integrate(x**2*(2*x**2+x)**2,x)","\frac{4 x^{7}}{7} + \frac{2 x^{6}}{3} + \frac{x^{5}}{5}"," ",0,"4*x**7/7 + 2*x**6/3 + x**5/5","A",0
3,1,15,0,0.058199," ","integrate(x*(x**2+2*x+1),x)","\frac{x^{4}}{4} + \frac{2 x^{3}}{3} + \frac{x^{2}}{2}"," ",0,"x**4/4 + 2*x**3/3 + x**2/2","A",0
4,1,2,0,0.057008," ","integrate(1/x,x)","\log{\left(x \right)}"," ",0,"log(x)","A",0
5,1,29,0,0.116385," ","integrate((1+x)**3/(-1+x)**4,x)","\frac{- 18 x^{2} + 18 x - 8}{3 x^{3} - 9 x^{2} + 9 x - 3} + \log{\left(x - 1 \right)}"," ",0,"(-18*x**2 + 18*x - 8)/(3*x**3 - 9*x**2 + 9*x - 3) + log(x - 1)","A",0
6,1,24,0,0.148710," ","integrate(1/(-1+x)/x/(1+x)**2,x)","- \log{\left(x \right)} + \frac{\log{\left(x - 1 \right)}}{4} + \frac{3 \log{\left(x + 1 \right)}}{4} - \frac{1}{2 x + 2}"," ",0,"-log(x) + log(x - 1)/4 + 3*log(x + 1)/4 - 1/(2*x + 2)","A",0
7,1,144,0,0.879058," ","integrate((a*x+b)/(-p+x)/(-q+x),x)","\frac{\left(a p + b\right) \log{\left(x + \frac{- 2 a p q - b p - b q - \frac{p^{2} \left(a p + b\right)}{p - q} + \frac{2 p q \left(a p + b\right)}{p - q} - \frac{q^{2} \left(a p + b\right)}{p - q}}{a p + a q + 2 b} \right)}}{p - q} - \frac{\left(a q + b\right) \log{\left(x + \frac{- 2 a p q - b p - b q + \frac{p^{2} \left(a q + b\right)}{p - q} - \frac{2 p q \left(a q + b\right)}{p - q} + \frac{q^{2} \left(a q + b\right)}{p - q}}{a p + a q + 2 b} \right)}}{p - q}"," ",0,"(a*p + b)*log(x + (-2*a*p*q - b*p - b*q - p**2*(a*p + b)/(p - q) + 2*p*q*(a*p + b)/(p - q) - q**2*(a*p + b)/(p - q))/(a*p + a*q + 2*b))/(p - q) - (a*q + b)*log(x + (-2*a*p*q - b*p - b*q + p**2*(a*q + b)/(p - q) - 2*p*q*(a*q + b)/(p - q) + q**2*(a*q + b)/(p - q))/(a*p + a*q + 2*b))/(p - q)","B",0
8,1,124,0,0.207613," ","integrate(1/(a*x**2+b*x+c),x)","- \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{- 4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 a} \right)} + \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 a} \right)}"," ",0,"-sqrt(-1/(4*a*c - b**2))*log(x + (-4*a*c*sqrt(-1/(4*a*c - b**2)) + b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*a)) + sqrt(-1/(4*a*c - b**2))*log(x + (4*a*c*sqrt(-1/(4*a*c - b**2)) - b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*a))","B",0
9,1,26,0,0.160882," ","integrate((a*x+b)/(x**2+1),x)","\left(\frac{a}{2} - \frac{i b}{2}\right) \log{\left(x - i \right)} + \left(\frac{a}{2} + \frac{i b}{2}\right) \log{\left(x + i \right)}"," ",0,"(a/2 - I*b/2)*log(x - I) + (a/2 + I*b/2)*log(x + I)","C",0
10,1,22,0,0.108300," ","integrate(1/(x**2-2*x+3),x)","\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} - \frac{\sqrt{2}}{2} \right)}}{2}"," ",0,"sqrt(2)*atan(sqrt(2)*x/2 - sqrt(2)/2)/2","A",0
11,1,41,0,0.183676," ","integrate(1/(-1+x)**2/(x**2+1)**2,x)","\frac{- x^{2} - x}{4 x^{3} - 4 x^{2} + 4 x - 4} - \frac{\log{\left(x - 1 \right)}}{2} + \frac{\log{\left(x^{2} + 1 \right)}}{4} + \frac{\operatorname{atan}{\left(x \right)}}{4}"," ",0,"(-x**2 - x)/(4*x**3 - 4*x**2 + 4*x - 4) - log(x - 1)/2 + log(x**2 + 1)/4 + atan(x)/4","A",0
12,-1,0,0,0.000000," ","integrate(x/(-a+x)/(-b+x)/(-c+x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
13,1,121,0,0.704565," ","integrate(x/(a**2+x**2)/(b**2+x**2),x)","\frac{\log{\left(- \frac{a^{4}}{2 \left(a - b\right) \left(a + b\right)} + \frac{a^{2} b^{2}}{\left(a - b\right) \left(a + b\right)} + \frac{a^{2}}{2} - \frac{b^{4}}{2 \left(a - b\right) \left(a + b\right)} + \frac{b^{2}}{2} + x^{2} \right)}}{2 \left(a - b\right) \left(a + b\right)} - \frac{\log{\left(\frac{a^{4}}{2 \left(a - b\right) \left(a + b\right)} - \frac{a^{2} b^{2}}{\left(a - b\right) \left(a + b\right)} + \frac{a^{2}}{2} + \frac{b^{4}}{2 \left(a - b\right) \left(a + b\right)} + \frac{b^{2}}{2} + x^{2} \right)}}{2 \left(a - b\right) \left(a + b\right)}"," ",0,"log(-a**4/(2*(a - b)*(a + b)) + a**2*b**2/((a - b)*(a + b)) + a**2/2 - b**4/(2*(a - b)*(a + b)) + b**2/2 + x**2)/(2*(a - b)*(a + b)) - log(a**4/(2*(a - b)*(a + b)) - a**2*b**2/((a - b)*(a + b)) + a**2/2 + b**4/(2*(a - b)*(a + b)) + b**2/2 + x**2)/(2*(a - b)*(a + b))","B",0
14,1,393,0,1.257334," ","integrate(x**2/(a**2+x**2)/(b**2+x**2),x)","- \frac{i a \log{\left(- \frac{2 i a^{7}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} + \frac{4 i a^{5} b^{2}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} - \frac{2 i a^{3} b^{4}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} + \frac{i a^{3}}{\left(a - b\right) \left(a + b\right)} + \frac{i a b^{2}}{\left(a - b\right) \left(a + b\right)} + x \right)}}{2 \left(a - b\right) \left(a + b\right)} + \frac{i a \log{\left(\frac{2 i a^{7}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} - \frac{4 i a^{5} b^{2}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} + \frac{2 i a^{3} b^{4}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} - \frac{i a^{3}}{\left(a - b\right) \left(a + b\right)} - \frac{i a b^{2}}{\left(a - b\right) \left(a + b\right)} + x \right)}}{2 \left(a - b\right) \left(a + b\right)} - \frac{i b \log{\left(- \frac{2 i a^{4} b^{3}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} + \frac{4 i a^{2} b^{5}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} + \frac{i a^{2} b}{\left(a - b\right) \left(a + b\right)} - \frac{2 i b^{7}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} + \frac{i b^{3}}{\left(a - b\right) \left(a + b\right)} + x \right)}}{2 \left(a - b\right) \left(a + b\right)} + \frac{i b \log{\left(\frac{2 i a^{4} b^{3}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} - \frac{4 i a^{2} b^{5}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} - \frac{i a^{2} b}{\left(a - b\right) \left(a + b\right)} + \frac{2 i b^{7}}{\left(a - b\right)^{3} \left(a + b\right)^{3}} - \frac{i b^{3}}{\left(a - b\right) \left(a + b\right)} + x \right)}}{2 \left(a - b\right) \left(a + b\right)}"," ",0,"-I*a*log(-2*I*a**7/((a - b)**3*(a + b)**3) + 4*I*a**5*b**2/((a - b)**3*(a + b)**3) - 2*I*a**3*b**4/((a - b)**3*(a + b)**3) + I*a**3/((a - b)*(a + b)) + I*a*b**2/((a - b)*(a + b)) + x)/(2*(a - b)*(a + b)) + I*a*log(2*I*a**7/((a - b)**3*(a + b)**3) - 4*I*a**5*b**2/((a - b)**3*(a + b)**3) + 2*I*a**3*b**4/((a - b)**3*(a + b)**3) - I*a**3/((a - b)*(a + b)) - I*a*b**2/((a - b)*(a + b)) + x)/(2*(a - b)*(a + b)) - I*b*log(-2*I*a**4*b**3/((a - b)**3*(a + b)**3) + 4*I*a**2*b**5/((a - b)**3*(a + b)**3) + I*a**2*b/((a - b)*(a + b)) - 2*I*b**7/((a - b)**3*(a + b)**3) + I*b**3/((a - b)*(a + b)) + x)/(2*(a - b)*(a + b)) + I*b*log(2*I*a**4*b**3/((a - b)**3*(a + b)**3) - 4*I*a**2*b**5/((a - b)**3*(a + b)**3) - I*a**2*b/((a - b)*(a + b)) + 2*I*b**7/((a - b)**3*(a + b)**3) - I*b**3/((a - b)*(a + b)) + x)/(2*(a - b)*(a + b))","C",0
15,1,19,0,0.127616," ","integrate(x/(-1+x)/(x**2+1),x)","\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 - 1)/2 - log(x**2 + 1)/4 + atan(x)/2","A",0
16,1,41,0,0.134022," ","integrate(x/(x**3+1),x)","- \frac{\log{\left(x + 1 \right)}}{3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"-log(x + 1)/3 + log(x**2 - x + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/3","A",0
17,1,31,0,0.158241," ","integrate(x**3/(-1+x)**2/(x**3+1),x)","\frac{3 \log{\left(x - 1 \right)}}{4} - \frac{\log{\left(x + 1 \right)}}{12} - \frac{\log{\left(x^{2} - x + 1 \right)}}{3} - \frac{1}{2 x - 2}"," ",0,"3*log(x - 1)/4 - log(x + 1)/12 - log(x**2 - x + 1)/3 - 1/(2*x - 2)","A",0
18,1,73,0,0.155441," ","integrate(1/(x**4+1),x)","- \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{4}"," ",0,"-sqrt(2)*log(x**2 - sqrt(2)*x + 1)/8 + sqrt(2)*log(x**2 + sqrt(2)*x + 1)/8 + sqrt(2)*atan(sqrt(2)*x - 1)/4 + sqrt(2)*atan(sqrt(2)*x + 1)/4","A",0
19,1,73,0,0.151815," ","integrate(x**2/(x**4+1),x)","\frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{8} - \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{4}"," ",0,"sqrt(2)*log(x**2 - sqrt(2)*x + 1)/8 - sqrt(2)*log(x**2 + sqrt(2)*x + 1)/8 + sqrt(2)*atan(sqrt(2)*x - 1)/4 + sqrt(2)*atan(sqrt(2)*x + 1)/4","A",0
20,1,70,0,0.193454," ","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
21,1,20,0,0.061400," ","integrate((b*x+a)**p,x)","\frac{\begin{cases} \frac{\left(a + b x\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x \right)} & \text{otherwise} \end{cases}}{b}"," ",0,"Piecewise(((a + b*x)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x), True))/b","A",0
22,1,201,0,0.651477," ","integrate(x*(b*x+a)**p,x)","\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{a \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} + \frac{a}{a b^{2} + b^{3} x} + \frac{b x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} & \text{for}\: p = -2 \\- \frac{a \log{\left(\frac{a}{b} + x \right)}}{b^{2}} + \frac{x}{b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x\right)^{p}}{b^{2} p^{2} + 3 b^{2} p + 2 b^{2}} + \frac{a b p x \left(a + b x\right)^{p}}{b^{2} p^{2} + 3 b^{2} p + 2 b^{2}} + \frac{b^{2} p x^{2} \left(a + b x\right)^{p}}{b^{2} p^{2} + 3 b^{2} p + 2 b^{2}} + \frac{b^{2} x^{2} \left(a + b x\right)^{p}}{b^{2} p^{2} + 3 b^{2} p + 2 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**p*x**2/2, Eq(b, 0)), (a*log(a/b + x)/(a*b**2 + b**3*x) + a/(a*b**2 + b**3*x) + b*x*log(a/b + x)/(a*b**2 + b**3*x), Eq(p, -2)), (-a*log(a/b + x)/b**2 + x/b, Eq(p, -1)), (-a**2*(a + b*x)**p/(b**2*p**2 + 3*b**2*p + 2*b**2) + a*b*p*x*(a + b*x)**p/(b**2*p**2 + 3*b**2*p + 2*b**2) + b**2*p*x**2*(a + b*x)**p/(b**2*p**2 + 3*b**2*p + 2*b**2) + b**2*x**2*(a + b*x)**p/(b**2*p**2 + 3*b**2*p + 2*b**2), True))","A",0
23,1,597,0,1.235151," ","integrate(x**2*(b*x+a)**p,x)","\begin{cases} \frac{a^{p} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{3 a^{2}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{2 b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{2 a^{2}}{a b^{3} + b^{4} x} - \frac{2 a b x \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} + \frac{b^{2} x^{2}}{a b^{3} + b^{4} x} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{3}} - \frac{a x}{b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x\right)^{p}}{b^{3} p^{3} + 6 b^{3} p^{2} + 11 b^{3} p + 6 b^{3}} - \frac{2 a^{2} b p x \left(a + b x\right)^{p}}{b^{3} p^{3} + 6 b^{3} p^{2} + 11 b^{3} p + 6 b^{3}} + \frac{a b^{2} p^{2} x^{2} \left(a + b x\right)^{p}}{b^{3} p^{3} + 6 b^{3} p^{2} + 11 b^{3} p + 6 b^{3}} + \frac{a b^{2} p x^{2} \left(a + b x\right)^{p}}{b^{3} p^{3} + 6 b^{3} p^{2} + 11 b^{3} p + 6 b^{3}} + \frac{b^{3} p^{2} x^{3} \left(a + b x\right)^{p}}{b^{3} p^{3} + 6 b^{3} p^{2} + 11 b^{3} p + 6 b^{3}} + \frac{3 b^{3} p x^{3} \left(a + b x\right)^{p}}{b^{3} p^{3} + 6 b^{3} p^{2} + 11 b^{3} p + 6 b^{3}} + \frac{2 b^{3} x^{3} \left(a + b x\right)^{p}}{b^{3} p^{3} + 6 b^{3} p^{2} + 11 b^{3} p + 6 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**p*x**3/3, Eq(b, 0)), (2*a**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 3*a**2/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 2*b**2*x**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2), Eq(p, -3)), (-2*a**2*log(a/b + x)/(a*b**3 + b**4*x) - 2*a**2/(a*b**3 + b**4*x) - 2*a*b*x*log(a/b + x)/(a*b**3 + b**4*x) + b**2*x**2/(a*b**3 + b**4*x), Eq(p, -2)), (a**2*log(a/b + x)/b**3 - a*x/b**2 + x**2/(2*b), Eq(p, -1)), (2*a**3*(a + b*x)**p/(b**3*p**3 + 6*b**3*p**2 + 11*b**3*p + 6*b**3) - 2*a**2*b*p*x*(a + b*x)**p/(b**3*p**3 + 6*b**3*p**2 + 11*b**3*p + 6*b**3) + a*b**2*p**2*x**2*(a + b*x)**p/(b**3*p**3 + 6*b**3*p**2 + 11*b**3*p + 6*b**3) + a*b**2*p*x**2*(a + b*x)**p/(b**3*p**3 + 6*b**3*p**2 + 11*b**3*p + 6*b**3) + b**3*p**2*x**3*(a + b*x)**p/(b**3*p**3 + 6*b**3*p**2 + 11*b**3*p + 6*b**3) + 3*b**3*p*x**3*(a + b*x)**p/(b**3*p**3 + 6*b**3*p**2 + 11*b**3*p + 6*b**3) + 2*b**3*x**3*(a + b*x)**p/(b**3*p**3 + 6*b**3*p**2 + 11*b**3*p + 6*b**3), True))","A",0
24,1,7,0,0.061239," ","integrate(1/(b*x+a),x)","\frac{\log{\left(a + b x \right)}}{b}"," ",0,"log(a + b*x)/b","A",0
25,1,10,0,0.126893," ","integrate(1/(b*x+a)**2,x)","- \frac{1}{a b + b^{2} x}"," ",0,"-1/(a*b + b**2*x)","A",0
26,1,14,0,0.098852," ","integrate(x/(b*x+a),x)","- \frac{a \log{\left(a + b x \right)}}{b^{2}} + \frac{x}{b}"," ",0,"-a*log(a + b*x)/b**2 + x/b","A",0
27,1,26,0,0.111397," ","integrate(x**2/(b*x+a),x)","\frac{a^{2} \log{\left(a + b x \right)}}{b^{3}} - \frac{a x}{b^{2}} + \frac{x^{2}}{2 b}"," ",0,"a**2*log(a + b*x)/b**3 - a*x/b**2 + x**2/(2*b)","A",0
28,1,10,0,0.140725," ","integrate(1/x/(b*x+a),x)","\frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a}"," ",0,"(log(x) - log(a/b + x))/a","A",0
29,1,19,0,0.174504," ","integrate(1/x**2/(b*x+a),x)","- \frac{1}{a x} + \frac{b \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{2}}"," ",0,"-1/(a*x) + b*(-log(x) + log(a/b + x))/a**2","A",0
30,1,37,0,0.255623," ","integrate(1/x**2/(b*x+a)**2,x)","\frac{- a - 2 b x}{a^{3} x + a^{2} b x^{2}} + \frac{2 b \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{3}}"," ",0,"(-a - 2*b*x)/(a**3*x + a**2*b*x**2) + 2*b*(-log(x) + log(a/b + x))/a**3","A",0
31,1,20,0,0.110265," ","integrate(1/(c**2+x**2),x)","\frac{- \frac{i \log{\left(- i c + x \right)}}{2} + \frac{i \log{\left(i c + x \right)}}{2}}{c}"," ",0,"(-I*log(-I*c + x)/2 + I*log(I*c + x)/2)/c","C",0
32,1,15,0,0.119388," ","integrate(1/(c**2-x**2),x)","- \frac{\frac{\log{\left(- c + x \right)}}{2} - \frac{\log{\left(c + x \right)}}{2}}{c}"," ",0,"-(log(-c + x)/2 - log(c + x)/2)/c","B",0
33,1,78,0,0.298385," ","integrate(1/(2*x**3-1),x)","\frac{2^{\frac{2}{3}} \log{\left(x - \frac{2^{\frac{2}{3}}}{2} \right)}}{6} - \frac{2^{\frac{2}{3}} \log{\left(x^{2} + \frac{2^{\frac{2}{3}} x}{2} + \frac{\sqrt[3]{2}}{2} \right)}}{12} - \frac{2^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt[3]{2} \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"2**(2/3)*log(x - 2**(2/3)/2)/6 - 2**(2/3)*log(x**2 + 2**(2/3)*x/2 + 2**(1/3)/2)/12 - 2**(2/3)*sqrt(3)*atan(2*2**(1/3)*sqrt(3)*x/3 + sqrt(3)/3)/6","A",0
34,1,71,0,0.296407," ","integrate(1/(x**3-2),x)","\frac{\sqrt[3]{2} \log{\left(x - \sqrt[3]{2} \right)}}{6} - \frac{\sqrt[3]{2} \log{\left(x^{2} + \sqrt[3]{2} x + 2^{\frac{2}{3}} \right)}}{12} - \frac{\sqrt[3]{2} \sqrt{3} \operatorname{atan}{\left(\frac{2^{\frac{2}{3}} \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"2**(1/3)*log(x - 2**(1/3))/6 - 2**(1/3)*log(x**2 + 2**(1/3)*x + 2**(2/3))/12 - 2**(1/3)*sqrt(3)*atan(2**(2/3)*sqrt(3)*x/3 + sqrt(3)/3)/6","A",0
35,1,20,0,0.153903," ","integrate(1/(a*x**3-b),x)","\operatorname{RootSum} {\left(27 t^{3} a b^{2} - 1, \left( t \mapsto t \log{\left(- 3 t b + x \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*a*b**2 - 1, Lambda(_t, _t*log(-3*_t*b + x)))","A",0
36,1,46,0,0.312189," ","integrate(1/(x**4-2),x)","\frac{\sqrt[4]{2} \log{\left(x - \sqrt[4]{2} \right)}}{8} - \frac{\sqrt[4]{2} \log{\left(x + \sqrt[4]{2} \right)}}{8} - \frac{\sqrt[4]{2} \operatorname{atan}{\left(\frac{2^{\frac{3}{4}} x}{2} \right)}}{4}"," ",0,"2**(1/4)*log(x - 2**(1/4))/8 - 2**(1/4)*log(x + 2**(1/4))/8 - 2**(1/4)*atan(2**(3/4)*x/2)/4","A",0
37,1,48,0,0.316613," ","integrate(1/(5*x**4-1),x)","\frac{5^{\frac{3}{4}} \log{\left(x - \frac{5^{\frac{3}{4}}}{5} \right)}}{20} - \frac{5^{\frac{3}{4}} \log{\left(x + \frac{5^{\frac{3}{4}}}{5} \right)}}{20} - \frac{5^{\frac{3}{4}} \operatorname{atan}{\left(\sqrt[4]{5} x \right)}}{10}"," ",0,"5**(3/4)*log(x - 5**(3/4)/5)/20 - 5**(3/4)*log(x + 5**(3/4)/5)/20 - 5**(3/4)*atan(5**(1/4)*x)/10","A",0
38,1,151,0,0.403087," ","integrate(1/(3*x**4+7),x)","- \frac{\sqrt[4]{189} \sqrt{2} \log{\left(x^{2} - \frac{\sqrt[4]{189} \sqrt{2} x}{3} + \frac{\sqrt{21}}{3} \right)}}{168} + \frac{\sqrt[4]{189} \sqrt{2} \log{\left(x^{2} + \frac{\sqrt[4]{189} \sqrt{2} x}{3} + \frac{\sqrt{21}}{3} \right)}}{168} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt[4]{7} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt[4]{3} \cdot 7^{\frac{3}{4}} x}{7} - 1 \right)}}{84} + \frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \sqrt[4]{7} \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt[4]{3} \cdot 7^{\frac{3}{4}} x}{7} + 1 \right)}}{84}"," ",0,"-189**(1/4)*sqrt(2)*log(x**2 - 189**(1/4)*sqrt(2)*x/3 + sqrt(21)/3)/168 + 189**(1/4)*sqrt(2)*log(x**2 + 189**(1/4)*sqrt(2)*x/3 + sqrt(21)/3)/168 + sqrt(2)*3**(3/4)*7**(1/4)*atan(sqrt(2)*3**(1/4)*7**(3/4)*x/7 - 1)/84 + sqrt(2)*3**(3/4)*7**(1/4)*atan(sqrt(2)*3**(1/4)*7**(3/4)*x/7 + 1)/84","A",0
39,1,146,0,0.449530," ","integrate(1/(x**4+3*x**2-1),x)","\sqrt{\frac{3}{104} + \frac{\sqrt{13}}{104}} \log{\left(x - 22 \sqrt{\frac{3}{104} + \frac{\sqrt{13}}{104}} + 312 \left(\frac{3}{104} + \frac{\sqrt{13}}{104}\right)^{\frac{3}{2}} \right)} - \sqrt{\frac{3}{104} + \frac{\sqrt{13}}{104}} \log{\left(x - 312 \left(\frac{3}{104} + \frac{\sqrt{13}}{104}\right)^{\frac{3}{2}} + 22 \sqrt{\frac{3}{104} + \frac{\sqrt{13}}{104}} \right)} - 2 \sqrt{- \frac{3}{104} + \frac{\sqrt{13}}{104}} \operatorname{atan}{\left(\frac{2 \sqrt{2} x}{3 \sqrt{-3 + \sqrt{13}} + \sqrt{13} \sqrt{-3 + \sqrt{13}}} \right)}"," ",0,"sqrt(3/104 + sqrt(13)/104)*log(x - 22*sqrt(3/104 + sqrt(13)/104) + 312*(3/104 + sqrt(13)/104)**(3/2)) - sqrt(3/104 + sqrt(13)/104)*log(x - 312*(3/104 + sqrt(13)/104)**(3/2) + 22*sqrt(3/104 + sqrt(13)/104)) - 2*sqrt(-3/104 + sqrt(13)/104)*atan(2*sqrt(2)*x/(3*sqrt(-3 + sqrt(13)) + sqrt(13)*sqrt(-3 + sqrt(13))))","B",0
40,1,24,0,0.354331," ","integrate(1/(x**4-3*x**2-1),x)","\operatorname{RootSum} {\left(2704 t^{4} + 156 t^{2} - 1, \left( t \mapsto t \log{\left(- 312 t^{3} - 22 t + x \right)} \right)\right)}"," ",0,"RootSum(2704*_t**4 + 156*_t**2 - 1, Lambda(_t, _t*log(-312*_t**3 - 22*_t + x)))","A",0
41,1,158,0,0.354726," ","integrate(1/(x**4-3*x**2+1),x)","\left(\frac{\sqrt{5}}{20} + \frac{1}{4}\right) \log{\left(x - \frac{7}{2} - \frac{7 \sqrt{5}}{10} + 120 \left(\frac{\sqrt{5}}{20} + \frac{1}{4}\right)^{3} \right)} + \left(\frac{1}{4} - \frac{\sqrt{5}}{20}\right) \log{\left(x - \frac{7}{2} + 120 \left(\frac{1}{4} - \frac{\sqrt{5}}{20}\right)^{3} + \frac{7 \sqrt{5}}{10} \right)} + \left(- \frac{1}{4} + \frac{\sqrt{5}}{20}\right) \log{\left(x - \frac{7 \sqrt{5}}{10} + 120 \left(- \frac{1}{4} + \frac{\sqrt{5}}{20}\right)^{3} + \frac{7}{2} \right)} + \left(- \frac{1}{4} - \frac{\sqrt{5}}{20}\right) \log{\left(x + 120 \left(- \frac{1}{4} - \frac{\sqrt{5}}{20}\right)^{3} + \frac{7 \sqrt{5}}{10} + \frac{7}{2} \right)}"," ",0,"(sqrt(5)/20 + 1/4)*log(x - 7/2 - 7*sqrt(5)/10 + 120*(sqrt(5)/20 + 1/4)**3) + (1/4 - sqrt(5)/20)*log(x - 7/2 + 120*(1/4 - sqrt(5)/20)**3 + 7*sqrt(5)/10) + (-1/4 + sqrt(5)/20)*log(x - 7*sqrt(5)/10 + 120*(-1/4 + sqrt(5)/20)**3 + 7/2) + (-1/4 - sqrt(5)/20)*log(x + 120*(-1/4 - sqrt(5)/20)**3 + 7*sqrt(5)/10 + 7/2)","B",0
42,1,24,0,0.367451," ","integrate(1/(x**4-4*x**2+1),x)","\operatorname{RootSum} {\left(2304 t^{4} - 192 t^{2} + 1, \left( t \mapsto t \log{\left(384 t^{3} - 28 t + x \right)} \right)\right)}"," ",0,"RootSum(2304*_t**4 - 192*_t**2 + 1, Lambda(_t, _t*log(384*_t**3 - 28*_t + x)))","A",0
43,1,92,0,0.215068," ","integrate(1/(x**4+4*x**2+1),x)","- 2 \sqrt{\frac{1}{24} - \frac{\sqrt{3}}{48}} \operatorname{atan}{\left(\frac{x}{\sqrt{3} \sqrt{2 - \sqrt{3}} + 2 \sqrt{2 - \sqrt{3}}} \right)} - 2 \sqrt{\frac{\sqrt{3}}{48} + \frac{1}{24}} \operatorname{atan}{\left(\frac{x}{- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} \sqrt{\sqrt{3} + 2}} \right)}"," ",0,"-2*sqrt(1/24 - sqrt(3)/48)*atan(x/(sqrt(3)*sqrt(2 - sqrt(3)) + 2*sqrt(2 - sqrt(3)))) - 2*sqrt(sqrt(3)/48 + 1/24)*atan(x/(-2*sqrt(sqrt(3) + 2) + sqrt(3)*sqrt(sqrt(3) + 2)))","A",0
44,1,994,0,1.137961," ","integrate(1/(x**4+x**2+2),x)","\sqrt{\frac{1}{224} + \frac{\sqrt{2}}{112}} \log{\left(x^{2} + x \left(- \frac{4 \sqrt{7} \sqrt{1 + 2 \sqrt{2}}}{7} + \frac{5 \sqrt{14} \sqrt{1 + 2 \sqrt{2}}}{28} + \frac{3 \sqrt{14} \sqrt{1 + 2 \sqrt{2}} \sqrt{4 \sqrt{2} + 9}}{28}\right) - \frac{33 \sqrt{4 \sqrt{2} + 9}}{28} - \frac{11}{28} + \frac{11 \sqrt{2} \sqrt{4 \sqrt{2} + 9}}{28} + \frac{83 \sqrt{2}}{28} \right)} - \sqrt{\frac{1}{224} + \frac{\sqrt{2}}{112}} \log{\left(x^{2} + x \left(- \frac{3 \sqrt{14} \sqrt{1 + 2 \sqrt{2}} \sqrt{4 \sqrt{2} + 9}}{28} - \frac{5 \sqrt{14} \sqrt{1 + 2 \sqrt{2}}}{28} + \frac{4 \sqrt{7} \sqrt{1 + 2 \sqrt{2}}}{7}\right) - \frac{33 \sqrt{4 \sqrt{2} + 9}}{28} - \frac{11}{28} + \frac{11 \sqrt{2} \sqrt{4 \sqrt{2} + 9}}{28} + \frac{83 \sqrt{2}}{28} \right)} + 2 \sqrt{- \frac{\sqrt{4 \sqrt{2} + 9}}{112} + \frac{1}{224} + \frac{3 \sqrt{2}}{112}} \operatorname{atan}{\left(\frac{4 \sqrt{14} x}{\sqrt{4 \sqrt{2} + 9} \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}} + 7 \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}}} - \frac{8 \sqrt{2} \sqrt{1 + 2 \sqrt{2}}}{\sqrt{4 \sqrt{2} + 9} \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}} + 7 \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}}} + \frac{5 \sqrt{1 + 2 \sqrt{2}}}{\sqrt{4 \sqrt{2} + 9} \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}} + 7 \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}}} + \frac{3 \sqrt{1 + 2 \sqrt{2}} \sqrt{4 \sqrt{2} + 9}}{\sqrt{4 \sqrt{2} + 9} \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}} + 7 \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}}} \right)} + 2 \sqrt{- \frac{\sqrt{4 \sqrt{2} + 9}}{112} + \frac{1}{224} + \frac{3 \sqrt{2}}{112}} \operatorname{atan}{\left(\frac{4 \sqrt{14} x}{\sqrt{4 \sqrt{2} + 9} \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}} + 7 \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}}} - \frac{3 \sqrt{1 + 2 \sqrt{2}} \sqrt{4 \sqrt{2} + 9}}{\sqrt{4 \sqrt{2} + 9} \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}} + 7 \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}}} - \frac{5 \sqrt{1 + 2 \sqrt{2}}}{\sqrt{4 \sqrt{2} + 9} \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}} + 7 \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}}} + \frac{8 \sqrt{2} \sqrt{1 + 2 \sqrt{2}}}{\sqrt{4 \sqrt{2} + 9} \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}} + 7 \sqrt{- 2 \sqrt{4 \sqrt{2} + 9} + 1 + 6 \sqrt{2}}} \right)}"," ",0,"sqrt(1/224 + sqrt(2)/112)*log(x**2 + x*(-4*sqrt(7)*sqrt(1 + 2*sqrt(2))/7 + 5*sqrt(14)*sqrt(1 + 2*sqrt(2))/28 + 3*sqrt(14)*sqrt(1 + 2*sqrt(2))*sqrt(4*sqrt(2) + 9)/28) - 33*sqrt(4*sqrt(2) + 9)/28 - 11/28 + 11*sqrt(2)*sqrt(4*sqrt(2) + 9)/28 + 83*sqrt(2)/28) - sqrt(1/224 + sqrt(2)/112)*log(x**2 + x*(-3*sqrt(14)*sqrt(1 + 2*sqrt(2))*sqrt(4*sqrt(2) + 9)/28 - 5*sqrt(14)*sqrt(1 + 2*sqrt(2))/28 + 4*sqrt(7)*sqrt(1 + 2*sqrt(2))/7) - 33*sqrt(4*sqrt(2) + 9)/28 - 11/28 + 11*sqrt(2)*sqrt(4*sqrt(2) + 9)/28 + 83*sqrt(2)/28) + 2*sqrt(-sqrt(4*sqrt(2) + 9)/112 + 1/224 + 3*sqrt(2)/112)*atan(4*sqrt(14)*x/(sqrt(4*sqrt(2) + 9)*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2)) + 7*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2))) - 8*sqrt(2)*sqrt(1 + 2*sqrt(2))/(sqrt(4*sqrt(2) + 9)*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2)) + 7*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2))) + 5*sqrt(1 + 2*sqrt(2))/(sqrt(4*sqrt(2) + 9)*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2)) + 7*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2))) + 3*sqrt(1 + 2*sqrt(2))*sqrt(4*sqrt(2) + 9)/(sqrt(4*sqrt(2) + 9)*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2)) + 7*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2)))) + 2*sqrt(-sqrt(4*sqrt(2) + 9)/112 + 1/224 + 3*sqrt(2)/112)*atan(4*sqrt(14)*x/(sqrt(4*sqrt(2) + 9)*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2)) + 7*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2))) - 3*sqrt(1 + 2*sqrt(2))*sqrt(4*sqrt(2) + 9)/(sqrt(4*sqrt(2) + 9)*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2)) + 7*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2))) - 5*sqrt(1 + 2*sqrt(2))/(sqrt(4*sqrt(2) + 9)*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2)) + 7*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2))) + 8*sqrt(2)*sqrt(1 + 2*sqrt(2))/(sqrt(4*sqrt(2) + 9)*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2)) + 7*sqrt(-2*sqrt(4*sqrt(2) + 9) + 1 + 6*sqrt(2))))","B",0
45,1,24,0,0.544700," ","integrate(1/(x**4-x**2+2),x)","\operatorname{RootSum} {\left(1568 t^{4} + 28 t^{2} + 1, \left( t \mapsto t \log{\left(- 112 t^{3} + 6 t + x \right)} \right)\right)}"," ",0,"RootSum(1568*_t**4 + 28*_t**2 + 1, Lambda(_t, _t*log(-112*_t**3 + 6*_t + x)))","A",0
46,1,83,0,0.254464," ","integrate(1/(x**6-1),x)","\frac{\log{\left(x - 1 \right)}}{6} - \frac{\log{\left(x + 1 \right)}}{6} + \frac{\log{\left(x^{2} - x + 1 \right)}}{12} - \frac{\log{\left(x^{2} + x + 1 \right)}}{12} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"log(x - 1)/6 - log(x + 1)/6 + log(x**2 - x + 1)/12 - log(x**2 + x + 1)/12 - sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/6","A",0
47,1,14,0,0.565971," ","integrate(1/(x**6-2),x)","\operatorname{RootSum} {\left(1492992 t^{6} - 1, \left( t \mapsto t \log{\left(- 12 t + x \right)} \right)\right)}"," ",0,"RootSum(1492992*_t**6 - 1, Lambda(_t, _t*log(-12*_t + x)))","A",0
48,1,14,0,0.277636," ","integrate(1/(x**6+2),x)","\operatorname{RootSum} {\left(1492992 t^{6} + 1, \left( t \mapsto t \log{\left(12 t + x \right)} \right)\right)}"," ",0,"RootSum(1492992*_t**6 + 1, Lambda(_t, _t*log(12*_t + x)))","A",0
49,1,14,0,2.823847," ","integrate(1/(x**8+1),x)","\operatorname{RootSum} {\left(16777216 t^{8} + 1, \left( t \mapsto t \log{\left(8 t + x \right)} \right)\right)}"," ",0,"RootSum(16777216*_t**8 + 1, Lambda(_t, _t*log(8*_t + x)))","A",0
50,1,44,0,161.867935," ","integrate(1/(x**8-1),x)","\frac{\log{\left(x - 1 \right)}}{8} - \frac{\log{\left(x + 1 \right)}}{8} + \frac{i \log{\left(x - i \right)}}{8} - \frac{i \log{\left(x + i \right)}}{8} + \operatorname{RootSum} {\left(4096 t^{4} + 1, \left( t \mapsto t \log{\left(- 8 t + x \right)} \right)\right)}"," ",0,"log(x - 1)/8 - log(x + 1)/8 + I*log(x - I)/8 - I*log(x + I)/8 + RootSum(4096*_t**4 + 1, Lambda(_t, _t*log(-8*_t + x)))","C",0
51,1,165,0,0.222323," ","integrate(1/(x**8-x**4+1),x)","\frac{\sqrt{6} \left(2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} - \frac{1}{3} \right)} + 2 \operatorname{atan}{\left(\sqrt{6} x^{3} - 4 x^{2} + 2 \sqrt{6} x - 3 \right)}\right)}{24} + \frac{\sqrt{6} \left(2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} + \frac{1}{3} \right)} + 2 \operatorname{atan}{\left(\sqrt{6} x^{3} + 4 x^{2} + 2 \sqrt{6} x + 3 \right)}\right)}{24} - \frac{\sqrt{6} \log{\left(x^{4} - \sqrt{6} x^{3} + 3 x^{2} - \sqrt{6} x + 1 \right)}}{24} + \frac{\sqrt{6} \log{\left(x^{4} + \sqrt{6} x^{3} + 3 x^{2} + \sqrt{6} x + 1 \right)}}{24}"," ",0,"sqrt(6)*(2*atan(sqrt(6)*x/3 - 1/3) + 2*atan(sqrt(6)*x**3 - 4*x**2 + 2*sqrt(6)*x - 3))/24 + sqrt(6)*(2*atan(sqrt(6)*x/3 + 1/3) + 2*atan(sqrt(6)*x**3 + 4*x**2 + 2*sqrt(6)*x + 3))/24 - sqrt(6)*log(x**4 - sqrt(6)*x**3 + 3*x**2 - sqrt(6)*x + 1)/24 + sqrt(6)*log(x**4 + sqrt(6)*x**3 + 3*x**2 + sqrt(6)*x + 1)/24","A",0
52,1,46,0,0.172021," ","integrate(x**7/(x**12+1),x)","- \frac{\log{\left(x^{4} + 1 \right)}}{12} + \frac{\log{\left(x^{8} - x^{4} + 1 \right)}}{24} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} - \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"-log(x**4 + 1)/12 + log(x**8 - x**4 + 1)/24 + sqrt(3)*atan(2*sqrt(3)*x**4/3 - sqrt(3)/3)/12","A",0
53,1,5,0,0.079500," ","integrate(ln(x),x)","x \log{\left(x \right)} - x"," ",0,"x*log(x) - x","A",0
54,1,12,0,0.087593," ","integrate(x*ln(x),x)","\frac{x^{2} \log{\left(x \right)}}{2} - \frac{x^{2}}{4}"," ",0,"x**2*log(x)/2 - x**2/4","A",0
55,1,12,0,0.090864," ","integrate(x**2*ln(x),x)","\frac{x^{3} \log{\left(x \right)}}{3} - \frac{x^{3}}{9}"," ",0,"x**3*log(x)/3 - x**3/9","A",0
56,1,56,0,0.736621," ","integrate(x**p*ln(x),x)","\begin{cases} \frac{p x x^{p} \log{\left(x \right)}}{p^{2} + 2 p + 1} + \frac{x x^{p} \log{\left(x \right)}}{p^{2} + 2 p + 1} - \frac{x x^{p}}{p^{2} + 2 p + 1} & \text{for}\: p \neq -1 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x*x**p*log(x)/(p**2 + 2*p + 1) + x*x**p*log(x)/(p**2 + 2*p + 1) - x*x**p/(p**2 + 2*p + 1), Ne(p, -1)), (log(x)**2/2, True))","A",0
57,1,15,0,0.092717," ","integrate(ln(x)**2,x)","x \log{\left(x \right)}^{2} - 2 x \log{\left(x \right)} + 2 x"," ",0,"x*log(x)**2 - 2*x*log(x) + 2*x","A",0
58,1,133,0,0.288592," ","integrate(x**9*ln(x)**11,x)","\frac{x^{10} \log{\left(x \right)}^{11}}{10} - \frac{11 x^{10} \log{\left(x \right)}^{10}}{100} + \frac{11 x^{10} \log{\left(x \right)}^{9}}{100} - \frac{99 x^{10} \log{\left(x \right)}^{8}}{1000} + \frac{99 x^{10} \log{\left(x \right)}^{7}}{1250} - \frac{693 x^{10} \log{\left(x \right)}^{6}}{12500} + \frac{2079 x^{10} \log{\left(x \right)}^{5}}{62500} - \frac{2079 x^{10} \log{\left(x \right)}^{4}}{125000} + \frac{2079 x^{10} \log{\left(x \right)}^{3}}{312500} - \frac{6237 x^{10} \log{\left(x \right)}^{2}}{3125000} + \frac{6237 x^{10} \log{\left(x \right)}}{15625000} - \frac{6237 x^{10}}{156250000}"," ",0,"x**10*log(x)**11/10 - 11*x**10*log(x)**10/100 + 11*x**10*log(x)**9/100 - 99*x**10*log(x)**8/1000 + 99*x**10*log(x)**7/1250 - 693*x**10*log(x)**6/12500 + 2079*x**10*log(x)**5/62500 - 2079*x**10*log(x)**4/125000 + 2079*x**10*log(x)**3/312500 - 6237*x**10*log(x)**2/3125000 + 6237*x**10*log(x)/15625000 - 6237*x**10/156250000","A",0
59,1,5,0,0.086401," ","integrate(ln(x)**2/x,x)","\frac{\log{\left(x \right)}^{3}}{3}"," ",0,"log(x)**3/3","A",0
60,1,2,0,0.459141," ","integrate(1/ln(x),x)","\operatorname{li}{\left(x \right)}"," ",0,"li(x)","A",0
61,1,3,0,0.492513," ","integrate(1/ln(1+x),x)","\operatorname{li}{\left(x + 1 \right)}"," ",0,"li(x + 1)","A",0
62,1,3,0,0.096485," ","integrate(1/x/ln(x),x)","\log{\left(\log{\left(x \right)} \right)}"," ",0,"log(log(x))","A",0
63,1,14,0,0.652594," ","integrate(1/x**2/ln(x)**2,x)","- \operatorname{Ei}{\left(- \log{\left(x \right)} \right)} - \frac{1}{x \log{\left(x \right)}}"," ",0,"-Ei(-log(x)) - 1/(x*log(x))","A",0
64,1,15,0,0.880793," ","integrate(ln(x)**p/x,x)","\begin{cases} \frac{\log{\left(x \right)}^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(\log{\left(x \right)} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)**(p + 1)/(p + 1), Ne(p, -1)), (log(log(x)), True))","A",0
65,1,22,0,0.113875," ","integrate((a*x+b)*ln(x),x)","- \frac{a x^{2}}{4} - b x + \left(\frac{a x^{2}}{2} + b x\right) \log{\left(x \right)}"," ",0,"-a*x**2/4 - b*x + (a*x**2/2 + b*x)*log(x)","A",0
66,1,44,0,0.136728," ","integrate((a*x+b)**2*ln(x),x)","- \frac{a^{2} x^{3}}{9} - \frac{a b x^{2}}{2} - b^{2} x + \left(\frac{a^{2} x^{3}}{3} + a b x^{2} + b^{2} x\right) \log{\left(x \right)}"," ",0,"-a**2*x**3/9 - a*b*x**2/2 - b**2*x + (a**2*x**3/3 + a*b*x**2 + b**2*x)*log(x)","A",0
67,1,24,0,0.357666," ","integrate(ln(x)/(a*x+b)**2,x)","- \frac{\log{\left(x \right)}}{a^{2} x + a b} + \frac{\log{\left(x \right)} - \log{\left(x + \frac{b}{a} \right)}}{a b}"," ",0,"-log(x)/(a**2*x + a*b) + (log(x) - log(x + b/a))/(a*b)","A",0
68,1,42,0,0.176411," ","integrate(x*ln(a*x+b),x)","- a \left(\frac{x^{2}}{4 a} - \frac{b x}{2 a^{2}} + \frac{b^{2} \log{\left(a x + b \right)}}{2 a^{3}}\right) + \frac{x^{2} \log{\left(a x + b \right)}}{2}"," ",0,"-a*(x**2/(4*a) - b*x/(2*a**2) + b**2*log(a*x + b)/(2*a**3)) + x**2*log(a*x + b)/2","A",0
69,1,54,0,0.191299," ","integrate(x**2*ln(a*x+b),x)","- a \left(\frac{x^{3}}{9 a} - \frac{b x^{2}}{6 a^{2}} + \frac{b^{2} x}{3 a^{3}} - \frac{b^{3} \log{\left(a x + b \right)}}{3 a^{4}}\right) + \frac{x^{3} \log{\left(a x + b \right)}}{3}"," ",0,"-a*(x**3/(9*a) - b*x**2/(6*a**2) + b**2*x/(3*a**3) - b**3*log(a*x + b)/(3*a**4)) + x**3*log(a*x + b)/3","A",0
70,1,36,0,0.161218," ","integrate(ln(a**2+x**2),x)","- 2 a \left(\frac{i \log{\left(- i a + x \right)}}{2} - \frac{i \log{\left(i a + x \right)}}{2}\right) + x \log{\left(a^{2} + x^{2} \right)} - 2 x"," ",0,"-2*a*(I*log(-I*a + x)/2 - I*log(I*a + x)/2) + x*log(a**2 + x**2) - 2*x","C",0
71,1,31,0,0.159637," ","integrate(x*ln(a**2+x**2),x)","\frac{a^{2} \log{\left(a^{2} + x^{2} \right)}}{2} + \frac{x^{2} \log{\left(a^{2} + x^{2} \right)}}{2} - \frac{x^{2}}{2}"," ",0,"a**2*log(a**2 + x**2)/2 + x**2*log(a**2 + x**2)/2 - x**2/2","A",0
72,1,53,0,0.193595," ","integrate(x**2*ln(a**2+x**2),x)","- 2 a^{3} \left(- \frac{i \log{\left(- i a + x \right)}}{6} + \frac{i \log{\left(i a + x \right)}}{6}\right) + \frac{2 a^{2} x}{3} + \frac{x^{3} \log{\left(a^{2} + x^{2} \right)}}{3} - \frac{2 x^{3}}{9}"," ",0,"-2*a**3*(-I*log(-I*a + x)/6 + I*log(I*a + x)/6) + 2*a**2*x/3 + x**3*log(a**2 + x**2)/3 - 2*x**3/9","C",0
73,1,63,0,0.208526," ","integrate(x**4*ln(a**2+x**2),x)","- 2 a^{5} \left(\frac{i \log{\left(- i a + x \right)}}{10} - \frac{i \log{\left(i a + x \right)}}{10}\right) - \frac{2 a^{4} x}{5} + \frac{2 a^{2} x^{3}}{15} + \frac{x^{5} \log{\left(a^{2} + x^{2} \right)}}{5} - \frac{2 x^{5}}{25}"," ",0,"-2*a**5*(I*log(-I*a + x)/10 - I*log(I*a + x)/10) - 2*a**4*x/5 + 2*a**2*x**3/15 + x**5*log(a**2 + x**2)/5 - 2*x**5/25","C",0
74,1,29,0,0.163420," ","integrate(ln(-a**2+x**2),x)","- 2 a \left(\frac{\log{\left(- a + x \right)}}{2} - \frac{\log{\left(a + x \right)}}{2}\right) + x \log{\left(- a^{2} + x^{2} \right)} - 2 x"," ",0,"-2*a*(log(-a + x)/2 - log(a + x)/2) + x*log(-a**2 + x**2) - 2*x","A",0
75,0,0,0,0.000000," ","integrate(ln(ln(ln(ln(x)))),x)","x \log{\left(\log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} \right)} - \int \frac{1}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}}\, dx"," ",0,"x*log(log(log(log(x)))) - Integral(1/(log(x)*log(log(x))*log(log(log(x)))), x)","F",0
76,1,3,0,0.060781," ","integrate(sin(x),x)","- \cos{\left(x \right)}"," ",0,"-cos(x)","A",0
77,1,2,0,0.059643," ","integrate(cos(x),x)","\sin{\left(x \right)}"," ",0,"sin(x)","A",0
78,1,5,0,0.064859," ","integrate(tan(x),x)","- \log{\left(\cos{\left(x \right)} \right)}"," ",0,"-log(cos(x))","A",0
79,1,3,0,0.068492," ","integrate(1/tan(x),x)","\log{\left(\sin{\left(x \right)} \right)}"," ",0,"log(sin(x))","A",0
80,1,75,0,0.359610," ","integrate(1/(1+tan(x))**2,x)","\frac{2 \log{\left(\tan{\left(x \right)} + 1 \right)} \tan{\left(x \right)}}{4 \tan{\left(x \right)} + 4} + \frac{2 \log{\left(\tan{\left(x \right)} + 1 \right)}}{4 \tan{\left(x \right)} + 4} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan{\left(x \right)}}{4 \tan{\left(x \right)} + 4} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4 \tan{\left(x \right)} + 4} - \frac{2}{4 \tan{\left(x \right)} + 4}"," ",0,"2*log(tan(x) + 1)*tan(x)/(4*tan(x) + 4) + 2*log(tan(x) + 1)/(4*tan(x) + 4) - log(tan(x)**2 + 1)*tan(x)/(4*tan(x) + 4) - log(tan(x)**2 + 1)/(4*tan(x) + 4) - 2/(4*tan(x) + 4)","B",0
81,1,15,0,0.108352," ","integrate(1/cos(x),x)","- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}"," ",0,"-log(sin(x) - 1)/2 + log(sin(x) + 1)/2","B",0
82,1,15,0,0.108712," ","integrate(1/sin(x),x)","\frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2}"," ",0,"log(cos(x) - 1)/2 - log(cos(x) + 1)/2","B",0
83,1,10,0,0.063205," ","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
84,1,15,0,0.569060," ","integrate(x**3*sin(x**2),x)","- \frac{x^{2} \cos{\left(x^{2} \right)}}{2} + \frac{\sin{\left(x^{2} \right)}}{2}"," ",0,"-x**2*cos(x**2)/2 + sin(x**2)/2","A",0
85,1,8,0,0.065387," ","integrate(sin(x)**3,x)","\frac{\cos^{3}{\left(x \right)}}{3} - \cos{\left(x \right)}"," ",0,"cos(x)**3/3 - cos(x)","A",0
86,0,0,0,0.000000," ","integrate(sin(x)**p,x)","\int \sin^{p}{\left(x \right)}\, dx"," ",0,"Integral(sin(x)**p, x)","F",0
87,1,17,0,1.148397," ","integrate(cos(x)*(1+sin(x)**2)**2,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
88,1,10,0,0.061743," ","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
89,1,8,0,0.065735," ","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
90,1,5,0,0.060820," ","integrate(1/cos(x)**2,x)","\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}"," ",0,"sin(x)/cos(x)","B",0
91,1,20,0,0.565817," ","integrate(sin(x)*sin(2*x),x)","- \frac{2 \sin{\left(x \right)} \cos{\left(2 x \right)}}{3} + \frac{\sin{\left(2 x \right)} \cos{\left(x \right)}}{3}"," ",0,"-2*sin(x)*cos(2*x)/3 + sin(2*x)*cos(x)/3","A",0
92,1,7,0,0.178967," ","integrate(x*sin(x),x)","- x \cos{\left(x \right)} + \sin{\left(x \right)}"," ",0,"-x*cos(x) + sin(x)","A",0
93,1,17,0,0.320846," ","integrate(x**2*sin(x),x)","- x^{2} \cos{\left(x \right)} + 2 x \sin{\left(x \right)} + 2 \cos{\left(x \right)}"," ",0,"-x**2*cos(x) + 2*x*sin(x) + 2*cos(x)","A",0
94,1,36,0,0.333533," ","integrate(x*sin(x)**2,x)","\frac{x^{2} \sin^{2}{\left(x \right)}}{4} + \frac{x^{2} \cos^{2}{\left(x \right)}}{4} - \frac{x \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\sin^{2}{\left(x \right)}}{4}"," ",0,"x**2*sin(x)**2/4 + x**2*cos(x)**2/4 - x*sin(x)*cos(x)/2 + sin(x)**2/4","A",0
95,1,56,0,0.629365," ","integrate(x**2*sin(x)**2,x)","\frac{x^{3} \sin^{2}{\left(x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(x \right)}}{6} - \frac{x^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{x \sin^{2}{\left(x \right)}}{4} - \frac{x \cos^{2}{\left(x \right)}}{4} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{4}"," ",0,"x**3*sin(x)**2/6 + x**3*cos(x)**2/6 - x**2*sin(x)*cos(x)/2 + x*sin(x)**2/4 - x*cos(x)**2/4 + sin(x)*cos(x)/4","A",0
96,1,39,0,0.599649," ","integrate(x*sin(x)**3,x)","- x \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{2 x \cos^{3}{\left(x \right)}}{3} + \frac{7 \sin^{3}{\left(x \right)}}{9} + \frac{2 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3}"," ",0,"-x*sin(x)**2*cos(x) - 2*x*cos(x)**3/3 + 7*sin(x)**3/9 + 2*sin(x)*cos(x)**2/3","A",0
97,1,7,0,0.175449," ","integrate(x*cos(x),x)","x \sin{\left(x \right)} + \cos{\left(x \right)}"," ",0,"x*sin(x) + cos(x)","A",0
98,1,17,0,0.319456," ","integrate(x**2*cos(x),x)","x^{2} \sin{\left(x \right)} + 2 x \cos{\left(x \right)} - 2 \sin{\left(x \right)}"," ",0,"x**2*sin(x) + 2*x*cos(x) - 2*sin(x)","A",0
99,1,36,0,0.336793," ","integrate(x*cos(x)**2,x)","\frac{x^{2} \sin^{2}{\left(x \right)}}{4} + \frac{x^{2} \cos^{2}{\left(x \right)}}{4} + \frac{x \sin{\left(x \right)} \cos{\left(x \right)}}{2} - \frac{\sin^{2}{\left(x \right)}}{4}"," ",0,"x**2*sin(x)**2/4 + x**2*cos(x)**2/4 + x*sin(x)*cos(x)/2 - sin(x)**2/4","A",0
100,1,56,0,0.619437," ","integrate(x**2*cos(x)**2,x)","\frac{x^{3} \sin^{2}{\left(x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(x \right)}}{6} + \frac{x^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{2} - \frac{x \sin^{2}{\left(x \right)}}{4} + \frac{x \cos^{2}{\left(x \right)}}{4} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{4}"," ",0,"x**3*sin(x)**2/6 + x**3*cos(x)**2/6 + x**2*sin(x)*cos(x)/2 - x*sin(x)**2/4 + x*cos(x)**2/4 - sin(x)*cos(x)/4","A",0
101,1,39,0,0.612637," ","integrate(x*cos(x)**3,x)","\frac{2 x \sin^{3}{\left(x \right)}}{3} + x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{2 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{3} + \frac{7 \cos^{3}{\left(x \right)}}{9}"," ",0,"2*x*sin(x)**3/3 + x*sin(x)*cos(x)**2 + 2*sin(x)**2*cos(x)/3 + 7*cos(x)**3/9","A",0
102,1,2,0,0.614279," ","integrate(sin(x)/x,x)","\operatorname{Si}{\left(x \right)}"," ",0,"Si(x)","A",0
103,1,12,0,0.997579," ","integrate(cos(x)/x,x)","- \log{\left(x \right)} + \frac{\log{\left(x^{2} \right)}}{2} + \operatorname{Ci}{\left(x \right)}"," ",0,"-log(x) + log(x**2)/2 + Ci(x)","B",0
104,1,17,0,1.451797," ","integrate(sin(x)/x**2,x)","- \log{\left(x \right)} + \frac{\log{\left(x^{2} \right)}}{2} + \operatorname{Ci}{\left(x \right)} - \frac{\sin{\left(x \right)}}{x}"," ",0,"-log(x) + log(x**2)/2 + Ci(x) - sin(x)/x","B",0
105,1,10,0,1.084924," ","integrate(sin(x)**2/x,x)","\frac{\log{\left(x \right)}}{2} - \frac{\operatorname{Ci}{\left(2 x \right)}}{2}"," ",0,"log(x)/2 - Ci(2*x)/2","A",0
106,1,12,0,0.094046," ","integrate(tan(x)**3,x)","\log{\left(\cos{\left(x \right)} \right)} + \frac{1}{2 \cos^{2}{\left(x \right)}}"," ",0,"log(cos(x)) + 1/(2*cos(x)**2)","A",0
107,1,14,0,0.139219," ","integrate(sin(b*x+a),x)","\begin{cases} - \frac{\cos{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-cos(a + b*x)/b, Ne(b, 0)), (x*sin(a), True))","A",0
108,1,12,0,0.138546," ","integrate(cos(b*x+a),x)","\begin{cases} \frac{\sin{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sin(a + b*x)/b, Ne(b, 0)), (x*cos(a), True))","A",0
109,1,19,0,0.132512," ","integrate(tan(b*x+a),x)","\begin{cases} \frac{\log{\left(\tan^{2}{\left(a + b x \right)} + 1 \right)}}{2 b} & \text{for}\: b \neq 0 \\x \tan{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(tan(a + b*x)**2 + 1)/(2*b), Ne(b, 0)), (x*tan(a), True))","A",0
110,1,29,0,0.334478," ","integrate(1/tan(b*x+a),x)","\begin{cases} - \frac{\log{\left(\tan^{2}{\left(a + b x \right)} + 1 \right)}}{2 b} + \frac{\log{\left(\tan{\left(a + b x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x}{\tan{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(a + b*x)**2 + 1)/(2*b) + log(tan(a + b*x))/b, Ne(b, 0)), (x/tan(a), True))","A",0
111,1,17,0,0.533316," ","integrate(1/sin(b*x+a),x)","\begin{cases} \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x}{\sin{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(tan(a/2 + b*x/2))/b, Ne(b, 0)), (x/sin(a), True))","A",0
112,1,34,0,0.609530," ","integrate(1/cos(b*x+a),x)","\begin{cases} - \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)}}{b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x}{\cos{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(a/2 + b*x/2) - 1)/b + log(tan(a/2 + b*x/2) + 1)/b, Ne(b, 0)), (x/cos(a), True))","A",0
113,1,46,0,0.227299," ","integrate(sin(b*x+a)**2,x)","\begin{cases} \frac{x \sin^{2}{\left(a + b x \right)}}{2} + \frac{x \cos^{2}{\left(a + b x \right)}}{2} - \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 - sin(a + b*x)*cos(a + b*x)/(2*b), Ne(b, 0)), (x*sin(a)**2, True))","A",0
114,1,37,0,0.468091," ","integrate(sin(b*x+a)**3,x)","\begin{cases} - \frac{\sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 \cos^{3}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**2*cos(a + b*x)/b - 2*cos(a + b*x)**3/(3*b), Ne(b, 0)), (x*sin(a)**3, True))","A",0
115,1,46,0,0.225022," ","integrate(cos(b*x+a)**2,x)","\begin{cases} \frac{x \sin^{2}{\left(a + b x \right)}}{2} + \frac{x \cos^{2}{\left(a + b x \right)}}{2} + \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\x \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 + sin(a + b*x)*cos(a + b*x)/(2*b), Ne(b, 0)), (x*cos(a)**2, True))","A",0
116,1,36,0,0.481970," ","integrate(cos(b*x+a)**3,x)","\begin{cases} \frac{2 \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{\sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sin(a + b*x)**3/(3*b) + sin(a + b*x)*cos(a + b*x)**2/b, Ne(b, 0)), (x*cos(a)**3, True))","A",0
117,1,58,0,1.198268," ","integrate(1/cos(b*x+a)**2,x)","\begin{cases} \tilde{\infty} x & \text{for}\: \left(a = - \frac{\pi}{2} \vee a = - b x - \frac{\pi}{2}\right) \wedge \left(a = - b x - \frac{\pi}{2} \vee b = 0\right) \\\frac{x}{\cos^{2}{\left(a \right)}} & \text{for}\: b = 0 \\- \frac{2 \tan{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, (Eq(b, 0) | Eq(a, -b*x - pi/2)) & (Eq(a, -pi/2) | Eq(a, -b*x - pi/2))), (x/cos(a)**2, Eq(b, 0)), (-2*tan(a/2 + b*x/2)/(b*tan(a/2 + b*x/2)**2 - b), True))","A",0
118,1,3,0,0.190641," ","integrate(1/(1+cos(x)),x)","\tan{\left(\frac{x}{2} \right)}"," ",0,"tan(x/2)","A",0
119,1,7,0,0.341532," ","integrate(1/(1-cos(x)),x)","- \frac{1}{\tan{\left(\frac{x}{2} \right)}}"," ",0,"-1/tan(x/2)","A",0
120,1,8,0,0.363824," ","integrate(1/(1+sin(x)),x)","- \frac{2}{\tan{\left(\frac{x}{2} \right)} + 1}"," ",0,"-2/(tan(x/2) + 1)","A",0
121,1,8,0,0.371818," ","integrate(1/(1-sin(x)),x)","- \frac{2}{\tan{\left(\frac{x}{2} \right)} - 1}"," ",0,"-2/(tan(x/2) - 1)","A",0
122,1,133,0,8.694033," ","integrate(1/(a+b*sin(x)),x)","\begin{cases} \frac{2 \sqrt{b^{2}}}{b^{2} \tan{\left(\frac{x}{2} \right)} - b \sqrt{b^{2}}} & \text{for}\: a = - \sqrt{b^{2}} \\- \frac{2 \sqrt{b^{2}}}{b^{2} \tan{\left(\frac{x}{2} \right)} + b \sqrt{b^{2}}} & \text{for}\: a = \sqrt{b^{2}} \\\frac{\log{\left(\tan{\left(\frac{x}{2} \right)} \right)}}{b} & \text{for}\: a = 0 \\\frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{\sqrt{- a^{2} + b^{2}}} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{\sqrt{- a^{2} + b^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b**2)/(b**2*tan(x/2) - b*sqrt(b**2)), Eq(a, -sqrt(b**2))), (-2*sqrt(b**2)/(b**2*tan(x/2) + b*sqrt(b**2)), Eq(a, sqrt(b**2))), (log(tan(x/2))/b, Eq(a, 0)), (log(tan(x/2) + b/a - sqrt(-a**2 + b**2)/a)/sqrt(-a**2 + b**2) - log(tan(x/2) + b/a + sqrt(-a**2 + b**2)/a)/sqrt(-a**2 + b**2), True))","A",0
123,-1,0,0,0.000000," ","integrate(1/(a+cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,1,105,0,1.127926," ","integrate(x**2*sin(b*x+a)**2,x)","\begin{cases} \frac{x^{3} \sin^{2}{\left(a + b x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(a + b x \right)}}{6} - \frac{x^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} + \frac{x \sin^{2}{\left(a + b x \right)}}{4 b^{2}} - \frac{x \cos^{2}{\left(a + b x \right)}}{4 b^{2}} + \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} \sin^{2}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3*sin(a + b*x)**2/6 + x**3*cos(a + b*x)**2/6 - x**2*sin(a + b*x)*cos(a + b*x)/(2*b) + x*sin(a + b*x)**2/(4*b**2) - x*cos(a + b*x)**2/(4*b**2) + sin(a + b*x)*cos(a + b*x)/(4*b**3), Ne(b, 0)), (x**3*sin(a)**2/3, True))","A",0
125,1,20,0,0.556156," ","integrate(cos(x)*cos(2*x),x)","- \frac{\sin{\left(x \right)} \cos{\left(2 x \right)}}{3} + \frac{2 \sin{\left(2 x \right)} \cos{\left(x \right)}}{3}"," ",0,"-sin(x)*cos(2*x)/3 + 2*sin(2*x)*cos(x)/3","A",0
126,1,105,0,1.112020," ","integrate(x**2*cos(b*x+a)**2,x)","\begin{cases} \frac{x^{3} \sin^{2}{\left(a + b x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(a + b x \right)}}{6} + \frac{x^{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{x \sin^{2}{\left(a + b x \right)}}{4 b^{2}} + \frac{x \cos^{2}{\left(a + b x \right)}}{4 b^{2}} - \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{4 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} \cos^{2}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3*sin(a + b*x)**2/6 + x**3*cos(a + b*x)**2/6 + x**2*sin(a + b*x)*cos(a + b*x)/(2*b) - x*sin(a + b*x)**2/(4*b**2) + x*cos(a + b*x)**2/(4*b**2) - sin(a + b*x)*cos(a + b*x)/(4*b**3), Ne(b, 0)), (x**3*cos(a)**2/3, True))","A",0
127,1,14,0,0.094329," ","integrate(1/tan(x)**3,x)","- \log{\left(\sin{\left(x \right)} \right)} - \frac{1}{2 \sin^{2}{\left(x \right)}}"," ",0,"-log(sin(x)) - 1/(2*sin(x)**2)","A",0
128,0,0,0,0.000000," ","integrate(x**3*tan(x)**4,x)","\int x^{3} \tan^{4}{\left(x \right)}\, dx"," ",0,"Integral(x**3*tan(x)**4, x)","F",0
129,0,0,0,0.000000," ","integrate(x**3*tan(x)**6,x)","\int x^{3} \tan^{6}{\left(x \right)}\, dx"," ",0,"Integral(x**3*tan(x)**6, x)","F",0
130,1,19,0,0.173817," ","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
131,1,26,0,0.519711," ","integrate(cos(3*x)*sin(2*x),x)","\frac{3 \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{5} + \frac{2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{5}"," ",0,"3*sin(2*x)*sin(3*x)/5 + 2*cos(2*x)*cos(3*x)/5","B",0
132,1,14,0,0.070193," ","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
133,1,12,0,0.075317," ","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
134,1,104,0,1.041991," ","integrate(d**x*sin(x),x)","\begin{cases} \frac{x e^{- i x} \sin{\left(x \right)}}{2} - \frac{i x e^{- i x} \cos{\left(x \right)}}{2} - \frac{e^{- i x} \cos{\left(x \right)}}{2} & \text{for}\: d = e^{- i} \\\frac{x e^{i x} \sin{\left(x \right)}}{2} + \frac{i x e^{i x} \cos{\left(x \right)}}{2} - \frac{e^{i x} \cos{\left(x \right)}}{2} & \text{for}\: d = e^{i} \\\frac{d^{x} \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{2} + 1} - \frac{d^{x} \cos{\left(x \right)}}{\log{\left(d \right)}^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(-I*x)*sin(x)/2 - I*x*exp(-I*x)*cos(x)/2 - exp(-I*x)*cos(x)/2, Eq(d, exp(-I))), (x*exp(I*x)*sin(x)/2 + I*x*exp(I*x)*cos(x)/2 - exp(I*x)*cos(x)/2, Eq(d, exp(I))), (d**x*log(d)*sin(x)/(log(d)**2 + 1) - d**x*cos(x)/(log(d)**2 + 1), True))","A",0
135,1,107,0,1.029829," ","integrate(d**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}\: d = 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}\: d = e^{i} \\\frac{d^{x} \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{2} + 1} + \frac{d^{x} \sin{\left(x \right)}}{\log{\left(d \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(d, 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(d, exp(I))), (d**x*log(d)*cos(x)/(log(d)**2 + 1) + d**x*sin(x)/(log(d)**2 + 1), True))","A",0
136,1,308,0,3.278924," ","integrate(d**x*x*sin(x),x)","\begin{cases} \frac{x^{2} e^{- i x} \sin{\left(x \right)}}{4} - \frac{i x^{2} e^{- i x} \cos{\left(x \right)}}{4} + \frac{i x e^{- i x} \sin{\left(x \right)}}{4} - \frac{x e^{- i x} \cos{\left(x \right)}}{4} + \frac{i e^{- i x} \cos{\left(x \right)}}{4} & \text{for}\: d = e^{- i} \\\frac{x^{2} e^{i x} \sin{\left(x \right)}}{4} + \frac{i x^{2} e^{i x} \cos{\left(x \right)}}{4} - \frac{i x e^{i x} \sin{\left(x \right)}}{4} - \frac{x e^{i x} \cos{\left(x \right)}}{4} - \frac{i e^{i x} \cos{\left(x \right)}}{4} & \text{for}\: d = e^{i} \\\frac{d^{x} x \log{\left(d \right)}^{3} \sin{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} - \frac{d^{x} x \log{\left(d \right)}^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} - \frac{d^{x} x \cos{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} - \frac{d^{x} \log{\left(d \right)}^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} + \frac{2 d^{x} \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} \sin{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2*exp(-I*x)*sin(x)/4 - I*x**2*exp(-I*x)*cos(x)/4 + I*x*exp(-I*x)*sin(x)/4 - x*exp(-I*x)*cos(x)/4 + I*exp(-I*x)*cos(x)/4, Eq(d, exp(-I))), (x**2*exp(I*x)*sin(x)/4 + I*x**2*exp(I*x)*cos(x)/4 - I*x*exp(I*x)*sin(x)/4 - x*exp(I*x)*cos(x)/4 - I*exp(I*x)*cos(x)/4, Eq(d, exp(I))), (d**x*x*log(d)**3*sin(x)/(log(d)**4 + 2*log(d)**2 + 1) - d**x*x*log(d)**2*cos(x)/(log(d)**4 + 2*log(d)**2 + 1) + d**x*x*log(d)*sin(x)/(log(d)**4 + 2*log(d)**2 + 1) - d**x*x*cos(x)/(log(d)**4 + 2*log(d)**2 + 1) - d**x*log(d)**2*sin(x)/(log(d)**4 + 2*log(d)**2 + 1) + 2*d**x*log(d)*cos(x)/(log(d)**4 + 2*log(d)**2 + 1) + d**x*sin(x)/(log(d)**4 + 2*log(d)**2 + 1), True))","A",0
137,1,304,0,3.244051," ","integrate(d**x*x*cos(x),x)","\begin{cases} \frac{i x^{2} e^{- i x} \sin{\left(x \right)}}{4} + \frac{x^{2} e^{- i x} \cos{\left(x \right)}}{4} + \frac{x e^{- i x} \sin{\left(x \right)}}{4} + \frac{i x e^{- i x} \cos{\left(x \right)}}{4} + \frac{e^{- i x} \cos{\left(x \right)}}{4} & \text{for}\: d = e^{- i} \\- \frac{i x^{2} e^{i x} \sin{\left(x \right)}}{4} + \frac{x^{2} e^{i x} \cos{\left(x \right)}}{4} + \frac{x e^{i x} \sin{\left(x \right)}}{4} - \frac{i x e^{i x} \cos{\left(x \right)}}{4} + \frac{e^{i x} \cos{\left(x \right)}}{4} & \text{for}\: d = e^{i} \\\frac{d^{x} x \log{\left(d \right)}^{3} \cos{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x \log{\left(d \right)}^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x \sin{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} - \frac{d^{x} \log{\left(d \right)}^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} - \frac{2 d^{x} \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} \cos{\left(x \right)}}{\log{\left(d \right)}^{4} + 2 \log{\left(d \right)}^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x**2*exp(-I*x)*sin(x)/4 + x**2*exp(-I*x)*cos(x)/4 + x*exp(-I*x)*sin(x)/4 + I*x*exp(-I*x)*cos(x)/4 + exp(-I*x)*cos(x)/4, Eq(d, exp(-I))), (-I*x**2*exp(I*x)*sin(x)/4 + x**2*exp(I*x)*cos(x)/4 + x*exp(I*x)*sin(x)/4 - I*x*exp(I*x)*cos(x)/4 + exp(I*x)*cos(x)/4, Eq(d, exp(I))), (d**x*x*log(d)**3*cos(x)/(log(d)**4 + 2*log(d)**2 + 1) + d**x*x*log(d)**2*sin(x)/(log(d)**4 + 2*log(d)**2 + 1) + d**x*x*log(d)*cos(x)/(log(d)**4 + 2*log(d)**2 + 1) + d**x*x*sin(x)/(log(d)**4 + 2*log(d)**2 + 1) - d**x*log(d)**2*cos(x)/(log(d)**4 + 2*log(d)**2 + 1) - 2*d**x*log(d)*sin(x)/(log(d)**4 + 2*log(d)**2 + 1) + d**x*cos(x)/(log(d)**4 + 2*log(d)**2 + 1), True))","A",0
138,1,665,0,8.456897," ","integrate(d**x*x**2*sin(x),x)","\begin{cases} \frac{x^{3} e^{- i x} \sin{\left(x \right)}}{6} - \frac{i x^{3} e^{- i x} \cos{\left(x \right)}}{6} + \frac{i x^{2} e^{- i x} \sin{\left(x \right)}}{4} - \frac{x^{2} e^{- i x} \cos{\left(x \right)}}{4} + \frac{x e^{- i x} \sin{\left(x \right)}}{4} + \frac{i x e^{- i x} \cos{\left(x \right)}}{4} + \frac{e^{- i x} \cos{\left(x \right)}}{4} & \text{for}\: d = e^{- i} \\\frac{x^{3} e^{i x} \sin{\left(x \right)}}{6} + \frac{i x^{3} e^{i x} \cos{\left(x \right)}}{6} - \frac{i x^{2} e^{i x} \sin{\left(x \right)}}{4} - \frac{x^{2} e^{i x} \cos{\left(x \right)}}{4} + \frac{x e^{i x} \sin{\left(x \right)}}{4} - \frac{i x e^{i x} \cos{\left(x \right)}}{4} + \frac{e^{i x} \cos{\left(x \right)}}{4} & \text{for}\: d = e^{i} \\\frac{d^{x} x^{2} \log{\left(d \right)}^{5} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{d^{x} x^{2} \log{\left(d \right)}^{4} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{2 d^{x} x^{2} \log{\left(d \right)}^{3} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{2 d^{x} x^{2} \log{\left(d \right)}^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x^{2} \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{d^{x} x^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{2 d^{x} x \log{\left(d \right)}^{4} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{4 d^{x} x \log{\left(d \right)}^{3} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{4 d^{x} x \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{2 d^{x} x \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{2 d^{x} \log{\left(d \right)}^{3} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} \log{\left(d \right)}^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{2 d^{x} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3*exp(-I*x)*sin(x)/6 - I*x**3*exp(-I*x)*cos(x)/6 + I*x**2*exp(-I*x)*sin(x)/4 - x**2*exp(-I*x)*cos(x)/4 + x*exp(-I*x)*sin(x)/4 + I*x*exp(-I*x)*cos(x)/4 + exp(-I*x)*cos(x)/4, Eq(d, exp(-I))), (x**3*exp(I*x)*sin(x)/6 + I*x**3*exp(I*x)*cos(x)/6 - I*x**2*exp(I*x)*sin(x)/4 - x**2*exp(I*x)*cos(x)/4 + x*exp(I*x)*sin(x)/4 - I*x*exp(I*x)*cos(x)/4 + exp(I*x)*cos(x)/4, Eq(d, exp(I))), (d**x*x**2*log(d)**5*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - d**x*x**2*log(d)**4*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 2*d**x*x**2*log(d)**3*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - 2*d**x*x**2*log(d)**2*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + d**x*x**2*log(d)*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - d**x*x**2*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - 2*d**x*x*log(d)**4*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 4*d**x*x*log(d)**3*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 4*d**x*x*log(d)*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 2*d**x*x*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 2*d**x*log(d)**3*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - 6*d**x*log(d)**2*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - 6*d**x*log(d)*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 2*d**x*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1), True))","B",0
139,1,668,0,8.473604," ","integrate(d**x*x**2*cos(x),x)","\begin{cases} \frac{i x^{3} e^{- i x} \sin{\left(x \right)}}{6} + \frac{x^{3} e^{- i x} \cos{\left(x \right)}}{6} + \frac{x^{2} e^{- i x} \sin{\left(x \right)}}{4} + \frac{i x^{2} e^{- i x} \cos{\left(x \right)}}{4} - \frac{i x e^{- i x} \sin{\left(x \right)}}{4} + \frac{x e^{- i x} \cos{\left(x \right)}}{4} - \frac{i e^{- i x} \cos{\left(x \right)}}{4} & \text{for}\: d = e^{- i} \\- \frac{i x^{3} e^{i x} \sin{\left(x \right)}}{6} + \frac{x^{3} e^{i x} \cos{\left(x \right)}}{6} + \frac{x^{2} e^{i x} \sin{\left(x \right)}}{4} - \frac{i x^{2} e^{i x} \cos{\left(x \right)}}{4} + \frac{i x e^{i x} \sin{\left(x \right)}}{4} + \frac{x e^{i x} \cos{\left(x \right)}}{4} + \frac{i e^{i x} \cos{\left(x \right)}}{4} & \text{for}\: d = e^{i} \\\frac{d^{x} x^{2} \log{\left(d \right)}^{5} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x^{2} \log{\left(d \right)}^{4} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{2 d^{x} x^{2} \log{\left(d \right)}^{3} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{2 d^{x} x^{2} \log{\left(d \right)}^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x^{2} \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{2 d^{x} x \log{\left(d \right)}^{4} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{4 d^{x} x \log{\left(d \right)}^{3} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{4 d^{x} x \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{2 d^{x} x \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{2 d^{x} \log{\left(d \right)}^{3} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} + \frac{6 d^{x} \log{\left(d \right)}^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} - \frac{2 d^{x} \sin{\left(x \right)}}{\log{\left(d \right)}^{6} + 3 \log{\left(d \right)}^{4} + 3 \log{\left(d \right)}^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x**3*exp(-I*x)*sin(x)/6 + x**3*exp(-I*x)*cos(x)/6 + x**2*exp(-I*x)*sin(x)/4 + I*x**2*exp(-I*x)*cos(x)/4 - I*x*exp(-I*x)*sin(x)/4 + x*exp(-I*x)*cos(x)/4 - I*exp(-I*x)*cos(x)/4, Eq(d, exp(-I))), (-I*x**3*exp(I*x)*sin(x)/6 + x**3*exp(I*x)*cos(x)/6 + x**2*exp(I*x)*sin(x)/4 - I*x**2*exp(I*x)*cos(x)/4 + I*x*exp(I*x)*sin(x)/4 + x*exp(I*x)*cos(x)/4 + I*exp(I*x)*cos(x)/4, Eq(d, exp(I))), (d**x*x**2*log(d)**5*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + d**x*x**2*log(d)**4*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 2*d**x*x**2*log(d)**3*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 2*d**x*x**2*log(d)**2*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + d**x*x**2*log(d)*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + d**x*x**2*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - 2*d**x*x*log(d)**4*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - 4*d**x*x*log(d)**3*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - 4*d**x*x*log(d)*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 2*d**x*x*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 2*d**x*log(d)**3*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) + 6*d**x*log(d)**2*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - 6*d**x*log(d)*cos(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1) - 2*d**x*sin(x)/(log(d)**6 + 3*log(d)**4 + 3*log(d)**2 + 1), True))","B",0
140,1,1355,0,22.171493," ","integrate(d**x*x**3*sin(x),x)","\begin{cases} \frac{x^{4} e^{- i x} \sin{\left(x \right)}}{8} - \frac{i x^{4} e^{- i x} \cos{\left(x \right)}}{8} + \frac{i x^{3} e^{- i x} \sin{\left(x \right)}}{4} - \frac{x^{3} e^{- i x} \cos{\left(x \right)}}{4} + \frac{3 x^{2} e^{- i x} \sin{\left(x \right)}}{8} + \frac{3 i x^{2} e^{- i x} \cos{\left(x \right)}}{8} - \frac{3 i x e^{- i x} \sin{\left(x \right)}}{8} + \frac{3 x e^{- i x} \cos{\left(x \right)}}{8} - \frac{3 i e^{- i x} \cos{\left(x \right)}}{8} & \text{for}\: d = e^{- i} \\\frac{x^{4} e^{i x} \sin{\left(x \right)}}{8} + \frac{i x^{4} e^{i x} \cos{\left(x \right)}}{8} - \frac{i x^{3} e^{i x} \sin{\left(x \right)}}{4} - \frac{x^{3} e^{i x} \cos{\left(x \right)}}{4} + \frac{3 x^{2} e^{i x} \sin{\left(x \right)}}{8} - \frac{3 i x^{2} e^{i x} \cos{\left(x \right)}}{8} + \frac{3 i x e^{i x} \sin{\left(x \right)}}{8} + \frac{3 x e^{i x} \cos{\left(x \right)}}{8} + \frac{3 i e^{i x} \cos{\left(x \right)}}{8} & \text{for}\: d = e^{i} \\\frac{d^{x} x^{3} \log{\left(d \right)}^{7} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{d^{x} x^{3} \log{\left(d \right)}^{6} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{3} \log{\left(d \right)}^{5} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{3 d^{x} x^{3} \log{\left(d \right)}^{4} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{3} \log{\left(d \right)}^{3} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{3 d^{x} x^{3} \log{\left(d \right)}^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x^{3} \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{d^{x} x^{3} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{3 d^{x} x^{2} \log{\left(d \right)}^{6} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{6 d^{x} x^{2} \log{\left(d \right)}^{5} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{3 d^{x} x^{2} \log{\left(d \right)}^{4} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{12 d^{x} x^{2} \log{\left(d \right)}^{3} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{2} \log{\left(d \right)}^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{6 d^{x} x^{2} \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{6 d^{x} x \log{\left(d \right)}^{5} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{18 d^{x} x \log{\left(d \right)}^{4} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{12 d^{x} x \log{\left(d \right)}^{3} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{12 d^{x} x \log{\left(d \right)}^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{18 d^{x} x \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{6 d^{x} x \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} \log{\left(d \right)}^{4} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{24 d^{x} \log{\left(d \right)}^{3} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{36 d^{x} \log{\left(d \right)}^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{24 d^{x} \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**4*exp(-I*x)*sin(x)/8 - I*x**4*exp(-I*x)*cos(x)/8 + I*x**3*exp(-I*x)*sin(x)/4 - x**3*exp(-I*x)*cos(x)/4 + 3*x**2*exp(-I*x)*sin(x)/8 + 3*I*x**2*exp(-I*x)*cos(x)/8 - 3*I*x*exp(-I*x)*sin(x)/8 + 3*x*exp(-I*x)*cos(x)/8 - 3*I*exp(-I*x)*cos(x)/8, Eq(d, exp(-I))), (x**4*exp(I*x)*sin(x)/8 + I*x**4*exp(I*x)*cos(x)/8 - I*x**3*exp(I*x)*sin(x)/4 - x**3*exp(I*x)*cos(x)/4 + 3*x**2*exp(I*x)*sin(x)/8 - 3*I*x**2*exp(I*x)*cos(x)/8 + 3*I*x*exp(I*x)*sin(x)/8 + 3*x*exp(I*x)*cos(x)/8 + 3*I*exp(I*x)*cos(x)/8, Eq(d, exp(I))), (d**x*x**3*log(d)**7*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - d**x*x**3*log(d)**6*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**3*log(d)**5*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 3*d**x*x**3*log(d)**4*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**3*log(d)**3*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 3*d**x*x**3*log(d)**2*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + d**x*x**3*log(d)*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - d**x*x**3*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 3*d**x*x**2*log(d)**6*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 6*d**x*x**2*log(d)**5*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 3*d**x*x**2*log(d)**4*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 12*d**x*x**2*log(d)**3*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**2*log(d)**2*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 6*d**x*x**2*log(d)*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**2*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 6*d**x*x*log(d)**5*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 18*d**x*x*log(d)**4*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 12*d**x*x*log(d)**3*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 12*d**x*x*log(d)**2*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 18*d**x*x*log(d)*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 6*d**x*x*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 6*d**x*log(d)**4*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 24*d**x*log(d)**3*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 36*d**x*log(d)**2*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 24*d**x*log(d)*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 6*d**x*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1), True))","B",0
141,1,1352,0,22.235324," ","integrate(d**x*x**3*cos(x),x)","\begin{cases} \frac{i x^{4} e^{- i x} \sin{\left(x \right)}}{8} + \frac{x^{4} e^{- i x} \cos{\left(x \right)}}{8} + \frac{x^{3} e^{- i x} \sin{\left(x \right)}}{4} + \frac{i x^{3} e^{- i x} \cos{\left(x \right)}}{4} - \frac{3 i x^{2} e^{- i x} \sin{\left(x \right)}}{8} + \frac{3 x^{2} e^{- i x} \cos{\left(x \right)}}{8} - \frac{3 x e^{- i x} \sin{\left(x \right)}}{8} - \frac{3 i x e^{- i x} \cos{\left(x \right)}}{8} - \frac{3 e^{- i x} \cos{\left(x \right)}}{8} & \text{for}\: d = e^{- i} \\- \frac{i x^{4} e^{i x} \sin{\left(x \right)}}{8} + \frac{x^{4} e^{i x} \cos{\left(x \right)}}{8} + \frac{x^{3} e^{i x} \sin{\left(x \right)}}{4} - \frac{i x^{3} e^{i x} \cos{\left(x \right)}}{4} + \frac{3 i x^{2} e^{i x} \sin{\left(x \right)}}{8} + \frac{3 x^{2} e^{i x} \cos{\left(x \right)}}{8} - \frac{3 x e^{i x} \sin{\left(x \right)}}{8} + \frac{3 i x e^{i x} \cos{\left(x \right)}}{8} - \frac{3 e^{i x} \cos{\left(x \right)}}{8} & \text{for}\: d = e^{i} \\\frac{d^{x} x^{3} \log{\left(d \right)}^{7} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x^{3} \log{\left(d \right)}^{6} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{3} \log{\left(d \right)}^{5} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{3} \log{\left(d \right)}^{4} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{3} \log{\left(d \right)}^{3} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{3} \log{\left(d \right)}^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x^{3} \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{d^{x} x^{3} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{3 d^{x} x^{2} \log{\left(d \right)}^{6} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} x^{2} \log{\left(d \right)}^{5} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{3 d^{x} x^{2} \log{\left(d \right)}^{4} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{12 d^{x} x^{2} \log{\left(d \right)}^{3} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{2} \log{\left(d \right)}^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} x^{2} \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{3 d^{x} x^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{6 d^{x} x \log{\left(d \right)}^{5} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{18 d^{x} x \log{\left(d \right)}^{4} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{12 d^{x} x \log{\left(d \right)}^{3} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{12 d^{x} x \log{\left(d \right)}^{2} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{18 d^{x} x \log{\left(d \right)} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} x \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} \log{\left(d \right)}^{4} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{24 d^{x} \log{\left(d \right)}^{3} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{36 d^{x} \log{\left(d \right)}^{2} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} + \frac{24 d^{x} \log{\left(d \right)} \sin{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} - \frac{6 d^{x} \cos{\left(x \right)}}{\log{\left(d \right)}^{8} + 4 \log{\left(d \right)}^{6} + 6 \log{\left(d \right)}^{4} + 4 \log{\left(d \right)}^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x**4*exp(-I*x)*sin(x)/8 + x**4*exp(-I*x)*cos(x)/8 + x**3*exp(-I*x)*sin(x)/4 + I*x**3*exp(-I*x)*cos(x)/4 - 3*I*x**2*exp(-I*x)*sin(x)/8 + 3*x**2*exp(-I*x)*cos(x)/8 - 3*x*exp(-I*x)*sin(x)/8 - 3*I*x*exp(-I*x)*cos(x)/8 - 3*exp(-I*x)*cos(x)/8, Eq(d, exp(-I))), (-I*x**4*exp(I*x)*sin(x)/8 + x**4*exp(I*x)*cos(x)/8 + x**3*exp(I*x)*sin(x)/4 - I*x**3*exp(I*x)*cos(x)/4 + 3*I*x**2*exp(I*x)*sin(x)/8 + 3*x**2*exp(I*x)*cos(x)/8 - 3*x*exp(I*x)*sin(x)/8 + 3*I*x*exp(I*x)*cos(x)/8 - 3*exp(I*x)*cos(x)/8, Eq(d, exp(I))), (d**x*x**3*log(d)**7*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + d**x*x**3*log(d)**6*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**3*log(d)**5*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**3*log(d)**4*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**3*log(d)**3*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**3*log(d)**2*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + d**x*x**3*log(d)*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + d**x*x**3*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 3*d**x*x**2*log(d)**6*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 6*d**x*x**2*log(d)**5*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 3*d**x*x**2*log(d)**4*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 12*d**x*x**2*log(d)**3*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**2*log(d)**2*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 6*d**x*x**2*log(d)*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 3*d**x*x**2*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 6*d**x*x*log(d)**5*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 18*d**x*x*log(d)**4*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 12*d**x*x*log(d)**3*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 12*d**x*x*log(d)**2*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 18*d**x*x*log(d)*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 6*d**x*x*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 6*d**x*log(d)**4*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 24*d**x*log(d)**3*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 36*d**x*log(d)**2*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) + 24*d**x*log(d)*sin(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1) - 6*d**x*cos(x)/(log(d)**8 + 4*log(d)**6 + 6*log(d)**4 + 4*log(d)**2 + 1), True))","B",0
142,1,114,0,12.668524," ","integrate(sin(x)*sin(2*x)*sin(3*x),x)","\frac{x \sin{\left(x \right)} \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{4} + \frac{x \sin{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{4} + \frac{x \sin{\left(2 x \right)} \cos{\left(x \right)} \cos{\left(3 x \right)}}{4} - \frac{x \sin{\left(3 x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)}}{4} - \frac{5 \sin{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(3 x \right)}}{24} - \frac{\sin{\left(2 x \right)} \sin{\left(3 x \right)} \cos{\left(x \right)}}{8} - \frac{\cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{6}"," ",0,"x*sin(x)*sin(2*x)*sin(3*x)/4 + x*sin(x)*cos(2*x)*cos(3*x)/4 + x*sin(2*x)*cos(x)*cos(3*x)/4 - x*sin(3*x)*cos(x)*cos(2*x)/4 - 5*sin(x)*sin(2*x)*cos(3*x)/24 - sin(2*x)*sin(3*x)*cos(x)/8 - cos(x)*cos(2*x)*cos(3*x)/6","B",0
143,1,112,0,12.701017," ","integrate(cos(x)*cos(2*x)*cos(3*x),x)","- \frac{x \sin{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(3 x \right)}}{4} + \frac{x \sin{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{4} + \frac{x \sin{\left(2 x \right)} \sin{\left(3 x \right)} \cos{\left(x \right)}}{4} + \frac{x \cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{4} + \frac{\sin{\left(x \right)} \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{24} - \frac{\sin{\left(2 x \right)} \cos{\left(x \right)} \cos{\left(3 x \right)}}{8} + \frac{\sin{\left(3 x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)}}{3}"," ",0,"-x*sin(x)*sin(2*x)*cos(3*x)/4 + x*sin(x)*sin(3*x)*cos(2*x)/4 + x*sin(2*x)*sin(3*x)*cos(x)/4 + x*cos(x)*cos(2*x)*cos(3*x)/4 + sin(x)*sin(2*x)*sin(3*x)/24 - sin(2*x)*cos(x)*cos(3*x)/8 + sin(3*x)*cos(x)*cos(2*x)/3","B",0
144,1,100,0,2.099664," ","integrate(x**2*sin(k*x)**3,x)","\begin{cases} - \frac{x^{2} \sin^{2}{\left(k x \right)} \cos{\left(k x \right)}}{k} - \frac{2 x^{2} \cos^{3}{\left(k x \right)}}{3 k} + \frac{14 x \sin^{3}{\left(k x \right)}}{9 k^{2}} + \frac{4 x \sin{\left(k x \right)} \cos^{2}{\left(k x \right)}}{3 k^{2}} + \frac{14 \sin^{2}{\left(k x \right)} \cos{\left(k x \right)}}{9 k^{3}} + \frac{40 \cos^{3}{\left(k x \right)}}{27 k^{3}} & \text{for}\: k \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x**2*sin(k*x)**2*cos(k*x)/k - 2*x**2*cos(k*x)**3/(3*k) + 14*x*sin(k*x)**3/(9*k**2) + 4*x*sin(k*x)*cos(k*x)**2/(3*k**2) + 14*sin(k*x)**2*cos(k*x)/(9*k**3) + 40*cos(k*x)**3/(27*k**3), Ne(k, 0)), (0, True))","A",0
145,-1,0,0,0.000000," ","integrate(x*cos(x)*cos(k/sin(x))/sin(x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,0,0,0,0.000000," ","integrate(cos(x)/sin(x)/tan(1/2*x),x)","\int \frac{\cos{\left(x \right)}}{\sin{\left(x \right)} \tan{\left(\frac{x}{2} \right)}}\, dx"," ",0,"Integral(cos(x)/(sin(x)*tan(x/2)), x)","F",0
147,-1,0,0,0.000000," ","integrate(sin(a*x)/(b+c*sin(a*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,1,15,0,0.379867," ","integrate(sin(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
149,1,15,0,0.389896," ","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
150,1,2,0,0.038023," ","integrate(exp(x),x)","e^{x}"," ",0,"exp(x)","A",0
151,1,8,0,0.088196," ","integrate(a**x,x)","\begin{cases} \frac{a^{x}}{\log{\left(a \right)}} & \text{for}\: \log{\left(a \right)} \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**x/log(a), Ne(log(a), 0)), (x, True))","A",0
152,1,7,0,0.049823," ","integrate(exp(a*x),x)","\begin{cases} \frac{e^{a x}}{a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((exp(a*x)/a, Ne(a, 0)), (x, True))","A",0
153,1,3,0,0.776859," ","integrate(exp(a*x)/x,x)","\operatorname{Ei}{\left(a x \right)}"," ",0,"Ei(a*x)","A",0
154,1,15,0,0.123616," ","integrate(1/(a+b*exp(m*x)),x)","\frac{x}{a} - \frac{\log{\left(\frac{a}{b} + e^{m x} \right)}}{a m}"," ",0,"x/a - log(a/b + exp(m*x))/(a*m)","A",0
155,1,8,0,0.088125," ","integrate(exp(2*x)/(1+exp(x)),x)","e^{x} - \log{\left(e^{x} + 1 \right)}"," ",0,"exp(x) - log(exp(x) + 1)","A",0
156,1,14,0,0.088152," ","integrate(exp(a*x+2*x),x)","\begin{cases} \frac{e^{a x + 2 x}}{a + 2} & \text{for}\: a + 2 \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((exp(a*x + 2*x)/(a + 2), Ne(a + 2, 0)), (x, True))","A",0
157,1,26,0,0.179881," ","integrate(1/(b/exp(m*x)+a*exp(m*x)),x)","\frac{\operatorname{RootSum} {\left(4 z^{2} a b + 1, \left( i \mapsto i \log{\left(- 2 i a + e^{- m x} \right)} \right)\right)}}{m}"," ",0,"RootSum(4*_z**2*a*b + 1, Lambda(_i, _i*log(-2*_i*a + exp(-m*x))))/m","A",0
158,1,19,0,0.094407," ","integrate(exp(a*x)*x,x)","\begin{cases} \frac{\left(a x - 1\right) e^{a x}}{a^{2}} & \text{for}\: a^{2} \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a*x - 1)*exp(a*x)/a**2, Ne(a**2, 0)), (x**2/2, True))","A",0
159,1,102,0,0.129281," ","integrate(exp(x)*x**20,x)","\left(x^{20} - 20 x^{19} + 380 x^{18} - 6840 x^{17} + 116280 x^{16} - 1860480 x^{15} + 27907200 x^{14} - 390700800 x^{13} + 5079110400 x^{12} - 60949324800 x^{11} + 670442572800 x^{10} - 6704425728000 x^{9} + 60339831552000 x^{8} - 482718652416000 x^{7} + 3379030566912000 x^{6} - 20274183401472000 x^{5} + 101370917007360000 x^{4} - 405483668029440000 x^{3} + 1216451004088320000 x^{2} - 2432902008176640000 x + 2432902008176640000\right) e^{x}"," ",0,"(x**20 - 20*x**19 + 380*x**18 - 6840*x**17 + 116280*x**16 - 1860480*x**15 + 27907200*x**14 - 390700800*x**13 + 5079110400*x**12 - 60949324800*x**11 + 670442572800*x**10 - 6704425728000*x**9 + 60339831552000*x**8 - 482718652416000*x**7 + 3379030566912000*x**6 - 20274183401472000*x**5 + 101370917007360000*x**4 - 405483668029440000*x**3 + 1216451004088320000*x**2 - 2432902008176640000*x + 2432902008176640000)*exp(x)","A",0
160,-2,0,0,0.000000," ","integrate(a**x/(b**x),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
161,1,24,0,0.571044," ","integrate(a**x*b**x,x)","\begin{cases} \frac{a^{x} b^{x}}{\log{\left(a \right)} + \log{\left(b \right)}} & \text{for}\: a \neq \frac{1}{b} \\\tilde{\infty} b^{x} \left(\frac{1}{b}\right)^{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**x*b**x/(log(a) + log(b)), Ne(a, 1/b)), (zoo*b**x*(1/b)**x, True))","A",0
162,0,0,0,0.000000," ","integrate(a**x/x**2,x)","\int \frac{a^{x}}{x^{2}}\, dx"," ",0,"Integral(a**x/x**2, x)","F",0
163,0,0,0,0.000000," ","integrate(a**x*x/(b*x+1)**2,x)","\int \frac{a^{x} x}{\left(b x + 1\right)^{2}}\, dx"," ",0,"Integral(a**x*x/(b*x + 1)**2, x)","F",0
164,1,12,0,0.117416," ","integrate(exp(a*x)*x/(a*x+1)**2,x)","\frac{e^{a x}}{a^{3} x + a^{2}}"," ",0,"exp(a*x)/(a**3*x + a**2)","A",0
165,1,17,0,0.097917," ","integrate(k**(x**2)*x,x)","\begin{cases} \frac{k^{x^{2}}}{2 \log{\left(k \right)}} & \text{for}\: 2 \log{\left(k \right)} \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((k**(x**2)/(2*log(k)), Ne(2*log(k), 0)), (x**2/2, True))","A",0
166,1,8,0,0.199250," ","integrate(exp(x**2),x)","\frac{\sqrt{\pi} \operatorname{erfi}{\left(x \right)}}{2}"," ",0,"sqrt(pi)*erfi(x)/2","A",0
167,1,5,0,0.081518," ","integrate(exp(x**2)*x,x)","\frac{e^{x^{2}}}{2}"," ",0,"exp(x**2)/2","A",0
168,1,14,0,0.097554," ","integrate(exp(1/x)*(1+x)/x**4,x)","\frac{\left(- x^{2} + x - 1\right) e^{\frac{1}{x}}}{x^{2}}"," ",0,"(-x**2 + x - 1)*exp(1/x)/x**2","A",0
169,1,31,0,0.349025," ","integrate(exp(1-exp(x**2)*x+2*x**2)*(2*x**3+x)/(1-exp(x**2)*x)**2,x)","- \frac{e^{2 x^{2} - x e^{x^{2}} + 1}}{x e^{3 x^{2}} - e^{2 x^{2}}}"," ",0,"-exp(2*x**2 - x*exp(x**2) + 1)/(x*exp(3*x**2) - exp(2*x**2))","A",0
170,0,0,0,0.000000," ","integrate(exp(exp(exp(exp(x)))),x)","\int e^{e^{e^{e^{x}}}}\, dx"," ",0,"Integral(exp(exp(exp(exp(x)))), x)","F",0
171,1,8,0,1.953908," ","integrate(exp(x)*ln(x),x)","e^{x} \log{\left(x \right)} - \operatorname{Ei}{\left(x \right)}"," ",0,"exp(x)*log(x) - Ei(x)","A",0
172,1,17,0,3.341753," ","integrate(exp(x)*x*ln(x),x)","\left(x e^{x} - e^{x}\right) \log{\left(x \right)} - e^{x} + \operatorname{Ei}{\left(x \right)}"," ",0,"(x*exp(x) - exp(x))*log(x) - exp(x) + Ei(x)","A",0
173,1,10,0,0.095648," ","integrate(exp(2*x)*ln(exp(x)),x)","\frac{\left(2 x - 1\right) e^{2 x}}{4}"," ",0,"(2*x - 1)*exp(2*x)/4","A",0
174,1,12,0,0.058581," ","integrate(2*x+x**2*2**(1/2),x)","\frac{\sqrt{2} x^{3}}{3} + x^{2}"," ",0,"sqrt(2)*x**3/3 + x**2","A",0
175,1,920,0,4.146336," ","integrate(ln(x)/(a*x+b)**(1/2),x)","\begin{cases} \frac{4 \sqrt{b} \operatorname{acoth}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x + \frac{b}{a}}} \right)}}{a} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a} \right)}}{\sqrt{a}} - \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(-1 + \frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} - \frac{4 \sqrt{x + \frac{b}{a}}}{\sqrt{a}} + \frac{2 i \pi \sqrt{x + \frac{b}{a}}}{\sqrt{a}} & \text{for}\: \left|{\frac{b}{a \left(x + \frac{b}{a}\right)}}\right| > 1 \wedge \left|{x + \frac{b}{a}}\right| < 1 \\\frac{4 \sqrt{b} \operatorname{atanh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x + \frac{b}{a}}} \right)}}{a} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a} \right)}}{\sqrt{a}} - \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(1 - \frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} - \frac{4 \sqrt{x + \frac{b}{a}}}{\sqrt{a}} & \text{for}\: \left|{x + \frac{b}{a}}\right| < 1 \\\frac{4 \sqrt{b} \operatorname{acoth}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x + \frac{b}{a}}} \right)}}{a} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a} \right)}}{\sqrt{a}} - \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(-1 + \frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} - \frac{4 \sqrt{x + \frac{b}{a}}}{\sqrt{a}} + \frac{2 i \pi \sqrt{x + \frac{b}{a}}}{\sqrt{a}} & \text{for}\: \left|{\frac{b}{a \left(x + \frac{b}{a}\right)}}\right| > 1 \wedge \frac{1}{\left|{x + \frac{b}{a}}\right|} < 1 \\\frac{4 \sqrt{b} \operatorname{atanh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x + \frac{b}{a}}} \right)}}{a} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a} \right)}}{\sqrt{a}} - \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(1 - \frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} - \frac{4 \sqrt{x + \frac{b}{a}}}{\sqrt{a}} & \text{for}\: \frac{1}{\left|{x + \frac{b}{a}}\right|} < 1 \\\frac{4 \sqrt{b} \operatorname{acoth}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x + \frac{b}{a}}} \right)}}{a} - \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(-1 + \frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} - \frac{4 \sqrt{x + \frac{b}{a}}}{\sqrt{a}} + \frac{{G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{3}{2} \\\frac{1}{2} & 0 \end{matrix} \middle| {x + \frac{b}{a}} \right)} \log{\left(\frac{b}{a} \right)}}{\sqrt{a}} + \frac{i \pi {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{3}{2} \\\frac{1}{2} & 0 \end{matrix} \middle| {x + \frac{b}{a}} \right)}}{\sqrt{a}} + \frac{{G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{3}{2}, 1 &  \\ & \frac{1}{2}, 0 \end{matrix} \middle| {x + \frac{b}{a}} \right)} \log{\left(\frac{b}{a} \right)}}{\sqrt{a}} + \frac{i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{3}{2}, 1 &  \\ & \frac{1}{2}, 0 \end{matrix} \middle| {x + \frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: \left|{\frac{b}{a \left(x + \frac{b}{a}\right)}}\right| > 1 \\\frac{4 \sqrt{b} \operatorname{atanh}{\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x + \frac{b}{a}}} \right)}}{a} - \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(\frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} + \frac{2 \sqrt{x + \frac{b}{a}} \log{\left(1 - \frac{b}{a \left(x + \frac{b}{a}\right)} \right)}}{\sqrt{a}} - \frac{4 \sqrt{x + \frac{b}{a}}}{\sqrt{a}} - \frac{2 i \pi \sqrt{x + \frac{b}{a}}}{\sqrt{a}} + \frac{{G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{3}{2} \\\frac{1}{2} & 0 \end{matrix} \middle| {x + \frac{b}{a}} \right)} \log{\left(\frac{b}{a} \right)}}{\sqrt{a}} + \frac{i \pi {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{3}{2} \\\frac{1}{2} & 0 \end{matrix} \middle| {x + \frac{b}{a}} \right)}}{\sqrt{a}} + \frac{{G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{3}{2}, 1 &  \\ & \frac{1}{2}, 0 \end{matrix} \middle| {x + \frac{b}{a}} \right)} \log{\left(\frac{b}{a} \right)}}{\sqrt{a}} + \frac{i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{3}{2}, 1 &  \\ & \frac{1}{2}, 0 \end{matrix} \middle| {x + \frac{b}{a}} \right)}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*sqrt(b)*acoth(sqrt(b)/(sqrt(a)*sqrt(x + b/a)))/a + 2*sqrt(x + b/a)*log(b/a)/sqrt(a) - 2*sqrt(x + b/a)*log(b/(a*(x + b/a)))/sqrt(a) + 2*sqrt(x + b/a)*log(-1 + b/(a*(x + b/a)))/sqrt(a) - 4*sqrt(x + b/a)/sqrt(a) + 2*I*pi*sqrt(x + b/a)/sqrt(a), (Abs(x + b/a) < 1) & (Abs(b/(a*(x + b/a))) > 1)), (4*sqrt(b)*atanh(sqrt(b)/(sqrt(a)*sqrt(x + b/a)))/a + 2*sqrt(x + b/a)*log(b/a)/sqrt(a) - 2*sqrt(x + b/a)*log(b/(a*(x + b/a)))/sqrt(a) + 2*sqrt(x + b/a)*log(1 - b/(a*(x + b/a)))/sqrt(a) - 4*sqrt(x + b/a)/sqrt(a), Abs(x + b/a) < 1), (4*sqrt(b)*acoth(sqrt(b)/(sqrt(a)*sqrt(x + b/a)))/a + 2*sqrt(x + b/a)*log(b/a)/sqrt(a) - 2*sqrt(x + b/a)*log(b/(a*(x + b/a)))/sqrt(a) + 2*sqrt(x + b/a)*log(-1 + b/(a*(x + b/a)))/sqrt(a) - 4*sqrt(x + b/a)/sqrt(a) + 2*I*pi*sqrt(x + b/a)/sqrt(a), (1/Abs(x + b/a) < 1) & (Abs(b/(a*(x + b/a))) > 1)), (4*sqrt(b)*atanh(sqrt(b)/(sqrt(a)*sqrt(x + b/a)))/a + 2*sqrt(x + b/a)*log(b/a)/sqrt(a) - 2*sqrt(x + b/a)*log(b/(a*(x + b/a)))/sqrt(a) + 2*sqrt(x + b/a)*log(1 - b/(a*(x + b/a)))/sqrt(a) - 4*sqrt(x + b/a)/sqrt(a), 1/Abs(x + b/a) < 1), (4*sqrt(b)*acoth(sqrt(b)/(sqrt(a)*sqrt(x + b/a)))/a - 2*sqrt(x + b/a)*log(b/(a*(x + b/a)))/sqrt(a) + 2*sqrt(x + b/a)*log(-1 + b/(a*(x + b/a)))/sqrt(a) - 4*sqrt(x + b/a)/sqrt(a) + meijerg(((1,), (3/2,)), ((1/2,), (0,)), x + b/a)*log(b/a)/sqrt(a) + I*pi*meijerg(((1,), (3/2,)), ((1/2,), (0,)), x + b/a)/sqrt(a) + meijerg(((3/2, 1), ()), ((), (1/2, 0)), x + b/a)*log(b/a)/sqrt(a) + I*pi*meijerg(((3/2, 1), ()), ((), (1/2, 0)), x + b/a)/sqrt(a), Abs(b/(a*(x + b/a))) > 1), (4*sqrt(b)*atanh(sqrt(b)/(sqrt(a)*sqrt(x + b/a)))/a - 2*sqrt(x + b/a)*log(b/(a*(x + b/a)))/sqrt(a) + 2*sqrt(x + b/a)*log(1 - b/(a*(x + b/a)))/sqrt(a) - 4*sqrt(x + b/a)/sqrt(a) - 2*I*pi*sqrt(x + b/a)/sqrt(a) + meijerg(((1,), (3/2,)), ((1/2,), (0,)), x + b/a)*log(b/a)/sqrt(a) + I*pi*meijerg(((1,), (3/2,)), ((1/2,), (0,)), x + b/a)/sqrt(a) + meijerg(((3/2, 1), ()), ((), (1/2, 0)), x + b/a)*log(b/a)/sqrt(a) + I*pi*meijerg(((3/2, 1), ()), ((), (1/2, 0)), x + b/a)/sqrt(a), True))","B",0
176,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(d*x+c)**(1/2),x)","\int \sqrt{a + b x} \sqrt{c + d x}\, dx"," ",0,"Integral(sqrt(a + b*x)*sqrt(c + d*x), x)","F",0
177,1,12,0,0.059593," ","integrate((b*x+a)**(1/2),x)","\frac{2 \left(a + b x\right)^{\frac{3}{2}}}{3 b}"," ",0,"2*(a + b*x)**(3/2)/(3*b)","A",0
178,1,202,0,1.141237," ","integrate(x*(b*x+a)**(1/2),x)","- \frac{4 a^{\frac{9}{2}} \sqrt{1 + \frac{b x}{a}}}{15 a^{2} b^{2} + 15 a b^{3} x} + \frac{4 a^{\frac{9}{2}}}{15 a^{2} b^{2} + 15 a b^{3} x} - \frac{2 a^{\frac{7}{2}} b x \sqrt{1 + \frac{b x}{a}}}{15 a^{2} b^{2} + 15 a b^{3} x} + \frac{4 a^{\frac{7}{2}} b x}{15 a^{2} b^{2} + 15 a b^{3} x} + \frac{8 a^{\frac{5}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{15 a^{2} b^{2} + 15 a b^{3} x} + \frac{6 a^{\frac{3}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{15 a^{2} b^{2} + 15 a b^{3} x}"," ",0,"-4*a**(9/2)*sqrt(1 + b*x/a)/(15*a**2*b**2 + 15*a*b**3*x) + 4*a**(9/2)/(15*a**2*b**2 + 15*a*b**3*x) - 2*a**(7/2)*b*x*sqrt(1 + b*x/a)/(15*a**2*b**2 + 15*a*b**3*x) + 4*a**(7/2)*b*x/(15*a**2*b**2 + 15*a*b**3*x) + 8*a**(5/2)*b**2*x**2*sqrt(1 + b*x/a)/(15*a**2*b**2 + 15*a*b**3*x) + 6*a**(3/2)*b**3*x**3*sqrt(1 + b*x/a)/(15*a**2*b**2 + 15*a*b**3*x)","B",0
179,1,666,0,1.749444," ","integrate(x**2*(b*x+a)**(1/2),x)","\frac{16 a^{\frac{23}{2}} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{23}{2}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{40 a^{\frac{21}{2}} b x \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{21}{2}} b x}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{30 a^{\frac{19}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{19}{2}} b^{2} x^{2}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{40 a^{\frac{17}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{17}{2}} b^{3} x^{3}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{100 a^{\frac{15}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{96 a^{\frac{13}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{30 a^{\frac{11}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}}"," ",0,"16*a**(23/2)*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) - 16*a**(23/2)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 40*a**(21/2)*b*x*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) - 48*a**(21/2)*b*x/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 30*a**(19/2)*b**2*x**2*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) - 48*a**(19/2)*b**2*x**2/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 40*a**(17/2)*b**3*x**3*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) - 16*a**(17/2)*b**3*x**3/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 100*a**(15/2)*b**4*x**4*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 96*a**(13/2)*b**5*x**5*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 30*a**(11/2)*b**6*x**6*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3)","B",0
180,1,68,0,1.408314," ","integrate((b*x+a)**(1/2)/x,x)","- 2 \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} + \frac{2 a}{\sqrt{b} \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{2 \sqrt{b} \sqrt{x}}{\sqrt{\frac{a}{b x} + 1}}"," ",0,"-2*sqrt(a)*asinh(sqrt(a)/(sqrt(b)*sqrt(x))) + 2*a/(sqrt(b)*sqrt(x)*sqrt(a/(b*x) + 1)) + 2*sqrt(b)*sqrt(x)/sqrt(a/(b*x) + 1)","B",0
181,1,44,0,1.870930," ","integrate((b*x+a)**(1/2)/x**2,x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x} + 1}}{\sqrt{x}} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}}"," ",0,"-sqrt(b)*sqrt(a/(b*x) + 1)/sqrt(x) - b*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a)","A",0
182,1,10,0,0.059164," ","integrate(1/(b*x+a)**(1/2),x)","\frac{2 \sqrt{a + b x}}{b}"," ",0,"2*sqrt(a + b*x)/b","A",0
183,1,162,0,1.109185," ","integrate(x/(b*x+a)**(1/2),x)","- \frac{4 a^{\frac{7}{2}} \sqrt{1 + \frac{b x}{a}}}{3 a^{2} b^{2} + 3 a b^{3} x} + \frac{4 a^{\frac{7}{2}}}{3 a^{2} b^{2} + 3 a b^{3} x} - \frac{2 a^{\frac{5}{2}} b x \sqrt{1 + \frac{b x}{a}}}{3 a^{2} b^{2} + 3 a b^{3} x} + \frac{4 a^{\frac{5}{2}} b x}{3 a^{2} b^{2} + 3 a b^{3} x} + \frac{2 a^{\frac{3}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{3 a^{2} b^{2} + 3 a b^{3} x}"," ",0,"-4*a**(7/2)*sqrt(1 + b*x/a)/(3*a**2*b**2 + 3*a*b**3*x) + 4*a**(7/2)/(3*a**2*b**2 + 3*a*b**3*x) - 2*a**(5/2)*b*x*sqrt(1 + b*x/a)/(3*a**2*b**2 + 3*a*b**3*x) + 4*a**(5/2)*b*x/(3*a**2*b**2 + 3*a*b**3*x) + 2*a**(3/2)*b**2*x**2*sqrt(1 + b*x/a)/(3*a**2*b**2 + 3*a*b**3*x)","B",0
184,1,600,0,1.701194," ","integrate(x**2/(b*x+a)**(1/2),x)","\frac{16 a^{\frac{21}{2}} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{21}{2}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{40 a^{\frac{19}{2}} b x \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{19}{2}} b x}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{30 a^{\frac{17}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{17}{2}} b^{2} x^{2}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{10 a^{\frac{15}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{15}{2}} b^{3} x^{3}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{10 a^{\frac{13}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{6 a^{\frac{11}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}}"," ",0,"16*a**(21/2)*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) - 16*a**(21/2)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 40*a**(19/2)*b*x*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) - 48*a**(19/2)*b*x/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 30*a**(17/2)*b**2*x**2*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) - 48*a**(17/2)*b**2*x**2/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 10*a**(15/2)*b**3*x**3*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) - 16*a**(15/2)*b**3*x**3/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 10*a**(13/2)*b**4*x**4*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 6*a**(11/2)*b**5*x**5*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3)","B",0
185,1,24,0,1.066233," ","integrate(1/x/(b*x+a)**(1/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}}"," ",0,"-2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a)","A",0
186,1,44,0,2.212196," ","integrate(1/x**2/(b*x+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x} + 1}}{a \sqrt{x}} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{a^{\frac{3}{2}}}"," ",0,"-sqrt(b)*sqrt(a/(b*x) + 1)/(a*sqrt(x)) + b*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/a**(3/2)","A",0
187,1,26,0,0.064700," ","integrate(((b*x+a)**(1/2))**p,x)","\frac{\begin{cases} \frac{\left(a + b x\right)^{\frac{p}{2} + 1}}{\frac{p}{2} + 1} & \text{for}\: \frac{p}{2} \neq -1 \\\log{\left(a + b x \right)} & \text{otherwise} \end{cases}}{b}"," ",0,"Piecewise(((a + b*x)**(p/2 + 1)/(p/2 + 1), Ne(p/2, -1)), (log(a + b*x), True))/b","A",0
188,1,216,0,0.693956," ","integrate(x*((b*x+a)**(1/2))**p,x)","\begin{cases} \frac{a^{\frac{p}{2}} x^{2}}{2} & \text{for}\: b = 0 \\\frac{a \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} + \frac{a}{a b^{2} + b^{3} x} + \frac{b x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} & \text{for}\: p = -4 \\- \frac{a \log{\left(\frac{a}{b} + x \right)}}{b^{2}} + \frac{x}{b} & \text{for}\: p = -2 \\- \frac{4 a^{2} \left(a + b x\right)^{\frac{p}{2}}}{b^{2} p^{2} + 6 b^{2} p + 8 b^{2}} + \frac{2 a b p x \left(a + b x\right)^{\frac{p}{2}}}{b^{2} p^{2} + 6 b^{2} p + 8 b^{2}} + \frac{2 b^{2} p x^{2} \left(a + b x\right)^{\frac{p}{2}}}{b^{2} p^{2} + 6 b^{2} p + 8 b^{2}} + \frac{4 b^{2} x^{2} \left(a + b x\right)^{\frac{p}{2}}}{b^{2} p^{2} + 6 b^{2} p + 8 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(p/2)*x**2/2, Eq(b, 0)), (a*log(a/b + x)/(a*b**2 + b**3*x) + a/(a*b**2 + b**3*x) + b*x*log(a/b + x)/(a*b**2 + b**3*x), Eq(p, -4)), (-a*log(a/b + x)/b**2 + x/b, Eq(p, -2)), (-4*a**2*(a + b*x)**(p/2)/(b**2*p**2 + 6*b**2*p + 8*b**2) + 2*a*b*p*x*(a + b*x)**(p/2)/(b**2*p**2 + 6*b**2*p + 8*b**2) + 2*b**2*p*x**2*(a + b*x)**(p/2)/(b**2*p**2 + 6*b**2*p + 8*b**2) + 4*b**2*x**2*(a + b*x)**(p/2)/(b**2*p**2 + 6*b**2*p + 8*b**2), True))","A",0
189,1,230,0,1.046005," ","integrate(atan(1/2*(2*x-2**(1/2))*2**(1/2)),x)","\frac{4 x^{3} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4 x^{2} - 4 \sqrt{2} x + 4} - \frac{\sqrt{2} x^{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{4 x^{2} - 4 \sqrt{2} x + 4} - \frac{6 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4 x^{2} - 4 \sqrt{2} x + 4} + \frac{2 x \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{4 x^{2} - 4 \sqrt{2} x + 4} + \frac{8 x \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4 x^{2} - 4 \sqrt{2} x + 4} - \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{4 x^{2} - 4 \sqrt{2} x + 4} - \frac{2 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4 x^{2} - 4 \sqrt{2} x + 4}"," ",0,"4*x**3*atan(sqrt(2)*x - 1)/(4*x**2 - 4*sqrt(2)*x + 4) - sqrt(2)*x**2*log(x**2 - sqrt(2)*x + 1)/(4*x**2 - 4*sqrt(2)*x + 4) - 6*sqrt(2)*x**2*atan(sqrt(2)*x - 1)/(4*x**2 - 4*sqrt(2)*x + 4) + 2*x*log(x**2 - sqrt(2)*x + 1)/(4*x**2 - 4*sqrt(2)*x + 4) + 8*x*atan(sqrt(2)*x - 1)/(4*x**2 - 4*sqrt(2)*x + 4) - sqrt(2)*log(x**2 - sqrt(2)*x + 1)/(4*x**2 - 4*sqrt(2)*x + 4) - 2*sqrt(2)*atan(sqrt(2)*x - 1)/(4*x**2 - 4*sqrt(2)*x + 4)","B",0
190,1,2,0,0.138345," ","integrate(1/(x**2-1)**(1/2),x)","\operatorname{acosh}{\left(x \right)}"," ",0,"acosh(x)","A",0
191,1,119,0,2.566198," ","integrate(x**(1/2)*(1+x)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\sqrt{x + 1} \right)}}{4} + \frac{\left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{x}} - \frac{3 \left(x + 1\right)^{\frac{3}{2}}}{4 \sqrt{x}} + \frac{\sqrt{x + 1}}{4 \sqrt{x}} & \text{for}\: \left|{x + 1}\right| > 1 \\\frac{i \operatorname{asin}{\left(\sqrt{x + 1} \right)}}{4} - \frac{i \left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{- x}} + \frac{3 i \left(x + 1\right)^{\frac{3}{2}}}{4 \sqrt{- x}} - \frac{i \sqrt{x + 1}}{4 \sqrt{- x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(sqrt(x + 1))/4 + (x + 1)**(5/2)/(2*sqrt(x)) - 3*(x + 1)**(3/2)/(4*sqrt(x)) + sqrt(x + 1)/(4*sqrt(x)), Abs(x + 1) > 1), (I*asin(sqrt(x + 1))/4 - I*(x + 1)**(5/2)/(2*sqrt(-x)) + 3*I*(x + 1)**(3/2)/(4*sqrt(-x)) - I*sqrt(x + 1)/(4*sqrt(-x)), True))","A",0
192,1,20,0,0.310382," ","integrate(sin(x**(1/2)),x)","- 2 \sqrt{x} \cos{\left(\sqrt{x} \right)} + 2 \sin{\left(\sqrt{x} \right)}"," ",0,"-2*sqrt(x)*cos(sqrt(x)) + 2*sin(sqrt(x))","A",0
193,1,8,0,0.968951," ","integrate(x/(-x**2+1)**(9/8),x)","\frac{4}{\sqrt[8]{1 - x^{2}}}"," ",0,"4/(1 - x**2)**(1/8)","A",0
194,1,19,0,0.920862," ","integrate(x/(-x**4+1)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(x^{2} \right)}}{2} & \text{for}\: \left|{x^{4}}\right| > 1 \\\frac{\operatorname{asin}{\left(x^{2} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(x**2)/2, Abs(x**4) > 1), (asin(x**2)/2, True))","A",0
195,1,8,0,0.919200," ","integrate(1/x/(x**4+1)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{1}{x^{2}} \right)}}{2}"," ",0,"-asinh(x**(-2))/2","A",0
196,0,0,0,0.000000," ","integrate(x/(x**4+x**2+1)**(1/2),x)","\int \frac{x}{\sqrt{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}\, dx"," ",0,"Integral(x/sqrt((x**2 - x + 1)*(x**2 + x + 1)), x)","F",0
197,0,0,0,0.000000," ","integrate(1/x/(-x**4+x**2-1)**(1/2),x)","\int \frac{1}{x \sqrt{- x^{4} + x^{2} - 1}}\, dx"," ",0,"Integral(1/(x*sqrt(-x**4 + x**2 - 1)), x)","F",0
198,0,0,0,0.000000," ","integrate((1+x)/(1-x)**2/(x**2+1)**(1/2),x)","\int \frac{x + 1}{\left(x - 1\right)^{2} \sqrt{x^{2} + 1}}\, dx"," ",0,"Integral((x + 1)/((x - 1)**2*sqrt(x**2 + 1)), x)","F",0
199,1,2,0,0.139802," ","integrate(1/(x**2+1)**(1/2),x)","\operatorname{asinh}{\left(x \right)}"," ",0,"asinh(x)","A",0
200,1,17,0,1.165058," ","integrate(1/2*(x**(1/2)*(1+x)**(1/2)+x**(1/2)*(2+x)**(1/2)+(1+x)**(1/2)*(2+x)**(1/2))/x**(1/2)/(1+x)**(1/2)/(2+x)**(1/2),x)","\sqrt{x} + \sqrt{x + 1} + \sqrt{x + 2}"," ",0,"sqrt(x) + sqrt(x + 1) + sqrt(x + 2)","A",0
201,1,19,0,1.338458," ","integrate(1/2*(-2*(x**3+1)**(1/2)+5*x**4*(x**3+1)**(1/2)-3*x**2*(x**5-2*x+1)**(1/2))/(x**3+1)**(1/2)/(x**5-2*x+1)**(1/2),x)","- \sqrt{x^{3} + 1} + \sqrt{x^{5} - 2 x + 1}"," ",0,"-sqrt(x**3 + 1) + sqrt(x**5 - 2*x + 1)","A",0
202,1,8,0,0.178443," ","integrate(10/(x**2-4)**(1/2)+1/(x**2-1)**(1/2),x)","10 \operatorname{acosh}{\left(\frac{x}{2} \right)} + \operatorname{acosh}{\left(x \right)}"," ",0,"10*acosh(x/2) + acosh(x)","A",0
203,1,51,0,1.316464," ","integrate((x+(a**2+x**2)**(1/2))**(1/2)/x,x)","\frac{\sqrt{x} \Gamma^{2}\left(- \frac{1}{4}\right) \Gamma\left(\frac{1}{4}\right) {{}_{3}F_{2}\left(\begin{matrix} - \frac{1}{4}, - \frac{1}{4}, \frac{1}{4} \\ \frac{1}{2}, \frac{3}{4} \end{matrix}\middle| {\frac{a^{2} e^{i \pi}}{x^{2}}} \right)}}{8 \pi \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(x)*gamma(-1/4)**2*gamma(1/4)*hyper((-1/4, -1/4, 1/4), (1/2, 3/4), a**2*exp_polar(I*pi)/x**2)/(8*pi*gamma(3/4))","C",0
204,1,48,0,154.692694," ","integrate(3/2*x**2/(1+x**3+(x**3+1)**(1/2)),x)","- \frac{\log{\left(2 \sqrt{x^{3} + 1} \right)}}{2} + \frac{\log{\left(2 \sqrt{x^{3} + 1} + 2 \right)}}{2} + \frac{\log{\left(3 x^{3} + 3 \sqrt{x^{3} + 1} + 3 \right)}}{2}"," ",0,"-log(2*sqrt(x**3 + 1))/2 + log(2*sqrt(x**3 + 1) + 2)/2 + log(3*x**3 + 3*sqrt(x**3 + 1) + 3)/2","B",0
205,1,66,0,1.144649," ","integrate(1/(2*h*r**2-alpha**2)**(1/2),r)","\begin{cases} \frac{\sqrt{2} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{h} r}{\alpha} \right)}}{2 \sqrt{h}} & \text{for}\: 2 \left|{\frac{h r^{2}}{\alpha^{2}}}\right| > 1 \\- \frac{\sqrt{2} i \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{h} r}{\alpha} \right)}}{2 \sqrt{h}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(2)*acosh(sqrt(2)*sqrt(h)*r/alpha)/(2*sqrt(h)), 2*Abs(h*r**2/alpha**2) > 1), (-sqrt(2)*I*asin(sqrt(2)*sqrt(h)*r/alpha)/(2*sqrt(h)), True))","A",0
206,1,42,0,1.248713," ","integrate(1/r/(2*h*r**2-alpha**2-epsilon**2)**(1/2),r)","- \frac{\operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{\operatorname{polar\_lift}{\left(- \alpha^{2} - \epsilon^{2} \right)}}}{2 \sqrt{h} r} \right)}}{\sqrt{\operatorname{polar\_lift}{\left(- \alpha^{2} - \epsilon^{2} \right)}}}"," ",0,"-asinh(sqrt(2)*sqrt(polar_lift(-alpha**2 - epsilon**2))/(2*sqrt(h)*r))/sqrt(polar_lift(-alpha**2 - epsilon**2))","A",0
207,0,0,0,0.000000," ","integrate(1/r/(2*h*r**2-alpha**2-2*k*r)**(1/2),r)","\int \frac{1}{r \sqrt{- \alpha^{2} + 2 h r^{2} - 2 k r}}\, dr"," ",0,"Integral(1/(r*sqrt(-alpha**2 + 2*h*r**2 - 2*k*r)), r)","F",0
208,0,0,0,0.000000," ","integrate(1/r/(2*h*r**2-alpha**2-epsilon**2-2*k*r)**(1/2),r)","\int \frac{1}{r \sqrt{- \alpha^{2} - \epsilon^{2} + 2 h r^{2} - 2 k r}}\, dr"," ",0,"Integral(1/(r*sqrt(-alpha**2 - epsilon**2 + 2*h*r**2 - 2*k*r)), r)","F",0
209,1,29,0,0.450322," ","integrate(r/(2*e*r**2-alpha**2)**(1/2),r)","\begin{cases} \frac{\sqrt{- \alpha^{2} + 2 e r^{2}}}{2 e} & \text{for}\: e \neq 0 \\\frac{r^{2}}{2 \sqrt{- \alpha^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(-alpha**2 + 2*e*r**2)/(2*e), Ne(e, 0)), (r**2/(2*sqrt(-alpha**2)), True))","A",0
210,1,36,0,0.588341," ","integrate(r/(2*e*r**2-alpha**2-epsilon**2)**(1/2),r)","\begin{cases} \frac{\sqrt{- \alpha^{2} + 2 e r^{2} - \epsilon^{2}}}{2 e} & \text{for}\: e \neq 0 \\\frac{r^{2}}{2 \sqrt{- \alpha^{2} - \epsilon^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(-alpha**2 + 2*e*r**2 - epsilon**2)/(2*e), Ne(e, 0)), (r**2/(2*sqrt(-alpha**2 - epsilon**2)), True))","A",0
211,0,0,0,0.000000," ","integrate(r/(-2*k*r**4+2*e*r**2-alpha**2)**(1/2),r)","\int \frac{r}{\sqrt{- \alpha^{2} + 2 e r^{2} - 2 k r^{4}}}\, dr"," ",0,"Integral(r/sqrt(-alpha**2 + 2*e*r**2 - 2*k*r**4), r)","F",0
212,0,0,0,0.000000," ","integrate(r/(2*e*r**2-alpha**2-2*k*r)**(1/2),r)","\int \frac{r}{\sqrt{- \alpha^{2} + 2 e r^{2} - 2 k r}}\, dr"," ",0,"Integral(r/sqrt(-alpha**2 + 2*e*r**2 - 2*k*r), r)","F",0
213,0,0,0,0.000000," ","integrate(1/r/(-2*k*r**4+2*h*r**2-alpha**2)**(1/2),r)","\int \frac{1}{r \sqrt{- \alpha^{2} + 2 h r^{2} - 2 k r^{4}}}\, dr"," ",0,"Integral(1/(r*sqrt(-alpha**2 + 2*h*r**2 - 2*k*r**4)), r)","F",0
214,0,0,0,0.000000," ","integrate(1/r/(-2*k*r**4+2*h*r**2-alpha**2-epsilon**2)**(1/2),r)","\int \frac{1}{r \sqrt{- \alpha^{2} - \epsilon^{2} + 2 h r^{2} - 2 k r^{4}}}\, dr"," ",0,"Integral(1/(r*sqrt(-alpha**2 - epsilon**2 + 2*h*r**2 - 2*k*r**4)), r)","F",0
215,1,10,0,0.321432," ","integrate(a*cos(5+3*x)*sin(5+3*x)**2,x)","\frac{a \sin^{3}{\left(3 x + 5 \right)}}{9}"," ",0,"a*sin(3*x + 5)**3/9","A",0
216,1,17,0,0.099430," ","integrate(ln(x**2)/x**3,x)","- \frac{\log{\left(x^{2} \right)}}{2 x^{2}} - \frac{1}{2 x^{2}}"," ",0,"-log(x**2)/(2*x**2) - 1/(2*x**2)","A",0
217,1,10,0,0.178855," ","integrate(x*sin(a+x),x)","- x \cos{\left(a + x \right)} + \sin{\left(a + x \right)}"," ",0,"-x*cos(a + x) + sin(a + x)","A",0
218,1,7,0,0.271979," ","integrate((-1+(1-x)*ln(x))/exp(x)/ln(x)**2,x)","\frac{x e^{- x}}{\log{\left(x \right)}}"," ",0,"x*exp(-x)/log(x)","A",0
219,1,20,0,0.135214," ","integrate(x**3/(a*x**2+b),x)","\frac{x^{2}}{2 a} - \frac{b \log{\left(a x^{2} + b \right)}}{2 a^{2}}"," ",0,"x**2/(2*a) - b*log(a*x**2 + b)/(2*a**2)","A",0
220,1,165,0,4.658733," ","integrate(x**(1/2)/(1+x)**(7/2),x)","\begin{cases} \frac{4 i \sqrt{-1 + \frac{1}{x + 1}}}{15} + \frac{2 i \sqrt{-1 + \frac{1}{x + 1}}}{15 \left(x + 1\right)} - \frac{2 i \sqrt{-1 + \frac{1}{x + 1}}}{5 \left(x + 1\right)^{2}} & \text{for}\: \frac{1}{\left|{x + 1}\right|} > 1 \\\frac{4 \sqrt{1 - \frac{1}{x + 1}} \left(x + 1\right)^{2}}{- 15 x + 15 \left(x + 1\right)^{2} - 15} - \frac{2 \sqrt{1 - \frac{1}{x + 1}} \left(x + 1\right)}{- 15 x + 15 \left(x + 1\right)^{2} - 15} - \frac{8 \sqrt{1 - \frac{1}{x + 1}}}{- 15 x + 15 \left(x + 1\right)^{2} - 15} + \frac{6 \sqrt{1 - \frac{1}{x + 1}}}{\left(x + 1\right) \left(- 15 x + 15 \left(x + 1\right)^{2} - 15\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*I*sqrt(-1 + 1/(x + 1))/15 + 2*I*sqrt(-1 + 1/(x + 1))/(15*(x + 1)) - 2*I*sqrt(-1 + 1/(x + 1))/(5*(x + 1)**2), 1/Abs(x + 1) > 1), (4*sqrt(1 - 1/(x + 1))*(x + 1)**2/(-15*x + 15*(x + 1)**2 - 15) - 2*sqrt(1 - 1/(x + 1))*(x + 1)/(-15*x + 15*(x + 1)**2 - 15) - 8*sqrt(1 - 1/(x + 1))/(-15*x + 15*(x + 1)**2 - 15) + 6*sqrt(1 - 1/(x + 1))/((x + 1)*(-15*x + 15*(x + 1)**2 - 15)), True))","B",0
221,1,7,0,0.092069," ","integrate(1/x/(1+x),x)","\log{\left(x \right)} - \log{\left(x + 1 \right)}"," ",0,"log(x) - log(x + 1)","A",0
222,1,39,0,0.310997," ","integrate(1/x**(1/2)/(-1+2*x),x)","\frac{\sqrt{2} \log{\left(\sqrt{x} - \frac{\sqrt{2}}{2} \right)}}{2} - \frac{\sqrt{2} \log{\left(\sqrt{x} + \frac{\sqrt{2}}{2} \right)}}{2}"," ",0,"sqrt(2)*log(sqrt(x) - sqrt(2)/2)/2 - sqrt(2)*log(sqrt(x) + sqrt(2)/2)/2","B",0
223,1,15,0,1.093703," ","integrate(x**(1/2)*(x**2+1),x)","\frac{2 x^{\frac{7}{2}}}{7} + \frac{2 x^{\frac{3}{2}}}{3}"," ",0,"2*x**(7/2)/7 + 2*x**(3/2)/3","A",0
224,1,153,0,1.693288," ","integrate((-a+x)**(1/3)/x,x)","\frac{4 \sqrt[3]{a} e^{- \frac{i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{- a + x} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{3 \Gamma\left(\frac{7}{3}\right)} - \frac{4 \sqrt[3]{a} \log{\left(1 - \frac{\sqrt[3]{- a + x} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{4 \sqrt[3]{a} e^{\frac{i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{- a + x} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{4 \sqrt[3]{- a + x} \Gamma\left(\frac{4}{3}\right)}{\Gamma\left(\frac{7}{3}\right)}"," ",0,"4*a**(1/3)*exp(-I*pi/3)*log(1 - (-a + x)**(1/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(4/3)/(3*gamma(7/3)) - 4*a**(1/3)*log(1 - (-a + x)**(1/3)*exp_polar(I*pi)/a**(1/3))*gamma(4/3)/(3*gamma(7/3)) + 4*a**(1/3)*exp(I*pi/3)*log(1 - (-a + x)**(1/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(4/3)/(3*gamma(7/3)) + 4*(-a + x)**(1/3)*gamma(4/3)/gamma(7/3)","C",0
225,1,7,0,0.190178," ","integrate(x*sinh(x),x)","x \cosh{\left(x \right)} - \sinh{\left(x \right)}"," ",0,"x*cosh(x) - sinh(x)","A",0
226,1,7,0,0.188496," ","integrate(x*cosh(x),x)","x \sinh{\left(x \right)} - \cosh{\left(x \right)}"," ",0,"x*sinh(x) - cosh(x)","A",0
227,1,7,0,0.152519," ","integrate(sinh(2*x)/cosh(2*x),x)","\frac{\log{\left(\cosh{\left(2 x \right)} \right)}}{2}"," ",0,"log(cosh(2*x))/2","A",0
228,1,22,0,0.392266," ","integrate((-1+I*eps*sinh(x))/(I*a-x+I*eps*cosh(x)),x)","- x + \log{\left(e^{2 x} + 1 + \frac{\left(2 a + 2 i x\right) e^{x}}{eps} \right)}"," ",0,"-x + log(exp(2*x) + 1 + (2*a + 2*I*x)*exp(x)/eps)","B",0
229,1,75,0,2.199808," ","integrate(cos(x)**2*sin(3+2*x),x)","- \frac{x \sin^{2}{\left(x \right)} \sin{\left(2 x + 3 \right)}}{4} - \frac{x \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x + 3 \right)}}{2} + \frac{x \sin{\left(2 x + 3 \right)} \cos^{2}{\left(x \right)}}{4} - \frac{\sin{\left(x \right)} \sin{\left(2 x + 3 \right)} \cos{\left(x \right)}}{4} - \frac{\cos^{2}{\left(x \right)} \cos{\left(2 x + 3 \right)}}{2}"," ",0,"-x*sin(x)**2*sin(2*x + 3)/4 - x*sin(x)*cos(x)*cos(2*x + 3)/2 + x*sin(2*x + 3)*cos(x)**2/4 - sin(x)*sin(2*x + 3)*cos(x)/4 - cos(x)**2*cos(2*x + 3)/2","B",0
230,1,15,0,0.249426," ","integrate(x*atan(x),x)","\frac{x^{2} \operatorname{atan}{\left(x \right)}}{2} - \frac{x}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2}"," ",0,"x**2*atan(x)/2 - x/2 + atan(x)/2","A",0
231,1,15,0,0.251003," ","integrate(x*acot(x),x)","\frac{x^{2} \operatorname{acot}{\left(x \right)}}{2} + \frac{x}{2} + \frac{\operatorname{acot}{\left(x \right)}}{2}"," ",0,"x**2*acot(x)/2 + x/2 + acot(x)/2","A",0
232,1,26,0,0.154373," ","integrate(x*ln(x**2+a),x)","\frac{a \log{\left(a + x^{2} \right)}}{2} + \frac{x^{2} \log{\left(a + x^{2} \right)}}{2} - \frac{x^{2}}{2}"," ",0,"a*log(a + x**2)/2 + x**2*log(a + x**2)/2 - x**2/2","A",0
233,1,32,0,0.536177," ","integrate(cos(x)*sin(a+x),x)","- \frac{x \sin{\left(x \right)} \cos{\left(a + x \right)}}{2} + \frac{x \sin{\left(a + x \right)} \cos{\left(x \right)}}{2} + \frac{\sin{\left(x \right)} \sin{\left(a + x \right)}}{2}"," ",0,"-x*sin(x)*cos(a + x)/2 + x*sin(a + x)*cos(x)/2 + sin(x)*sin(a + x)/2","B",0
234,1,32,0,0.537672," ","integrate(cos(a+x)*sin(x),x)","\frac{x \sin{\left(x \right)} \cos{\left(a + x \right)}}{2} - \frac{x \sin{\left(a + x \right)} \cos{\left(x \right)}}{2} + \frac{\sin{\left(x \right)} \sin{\left(a + x \right)}}{2}"," ",0,"x*sin(x)*cos(a + x)/2 - x*sin(a + x)*cos(x)/2 + sin(x)*sin(a + x)/2","B",0
235,0,0,0,0.000000," ","integrate((1+sin(x))**(1/2),x)","\int \sqrt{\sin{\left(x \right)} + 1}\, dx"," ",0,"Integral(sqrt(sin(x) + 1), x)","F",0
236,0,0,0,0.000000," ","integrate((1-sin(x))**(1/2),x)","\int \sqrt{1 - \sin{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(1 - sin(x)), x)","F",0
237,0,0,0,0.000000," ","integrate((1+cos(x))**(1/2),x)","\int \sqrt{\cos{\left(x \right)} + 1}\, dx"," ",0,"Integral(sqrt(cos(x) + 1), x)","F",0
238,0,0,0,0.000000," ","integrate((1-cos(x))**(1/2),x)","\int \sqrt{1 - \cos{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(1 - cos(x)), x)","F",0
239,1,63,0,0.385114," ","integrate(1/(-(-1+x)**(1/2)+x**(1/2)),x)","\frac{2 \sqrt{x} \sqrt{x - 1}}{- 3 \sqrt{x} + 3 \sqrt{x - 1}} - \frac{4 x}{- 3 \sqrt{x} + 3 \sqrt{x - 1}} + \frac{2}{- 3 \sqrt{x} + 3 \sqrt{x - 1}}"," ",0,"2*sqrt(x)*sqrt(x - 1)/(-3*sqrt(x) + 3*sqrt(x - 1)) - 4*x/(-3*sqrt(x) + 3*sqrt(x - 1)) + 2/(-3*sqrt(x) + 3*sqrt(x - 1))","B",0
240,1,20,0,0.138794," ","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
241,1,7,0,0.896571," ","integrate(x/(x**4+36)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{x^{2}}{6} \right)}}{2}"," ",0,"asinh(x**2/6)/2","A",0
242,0,0,0,0.000000," ","integrate(1/(x**(1/3)+x**(1/2)),x)","\int \frac{1}{\sqrt[3]{x} + \sqrt{x}}\, dx"," ",0,"Integral(1/(x**(1/3) + sqrt(x)), x)","F",0
243,1,31,0,0.138021," ","integrate(ln(3*x**2+2),x)","x \log{\left(3 x^{2} + 2 \right)} - 2 x + \frac{2 \sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{2} \right)}}{3}"," ",0,"x*log(3*x**2 + 2) - 2*x + 2*sqrt(6)*atan(sqrt(6)*x/2)/3","A",0
244,1,3,0,0.064524," ","integrate(cot(x),x)","\log{\left(\sin{\left(x \right)} \right)}"," ",0,"log(sin(x))","A",0
245,1,19,0,0.072713," ","integrate(cot(x)**4,x)","x + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{3}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}}"," ",0,"x + cos(x)/sin(x) - cos(x)**3/(3*sin(x)**3)","A",0
246,1,7,0,0.130420," ","integrate(tanh(x),x)","x - \log{\left(\tanh{\left(x \right)} + 1 \right)}"," ",0,"x - log(tanh(x) + 1)","B",0
247,1,12,0,0.319737," ","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
248,1,8,0,0.088246," ","integrate(b**x,x)","\begin{cases} \frac{b^{x}}{\log{\left(b \right)}} & \text{for}\: \log{\left(b \right)} \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**x/log(b), Ne(log(b), 0)), (x, True))","A",0
249,0,0,0,0.000000," ","integrate((2+1/x**4+x**4)**(1/2),x)","\int \sqrt{x^{4} + 2 + \frac{1}{x^{4}}}\, dx"," ",0,"Integral(sqrt(x**4 + 2 + x**(-4)), x)","F",0
250,1,12,0,0.076244," ","integrate((1+2*x)/(2+3*x),x)","\frac{2 x}{3} - \frac{\log{\left(3 x + 2 \right)}}{9}"," ",0,"2*x/3 - log(3*x + 2)/9","A",0
251,0,0,0,0.000000," ","integrate(x*ln(x+(x**2+1)**(1/2)),x)","\int x \log{\left(x + \sqrt{x^{2} + 1} \right)}\, dx"," ",0,"Integral(x*log(x + sqrt(x**2 + 1)), x)","F",0
252,1,109,0,4.949043," ","integrate(x*(1+exp(x)*sin(x))**2,x)","\frac{x^{2}}{2} + \frac{3 x e^{2 x} \sin^{2}{\left(x \right)}}{8} - \frac{x e^{2 x} \sin{\left(x \right)} \cos{\left(x \right)}}{4} + \frac{x e^{2 x} \cos^{2}{\left(x \right)}}{8} + x e^{x} \sin{\left(x \right)} - x e^{x} \cos{\left(x \right)} - \frac{e^{2 x} \sin^{2}{\left(x \right)}}{8} + \frac{e^{2 x} \sin{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{e^{2 x} \cos^{2}{\left(x \right)}}{8} + e^{x} \cos{\left(x \right)}"," ",0,"x**2/2 + 3*x*exp(2*x)*sin(x)**2/8 - x*exp(2*x)*sin(x)*cos(x)/4 + x*exp(2*x)*cos(x)**2/8 + x*exp(x)*sin(x) - x*exp(x)*cos(x) - exp(2*x)*sin(x)**2/8 + exp(2*x)*sin(x)*cos(x)/8 - exp(2*x)*cos(x)**2/8 + exp(x)*cos(x)","A",0
253,1,27,0,0.828337," ","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
254,1,17,0,0.106542," ","integrate(1/(-3+x)**4,x)","- \frac{1}{3 x^{3} - 27 x^{2} + 81 x - 81}"," ",0,"-1/(3*x**3 - 27*x**2 + 81*x - 81)","B",0
255,1,41,0,0.132518," ","integrate(x/(x**3-1),x)","\frac{\log{\left(x - 1 \right)}}{3} - \frac{\log{\left(x^{2} + x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"log(x - 1)/3 - log(x**2 + x + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3","A",0
256,1,15,0,0.096949," ","integrate(x/(x**4-1),x)","\frac{\log{\left(x^{2} - 1 \right)}}{4} - \frac{\log{\left(x^{2} + 1 \right)}}{4}"," ",0,"log(x**2 - 1)/4 - log(x**2 + 1)/4","B",0
257,0,0,0,0.000000," ","integrate((x**3+1)*ln(x)/(x**4+2),x)","\int \frac{\left(x + 1\right) \left(x^{2} - x + 1\right) \log{\left(x \right)}}{x^{4} + 2}\, dx"," ",0,"Integral((x + 1)*(x**2 - x + 1)*log(x)/(x**4 + 2), x)","F",0
258,1,37,0,1.199958," ","integrate(ln(x)+ln(1+x)+ln(2+x),x)","x \log{\left(x \right)} - 3 x + \left(x + \frac{1}{2}\right) \log{\left(x + 1 \right)} + \left(x + 1\right) \log{\left(x + 2 \right)} + \frac{\log{\left(x + 1 \right)}}{2} + \log{\left(x + 2 \right)}"," ",0,"x*log(x) - 3*x + (x + 1/2)*log(x + 1) + (x + 1)*log(x + 2) + log(x + 1)/2 + log(x + 2)","A",0
259,1,73,0,0.302604," ","integrate(1/(x**3+5),x)","\frac{\sqrt[3]{5} \log{\left(x + \sqrt[3]{5} \right)}}{15} - \frac{\sqrt[3]{5} \log{\left(x^{2} - \sqrt[3]{5} x + 5^{\frac{2}{3}} \right)}}{30} + \frac{\sqrt{3} \sqrt[3]{5} \operatorname{atan}{\left(\frac{2 \sqrt{3} \cdot 5^{\frac{2}{3}} x}{15} - \frac{\sqrt{3}}{3} \right)}}{15}"," ",0,"5**(1/3)*log(x + 5**(1/3))/15 - 5**(1/3)*log(x**2 - 5**(1/3)*x + 5**(2/3))/30 + sqrt(3)*5**(1/3)*atan(2*sqrt(3)*5**(2/3)*x/15 - sqrt(3)/3)/15","A",0
260,1,2,0,0.140893," ","integrate(1/(x**2+1)**(1/2),x)","\operatorname{asinh}{\left(x \right)}"," ",0,"asinh(x)","A",0
261,1,24,0,0.209084," ","integrate((x**2+3)**(1/2),x)","\frac{x \sqrt{x^{2} + 3}}{2} + \frac{3 \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3} \right)}}{2}"," ",0,"x*sqrt(x**2 + 3)/2 + 3*asinh(sqrt(3)*x/3)/2","A",0
262,1,8,0,0.078136," ","integrate(x/(1+x)**2,x)","\log{\left(x + 1 \right)} + \frac{1}{x + 1}"," ",0,"log(x + 1) + 1/(x + 1)","A",0
263,1,12,0,0.130294," ","integrate(asin(x),x)","x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}"," ",0,"x*asin(x) + sqrt(1 - x**2)","A",0
264,1,32,0,0.350661," ","integrate(x**2*asin(x),x)","\frac{x^{3} \operatorname{asin}{\left(x \right)}}{3} + \frac{x^{2} \sqrt{1 - x^{2}}}{9} + \frac{2 \sqrt{1 - x^{2}}}{9}"," ",0,"x**3*asin(x)/3 + x**2*sqrt(1 - x**2)/9 + 2*sqrt(1 - x**2)/9","A",0
265,0,0,0,0.000000," ","integrate(sec(x)**2/(1+sec(x)**2-3*tan(x)),x)","\int \frac{\sec^{2}{\left(x \right)}}{- 3 \tan{\left(x \right)} + \sec^{2}{\left(x \right)} + 1}\, dx"," ",0,"Integral(sec(x)**2/(-3*tan(x) + sec(x)**2 + 1), x)","F",0
266,1,10,0,0.067255," ","integrate(1/sec(x)**2,x)","\frac{x}{2} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}"," ",0,"x/2 + sin(x)*cos(x)/2","A",0
267,1,14,0,0.119607," ","integrate((5*x**2-3*x-2)/(-2+x)/x**2,x)","2 \log{\left(x \right)} + 3 \log{\left(x - 2 \right)} - \frac{1}{x}"," ",0,"2*log(x) + 3*log(x - 2) - 1/x","A",0
268,1,7,0,0.151223," ","integrate(1/(4*x**2+9)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{2 x}{3} \right)}}{2}"," ",0,"asinh(2*x/3)/2","A",0
269,1,3,0,0.143079," ","integrate(1/(x**2+4)**(1/2),x)","\operatorname{asinh}{\left(\frac{x}{2} \right)}"," ",0,"asinh(x/2)","A",0
270,1,22,0,0.117301," ","integrate(1/(9*x**2-12*x+10),x)","\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{2} - \frac{\sqrt{6}}{3} \right)}}{18}"," ",0,"sqrt(6)*atan(sqrt(6)*x/2 - sqrt(6)/3)/18","A",0
271,1,46,0,0.176152," ","integrate(1/(x**8-2*x**7+2*x**6-2*x**5+x**4),x)","2 \log{\left(x \right)} - \frac{5 \log{\left(x - 1 \right)}}{2} + \frac{\log{\left(x^{2} + 1 \right)}}{4} + \frac{- 15 x^{3} + 6 x^{2} + 4 x + 2}{6 x^{4} - 6 x^{3}}"," ",0,"2*log(x) - 5*log(x - 1)/2 + log(x**2 + 1)/4 + (-15*x**3 + 6*x**2 + 4*x + 2)/(6*x**4 - 6*x**3)","A",0
272,1,762,0,86.228208," ","integrate((a*x**3+b*x**2+c*x+d)/(-3+x)/x/(1+x),x)","a x - \frac{d \log{\left(x \right)}}{3} - \frac{\left(a - b + c - d\right) \log{\left(x + \frac{- 1512 a^{2} d + 1134 a^{2} \left(a - b + c - d\right) - 864 a b d + 648 a b \left(a - b + c - d\right) - 432 a c d + 324 a c \left(a - b + c - d\right) - 144 a d^{2} + 81 a \left(a - b + c - d\right)^{2} - 216 b^{2} d + 162 b^{2} \left(a - b + c - d\right) - 288 b d^{2} + 108 b d \left(a - b + c - d\right) + 81 b \left(a - b + c - d\right)^{2} - 72 c^{2} d + 54 c^{2} \left(a - b + c - d\right) + 144 c d^{2} - 72 c d \left(a - b + c - d\right) - 27 c \left(a - b + c - d\right)^{2} - 136 d^{3} - 54 d^{2} \left(a - b + c - d\right) + 117 d \left(a - b + c - d\right)^{2}}{1215 a^{3} - 567 a^{2} b + 1593 a^{2} c - 2691 a^{2} d - 567 a b^{2} + 378 a b c - 1638 a b d + 405 a c^{2} - 702 a c d - 351 a d^{2} - 81 b^{3} - 27 b^{2} c - 207 b^{2} d + 81 b c^{2} - 270 b c d - 27 b d^{2} + 27 c^{3} - 27 c^{2} d - 99 c d^{2} + 35 d^{3}} \right)}}{4} + \frac{\left(27 a + 9 b + 3 c + d\right) \log{\left(x + \frac{- 1512 a^{2} d - 378 a^{2} \left(27 a + 9 b + 3 c + d\right) - 864 a b d - 216 a b \left(27 a + 9 b + 3 c + d\right) - 432 a c d - 108 a c \left(27 a + 9 b + 3 c + d\right) - 144 a d^{2} + 9 a \left(27 a + 9 b + 3 c + d\right)^{2} - 216 b^{2} d - 54 b^{2} \left(27 a + 9 b + 3 c + d\right) - 288 b d^{2} - 36 b d \left(27 a + 9 b + 3 c + d\right) + 9 b \left(27 a + 9 b + 3 c + d\right)^{2} - 72 c^{2} d - 18 c^{2} \left(27 a + 9 b + 3 c + d\right) + 144 c d^{2} + 24 c d \left(27 a + 9 b + 3 c + d\right) - 3 c \left(27 a + 9 b + 3 c + d\right)^{2} - 136 d^{3} + 18 d^{2} \left(27 a + 9 b + 3 c + d\right) + 13 d \left(27 a + 9 b + 3 c + d\right)^{2}}{1215 a^{3} - 567 a^{2} b + 1593 a^{2} c - 2691 a^{2} d - 567 a b^{2} + 378 a b c - 1638 a b d + 405 a c^{2} - 702 a c d - 351 a d^{2} - 81 b^{3} - 27 b^{2} c - 207 b^{2} d + 81 b c^{2} - 270 b c d - 27 b d^{2} + 27 c^{3} - 27 c^{2} d - 99 c d^{2} + 35 d^{3}} \right)}}{12}"," ",0,"a*x - d*log(x)/3 - (a - b + c - d)*log(x + (-1512*a**2*d + 1134*a**2*(a - b + c - d) - 864*a*b*d + 648*a*b*(a - b + c - d) - 432*a*c*d + 324*a*c*(a - b + c - d) - 144*a*d**2 + 81*a*(a - b + c - d)**2 - 216*b**2*d + 162*b**2*(a - b + c - d) - 288*b*d**2 + 108*b*d*(a - b + c - d) + 81*b*(a - b + c - d)**2 - 72*c**2*d + 54*c**2*(a - b + c - d) + 144*c*d**2 - 72*c*d*(a - b + c - d) - 27*c*(a - b + c - d)**2 - 136*d**3 - 54*d**2*(a - b + c - d) + 117*d*(a - b + c - d)**2)/(1215*a**3 - 567*a**2*b + 1593*a**2*c - 2691*a**2*d - 567*a*b**2 + 378*a*b*c - 1638*a*b*d + 405*a*c**2 - 702*a*c*d - 351*a*d**2 - 81*b**3 - 27*b**2*c - 207*b**2*d + 81*b*c**2 - 270*b*c*d - 27*b*d**2 + 27*c**3 - 27*c**2*d - 99*c*d**2 + 35*d**3))/4 + (27*a + 9*b + 3*c + d)*log(x + (-1512*a**2*d - 378*a**2*(27*a + 9*b + 3*c + d) - 864*a*b*d - 216*a*b*(27*a + 9*b + 3*c + d) - 432*a*c*d - 108*a*c*(27*a + 9*b + 3*c + d) - 144*a*d**2 + 9*a*(27*a + 9*b + 3*c + d)**2 - 216*b**2*d - 54*b**2*(27*a + 9*b + 3*c + d) - 288*b*d**2 - 36*b*d*(27*a + 9*b + 3*c + d) + 9*b*(27*a + 9*b + 3*c + d)**2 - 72*c**2*d - 18*c**2*(27*a + 9*b + 3*c + d) + 144*c*d**2 + 24*c*d*(27*a + 9*b + 3*c + d) - 3*c*(27*a + 9*b + 3*c + d)**2 - 136*d**3 + 18*d**2*(27*a + 9*b + 3*c + d) + 13*d*(27*a + 9*b + 3*c + d)**2)/(1215*a**3 - 567*a**2*b + 1593*a**2*c - 2691*a**2*d - 567*a*b**2 + 378*a*b*c - 1638*a*b*d + 405*a*c**2 - 702*a*c*d - 351*a*d**2 - 81*b**3 - 27*b**2*c - 207*b**2*d + 81*b*c**2 - 270*b*c*d - 27*b*d**2 + 27*c**3 - 27*c**2*d - 99*c*d**2 + 35*d**3))/12","B",0
273,0,0,0,0.000000," ","integrate(1/(2-ln(x**2+1))**5,x)","- \frac{\int \frac{120 x^{2}}{x^{8} \log{\left(x^{2} + 1 \right)} - 2 x^{8}}\, dx + \int \frac{30 x^{4}}{x^{8} \log{\left(x^{2} + 1 \right)} - 2 x^{8}}\, dx + \int \frac{x^{8}}{x^{8} \log{\left(x^{2} + 1 \right)} - 2 x^{8}}\, dx + \int \frac{105}{x^{8} \log{\left(x^{2} + 1 \right)} - 2 x^{8}}\, dx}{384} + \frac{\frac{2 x^{8}}{3} + \frac{7 x^{6}}{6} + \frac{5 x^{4}}{2} + \frac{9 x^{2}}{2} + \left(\frac{x^{8}}{48} - \frac{5 x^{4}}{24} - \frac{x^{2}}{2} - \frac{5}{16}\right) \log{\left(x^{2} + 1 \right)}^{3} + \left(- \frac{x^{8}}{12} + \frac{x^{6}}{24} + \frac{11 x^{4}}{8} + \frac{25 x^{2}}{8} + \frac{15}{8}\right) \log{\left(x^{2} + 1 \right)}^{2} + \left(\frac{x^{8}}{4} - \frac{x^{6}}{6} - \frac{19 x^{4}}{6} - \frac{13 x^{2}}{2} - \frac{15}{4}\right) \log{\left(x^{2} + 1 \right)} + \frac{5}{2}}{8 x^{7} \log{\left(x^{2} + 1 \right)}^{4} - 64 x^{7} \log{\left(x^{2} + 1 \right)}^{3} + 192 x^{7} \log{\left(x^{2} + 1 \right)}^{2} - 256 x^{7} \log{\left(x^{2} + 1 \right)} + 128 x^{7}}"," ",0,"-(Integral(120*x**2/(x**8*log(x**2 + 1) - 2*x**8), x) + Integral(30*x**4/(x**8*log(x**2 + 1) - 2*x**8), x) + Integral(x**8/(x**8*log(x**2 + 1) - 2*x**8), x) + Integral(105/(x**8*log(x**2 + 1) - 2*x**8), x))/384 + (2*x**8/3 + 7*x**6/6 + 5*x**4/2 + 9*x**2/2 + (x**8/48 - 5*x**4/24 - x**2/2 - 5/16)*log(x**2 + 1)**3 + (-x**8/12 + x**6/24 + 11*x**4/8 + 25*x**2/8 + 15/8)*log(x**2 + 1)**2 + (x**8/4 - x**6/6 - 19*x**4/6 - 13*x**2/2 - 15/4)*log(x**2 + 1) + 5/2)/(8*x**7*log(x**2 + 1)**4 - 64*x**7*log(x**2 + 1)**3 + 192*x**7*log(x**2 + 1)**2 - 256*x**7*log(x**2 + 1) + 128*x**7)","F",0
274,1,26,0,0.474526," ","integrate(exp(x**2)/x+2*exp(x**2)*x*ln(x)+(-2+ln(x))/(x+ln(x)**2)**2+(1+1/x+2*ln(x)/x)/(x+ln(x)**2),x)","e^{x^{2}} \log{\left(x \right)} + \log{\left(x + \log{\left(x \right)}^{2} \right)} - \frac{\log{\left(x \right)}}{x + \log{\left(x \right)}^{2}}"," ",0,"exp(x**2)*log(x) + log(x + log(x)**2) - log(x)/(x + log(x)**2)","A",0
275,-1,0,0,0.000000," ","integrate(x**4*exp(1/2*x+x*z)*sin(pi*z)**4,z)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,1,15,0,0.309587," ","integrate(erf(x),x)","x \operatorname{erf}{\left(x \right)} + \frac{e^{- x^{2}}}{\sqrt{\pi}}"," ",0,"x*erf(x) + exp(-x**2)/sqrt(pi)","A",0
277,1,36,0,0.514262," ","integrate(erf(a+x),x)","a \operatorname{erf}{\left(a + x \right)} + x \operatorname{erf}{\left(a + x \right)} + \frac{e^{- a^{2}} e^{- x^{2}} e^{- 2 a x}}{\sqrt{\pi}}"," ",0,"a*erf(a + x) + x*erf(a + x) + exp(-a**2)*exp(-x**2)*exp(-2*a*x)/sqrt(pi)","A",0
278,0,0,0,0.000000," ","integrate((2*x**6+4*x**5+7*x**4-3*x**3-x**2-8*x-8)/(2*x**2-1)**2/(x**4+4*x**3+2*x**2+1)**(1/2),x)","\int \frac{2 x^{6} + 4 x^{5} + 7 x^{4} - 3 x^{3} - x^{2} - 8 x - 8}{\sqrt{\left(x + 1\right) \left(x^{3} + 3 x^{2} - x + 1\right)} \left(2 x^{2} - 1\right)^{2}}\, dx"," ",0,"Integral((2*x**6 + 4*x**5 + 7*x**4 - 3*x**3 - x**2 - 8*x - 8)/(sqrt((x + 1)*(x**3 + 3*x**2 - x + 1))*(2*x**2 - 1)**2), x)","F",0
279,0,0,0,0.000000," ","integrate((1+2*y)*(-5*y**2-5*y+1)**(1/2)/y/(1+y)/(2+y)/(-y**2-y+1)**(1/2),y)","\int \frac{\left(2 y + 1\right) \sqrt{- 5 y^{2} - 5 y + 1}}{y \left(y + 1\right) \left(y + 2\right) \sqrt{- y^{2} - y + 1}}\, dy"," ",0,"Integral((2*y + 1)*sqrt(-5*y**2 - 5*y + 1)/(y*(y + 1)*(y + 2)*sqrt(-y**2 - y + 1)), y)","F",0
280,-1,0,0,0.000000," ","integrate(x*(-(x**2-4)**(1/2)+x**2*(x**2-4)**(1/2)-4*(x**2-1)**(1/2)+x**2*(x**2-1)**(1/2))/(x**4-5*x**2+4)/(1+(x**2-4)**(1/2)+(x**2-1)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,0,0,0,0.000000," ","integrate(-2**(1/2)*(x**4+2*x**2+4*x+1)**(1/2)+x*(-1+2*2**(1/2)),x)","\int \left(x \left(-1 + 2 \sqrt{2}\right) - \sqrt{2} \sqrt{x^{4} + 2 x^{2} + 4 x + 1}\right)\, dx"," ",0,"Integral(x*(-1 + 2*sqrt(2)) - sqrt(2)*sqrt(x**4 + 2*x**2 + 4*x + 1), x)","F",0
282,1,330,0,21.735993," ","integrate(1/384*(pi**2*(4*mc**9-3*mc**8-48*mc**7*x+24*mc**6*x-144*mc**5*x**2+176*mc**3*x**3-24*mc**2*x**3+12*mc*x**4+3*x**4)+12*mc**3*pi**2*(-12*mc**2+3*mc-8*x)*x**2*ln(x/mc**2))/exp(x/y)/x**2,x)","- \frac{\pi^{2} mc^{9} \operatorname{E}_{2}\left(\frac{x}{y}\right)}{96 x} + \frac{\pi^{2} mc^{8} \operatorname{E}_{2}\left(\frac{x}{y}\right)}{128 x} - \frac{\pi^{2} mc^{7} \operatorname{Ei}{\left(- \frac{x}{y} \right)}}{8} + \frac{\pi^{2} mc^{6} \operatorname{Ei}{\left(- \frac{x}{y} \right)}}{16} + \frac{3 \pi^{2} mc^{5} y e^{- \frac{x}{y}}}{8} - \frac{3 \pi^{2} mc^{5} \left(y \operatorname{Ei}{\left(- \frac{x}{y} \right)} - y e^{- \frac{x}{y}} \log{\left(\frac{x}{mc^{2}} \right)}\right)}{8} + \frac{3 \pi^{2} mc^{4} \left(y \operatorname{Ei}{\left(- \frac{x}{y} \right)} - y e^{- \frac{x}{y}} \log{\left(\frac{x}{mc^{2}} \right)}\right)}{32} + \frac{11 \pi^{2} mc^{3} \left(- x y e^{- \frac{x}{y}} - y^{2} e^{- \frac{x}{y}}\right)}{24} - \frac{\pi^{2} mc^{3} \left(y^{2} \operatorname{Ei}{\left(- \frac{x}{y} \right)} - y^{2} e^{- \frac{x}{y}} + \left(- x y e^{- \frac{x}{y}} - y^{2} e^{- \frac{x}{y}}\right) \log{\left(\frac{x}{mc^{2}} \right)}\right)}{4} - \frac{\pi^{2} mc^{2} \left(- x y e^{- \frac{x}{y}} - y^{2} e^{- \frac{x}{y}}\right)}{16} + \frac{\pi^{2} mc \left(- x^{2} y e^{- \frac{x}{y}} - 2 x y^{2} e^{- \frac{x}{y}} - 2 y^{3} e^{- \frac{x}{y}}\right)}{32} + \frac{\pi^{2} \left(- x^{2} y e^{- \frac{x}{y}} - 2 x y^{2} e^{- \frac{x}{y}} - 2 y^{3} e^{- \frac{x}{y}}\right)}{128}"," ",0,"-pi**2*mc**9*expint(2, x/y)/(96*x) + pi**2*mc**8*expint(2, x/y)/(128*x) - pi**2*mc**7*Ei(-x/y)/8 + pi**2*mc**6*Ei(-x/y)/16 + 3*pi**2*mc**5*y*exp(-x/y)/8 - 3*pi**2*mc**5*(y*Ei(-x/y) - y*exp(-x/y)*log(x/mc**2))/8 + 3*pi**2*mc**4*(y*Ei(-x/y) - y*exp(-x/y)*log(x/mc**2))/32 + 11*pi**2*mc**3*(-x*y*exp(-x/y) - y**2*exp(-x/y))/24 - pi**2*mc**3*(y**2*Ei(-x/y) - y**2*exp(-x/y) + (-x*y*exp(-x/y) - y**2*exp(-x/y))*log(x/mc**2))/4 - pi**2*mc**2*(-x*y*exp(-x/y) - y**2*exp(-x/y))/16 + pi**2*mc*(-x**2*y*exp(-x/y) - 2*x*y**2*exp(-x/y) - 2*y**3*exp(-x/y))/32 + pi**2*(-x**2*y*exp(-x/y) - 2*x*y**2*exp(-x/y) - 2*y**3*exp(-x/y))/128","A",0
283,1,5,0,0.757827," ","integrate(sin(2*x)/cos(x),x)","- 2 \cos{\left(x \right)}"," ",0,"-2*cos(x)","A",0
284,1,76,0,0.221283," ","integrate((7*x**13+10*x**8+4*x**7-7*x**6-4*x**3-4*x**2+3*x+3)/(x**14-2*x**8-2*x**7-2*x**4-4*x**3-x**2+2*x+1),x)","\left(\frac{1}{2} + \frac{\sqrt{2}}{2}\right) \log{\left(x^{7} - \sqrt{2} x^{2} - 2 x \left(\frac{1}{2} + \frac{\sqrt{2}}{2}\right) - 1 \right)} + \left(\frac{1}{2} - \frac{\sqrt{2}}{2}\right) \log{\left(x^{7} + \sqrt{2} x^{2} - 2 x \left(\frac{1}{2} - \frac{\sqrt{2}}{2}\right) - 1 \right)}"," ",0,"(1/2 + sqrt(2)/2)*log(x**7 - sqrt(2)*x**2 - 2*x*(1/2 + sqrt(2)/2) - 1) + (1/2 - sqrt(2)/2)*log(x**7 + sqrt(2)*x**2 - 2*x*(1/2 - sqrt(2)/2) - 1)","A",0
