1,1,136,0,104.662525," ","integrate(x**4*ln(c*(b*x**2+a)**p),x)","\begin{cases} \frac{i a^{\frac{5}{2}} p \log{\left(a + b x^{2} \right)}}{5 b^{3} \sqrt{\frac{1}{b}}} - \frac{2 i a^{\frac{5}{2}} p \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{5 b^{3} \sqrt{\frac{1}{b}}} - \frac{2 a^{2} p x}{5 b^{2}} + \frac{2 a p x^{3}}{15 b} + \frac{p x^{5} \log{\left(a + b x^{2} \right)}}{5} - \frac{2 p x^{5}}{25} + \frac{x^{5} \log{\left(c \right)}}{5} & \text{for}\: b \neq 0 \\\frac{x^{5} \log{\left(a^{p} c \right)}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*a**(5/2)*p*log(a + b*x**2)/(5*b**3*sqrt(1/b)) - 2*I*a**(5/2)*p*log(-I*sqrt(a)*sqrt(1/b) + x)/(5*b**3*sqrt(1/b)) - 2*a**2*p*x/(5*b**2) + 2*a*p*x**3/(15*b) + p*x**5*log(a + b*x**2)/5 - 2*p*x**5/25 + x**5*log(c)/5, Ne(b, 0)), (x**5*log(a**p*c)/5, True))","A",0
2,1,70,0,6.461441," ","integrate(x**3*ln(c*(b*x**2+a)**p),x)","\begin{cases} - \frac{a^{2} p \log{\left(a + b x^{2} \right)}}{4 b^{2}} + \frac{a p x^{2}}{4 b} + \frac{p x^{4} \log{\left(a + b x^{2} \right)}}{4} - \frac{p x^{4}}{8} + \frac{x^{4} \log{\left(c \right)}}{4} & \text{for}\: b \neq 0 \\\frac{x^{4} \log{\left(a^{p} c \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*p*log(a + b*x**2)/(4*b**2) + a*p*x**2/(4*b) + p*x**4*log(a + b*x**2)/4 - p*x**4/8 + x**4*log(c)/4, Ne(b, 0)), (x**4*log(a**p*c)/4, True))","A",0
3,1,121,0,28.762137," ","integrate(x**2*ln(c*(b*x**2+a)**p),x)","\begin{cases} - \frac{i a^{\frac{3}{2}} p \log{\left(a + b x^{2} \right)}}{3 b^{2} \sqrt{\frac{1}{b}}} + \frac{2 i a^{\frac{3}{2}} p \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{3 b^{2} \sqrt{\frac{1}{b}}} + \frac{2 a p x}{3 b} + \frac{p x^{3} \log{\left(a + b x^{2} \right)}}{3} - \frac{2 p x^{3}}{9} + \frac{x^{3} \log{\left(c \right)}}{3} & \text{for}\: b \neq 0 \\\frac{x^{3} \log{\left(a^{p} c \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**(3/2)*p*log(a + b*x**2)/(3*b**2*sqrt(1/b)) + 2*I*a**(3/2)*p*log(-I*sqrt(a)*sqrt(1/b) + x)/(3*b**2*sqrt(1/b)) + 2*a*p*x/(3*b) + p*x**3*log(a + b*x**2)/3 - 2*p*x**3/9 + x**3*log(c)/3, Ne(b, 0)), (x**3*log(a**p*c)/3, True))","A",0
4,1,56,0,2.098153," ","integrate(x*ln(c*(b*x**2+a)**p),x)","\begin{cases} \frac{a p \log{\left(a + b x^{2} \right)}}{2 b} + \frac{p x^{2} \log{\left(a + b x^{2} \right)}}{2} - \frac{p x^{2}}{2} + \frac{x^{2} \log{\left(c \right)}}{2} & \text{for}\: b \neq 0 \\\frac{x^{2} \log{\left(a^{p} c \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*p*log(a + b*x**2)/(2*b) + p*x**2*log(a + b*x**2)/2 - p*x**2/2 + x**2*log(c)/2, Ne(b, 0)), (x**2*log(a**p*c)/2, True))","A",0
5,1,90,0,7.657451," ","integrate(ln(c*(b*x**2+a)**p),x)","\begin{cases} \frac{i \sqrt{a} p \log{\left(a + b x^{2} \right)}}{b \sqrt{\frac{1}{b}}} - \frac{2 i \sqrt{a} p \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{b \sqrt{\frac{1}{b}}} + p x \log{\left(a + b x^{2} \right)} - 2 p x + x \log{\left(c \right)} & \text{for}\: b \neq 0 \\x \log{\left(a^{p} c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*sqrt(a)*p*log(a + b*x**2)/(b*sqrt(1/b)) - 2*I*sqrt(a)*p*log(-I*sqrt(a)*sqrt(1/b) + x)/(b*sqrt(1/b)) + p*x*log(a + b*x**2) - 2*p*x + x*log(c), Ne(b, 0)), (x*log(a**p*c), True))","A",0
6,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)/x,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)/x, x)","F",0
7,1,377,0,25.687372," ","integrate(ln(c*(b*x**2+a)**p)/x**2,x)","\begin{cases} - \frac{\log{\left(0^{p} c \right)}}{x} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{p \log{\left(b \right)}}{x} - \frac{2 p \log{\left(x \right)}}{x} - \frac{2 p}{x} - \frac{\log{\left(c \right)}}{x} & \text{for}\: a = 0 \\- \frac{\log{\left(a^{p} c \right)}}{x} & \text{for}\: b = 0 \\\frac{i a^{\frac{3}{2}} p x \sqrt{\frac{1}{b}} \log{\left(a + b x^{2} \right)}}{\frac{a^{2} x}{b} + a x^{3}} - \frac{2 i a^{\frac{3}{2}} p x \sqrt{\frac{1}{b}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{\frac{a^{2} x}{b} + a x^{3}} + \frac{i a^{\frac{3}{2}} x \sqrt{\frac{1}{b}} \log{\left(c \right)}}{\frac{a^{2} x}{b} + a x^{3}} + \frac{i \sqrt{a} b p x^{3} \sqrt{\frac{1}{b}} \log{\left(a + b x^{2} \right)}}{\frac{a^{2} x}{b} + a x^{3}} - \frac{2 i \sqrt{a} b p x^{3} \sqrt{\frac{1}{b}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{\frac{a^{2} x}{b} + a x^{3}} + \frac{i \sqrt{a} b x^{3} \sqrt{\frac{1}{b}} \log{\left(c \right)}}{\frac{a^{2} x}{b} + a x^{3}} - \frac{a^{2} p \log{\left(a + b x^{2} \right)}}{a^{2} x + a b x^{3}} - \frac{a^{2} \log{\left(c \right)}}{a^{2} x + a b x^{3}} - \frac{a p x^{2} \log{\left(a + b x^{2} \right)}}{\frac{a^{2} x}{b} + a x^{3}} - \frac{a x^{2} \log{\left(c \right)}}{\frac{a^{2} x}{b} + a x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(0**p*c)/x, Eq(a, 0) & Eq(b, 0)), (-p*log(b)/x - 2*p*log(x)/x - 2*p/x - log(c)/x, Eq(a, 0)), (-log(a**p*c)/x, Eq(b, 0)), (I*a**(3/2)*p*x*sqrt(1/b)*log(a + b*x**2)/(a**2*x/b + a*x**3) - 2*I*a**(3/2)*p*x*sqrt(1/b)*log(-I*sqrt(a)*sqrt(1/b) + x)/(a**2*x/b + a*x**3) + I*a**(3/2)*x*sqrt(1/b)*log(c)/(a**2*x/b + a*x**3) + I*sqrt(a)*b*p*x**3*sqrt(1/b)*log(a + b*x**2)/(a**2*x/b + a*x**3) - 2*I*sqrt(a)*b*p*x**3*sqrt(1/b)*log(-I*sqrt(a)*sqrt(1/b) + x)/(a**2*x/b + a*x**3) + I*sqrt(a)*b*x**3*sqrt(1/b)*log(c)/(a**2*x/b + a*x**3) - a**2*p*log(a + b*x**2)/(a**2*x + a*b*x**3) - a**2*log(c)/(a**2*x + a*b*x**3) - a*p*x**2*log(a + b*x**2)/(a**2*x/b + a*x**3) - a*x**2*log(c)/(a**2*x/b + a*x**3), True))","A",0
8,1,82,0,4.662044," ","integrate(ln(c*(b*x**2+a)**p)/x**3,x)","\begin{cases} - \frac{p \log{\left(a + b x^{2} \right)}}{2 x^{2}} - \frac{\log{\left(c \right)}}{2 x^{2}} + \frac{b p \log{\left(x \right)}}{a} - \frac{b p \log{\left(a + b x^{2} \right)}}{2 a} & \text{for}\: a \neq 0 \\- \frac{p \log{\left(b \right)}}{2 x^{2}} - \frac{p \log{\left(x \right)}}{x^{2}} - \frac{p}{2 x^{2}} - \frac{\log{\left(c \right)}}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-p*log(a + b*x**2)/(2*x**2) - log(c)/(2*x**2) + b*p*log(x)/a - b*p*log(a + b*x**2)/(2*a), Ne(a, 0)), (-p*log(b)/(2*x**2) - p*log(x)/x**2 - p/(2*x**2) - log(c)/(2*x**2), True))","A",0
9,1,763,0,111.550824," ","integrate(ln(c*(b*x**2+a)**p)/x**4,x)","\begin{cases} - \frac{\log{\left(0^{p} c \right)}}{3 x^{3}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{\log{\left(a^{p} c \right)}}{3 x^{3}} & \text{for}\: b = 0 \\- \frac{p \log{\left(b \right)}}{3 x^{3}} - \frac{2 p \log{\left(x \right)}}{3 x^{3}} - \frac{2 p}{9 x^{3}} - \frac{\log{\left(c \right)}}{3 x^{3}} & \text{for}\: a = 0 \\- \frac{i a^{\frac{5}{2}} p \sqrt{\frac{1}{b}} \log{\left(a + b x^{2} \right)}}{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}} + 3 i a^{\frac{3}{2}} b x^{5} \sqrt{\frac{1}{b}}} - \frac{i a^{\frac{5}{2}} \sqrt{\frac{1}{b}} \log{\left(c \right)}}{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}} + 3 i a^{\frac{3}{2}} b x^{5} \sqrt{\frac{1}{b}}} - \frac{i a^{\frac{3}{2}} p x^{2} \sqrt{\frac{1}{b}} \log{\left(a + b x^{2} \right)}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} - \frac{2 i a^{\frac{3}{2}} p x^{2} \sqrt{\frac{1}{b}}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} - \frac{i a^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{b}} \log{\left(c \right)}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} - \frac{2 i \sqrt{a} b p x^{4} \sqrt{\frac{1}{b}}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} + \frac{a p x^{3} \log{\left(a + b x^{2} \right)}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} - \frac{2 a p x^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} + \frac{a x^{3} \log{\left(c \right)}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} + \frac{b p x^{5} \log{\left(a + b x^{2} \right)}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} - \frac{2 b p x^{5} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} + \frac{b x^{5} \log{\left(c \right)}}{\frac{3 i a^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{b}}}{b} + 3 i a^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(0**p*c)/(3*x**3), Eq(a, 0) & Eq(b, 0)), (-log(a**p*c)/(3*x**3), Eq(b, 0)), (-p*log(b)/(3*x**3) - 2*p*log(x)/(3*x**3) - 2*p/(9*x**3) - log(c)/(3*x**3), Eq(a, 0)), (-I*a**(5/2)*p*sqrt(1/b)*log(a + b*x**2)/(3*I*a**(5/2)*x**3*sqrt(1/b) + 3*I*a**(3/2)*b*x**5*sqrt(1/b)) - I*a**(5/2)*sqrt(1/b)*log(c)/(3*I*a**(5/2)*x**3*sqrt(1/b) + 3*I*a**(3/2)*b*x**5*sqrt(1/b)) - I*a**(3/2)*p*x**2*sqrt(1/b)*log(a + b*x**2)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)) - 2*I*a**(3/2)*p*x**2*sqrt(1/b)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)) - I*a**(3/2)*x**2*sqrt(1/b)*log(c)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)) - 2*I*sqrt(a)*b*p*x**4*sqrt(1/b)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)) + a*p*x**3*log(a + b*x**2)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)) - 2*a*p*x**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)) + a*x**3*log(c)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)) + b*p*x**5*log(a + b*x**2)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)) - 2*b*p*x**5*log(-I*sqrt(a)*sqrt(1/b) + x)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)) + b*x**5*log(c)/(3*I*a**(5/2)*x**3*sqrt(1/b)/b + 3*I*a**(3/2)*x**5*sqrt(1/b)), True))","A",0
10,1,102,0,14.045500," ","integrate(ln(c*(b*x**2+a)**p)/x**5,x)","\begin{cases} - \frac{p \log{\left(a + b x^{2} \right)}}{4 x^{4}} - \frac{\log{\left(c \right)}}{4 x^{4}} - \frac{b p}{4 a x^{2}} - \frac{b^{2} p \log{\left(x \right)}}{2 a^{2}} + \frac{b^{2} p \log{\left(a + b x^{2} \right)}}{4 a^{2}} & \text{for}\: a \neq 0 \\- \frac{p \log{\left(b \right)}}{4 x^{4}} - \frac{p \log{\left(x \right)}}{2 x^{4}} - \frac{p}{8 x^{4}} - \frac{\log{\left(c \right)}}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-p*log(a + b*x**2)/(4*x**4) - log(c)/(4*x**4) - b*p/(4*a*x**2) - b**2*p*log(x)/(2*a**2) + b**2*p*log(a + b*x**2)/(4*a**2), Ne(a, 0)), (-p*log(b)/(4*x**4) - p*log(x)/(2*x**4) - p/(8*x**4) - log(c)/(4*x**4), True))","A",0
11,-1,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
12,1,116,0,32.461069," ","integrate(ln(c*(b*x**2+a)**p)/x**7,x)","\begin{cases} - \frac{p \log{\left(a + b x^{2} \right)}}{6 x^{6}} - \frac{\log{\left(c \right)}}{6 x^{6}} - \frac{b p}{12 a x^{4}} + \frac{b^{2} p}{6 a^{2} x^{2}} + \frac{b^{3} p \log{\left(x \right)}}{3 a^{3}} - \frac{b^{3} p \log{\left(a + b x^{2} \right)}}{6 a^{3}} & \text{for}\: a \neq 0 \\- \frac{p \log{\left(b \right)}}{6 x^{6}} - \frac{p \log{\left(x \right)}}{3 x^{6}} - \frac{p}{18 x^{6}} - \frac{\log{\left(c \right)}}{6 x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-p*log(a + b*x**2)/(6*x**6) - log(c)/(6*x**6) - b*p/(12*a*x**4) + b**2*p/(6*a**2*x**2) + b**3*p*log(x)/(3*a**3) - b**3*p*log(a + b*x**2)/(6*a**3), Ne(a, 0)), (-p*log(b)/(6*x**6) - p*log(x)/(3*x**6) - p/(18*x**6) - log(c)/(6*x**6), True))","A",0
13,1,70,0,19.678987," ","integrate(x**5*ln(c*(b*x**3+a)**p),x)","\begin{cases} - \frac{a^{2} p \log{\left(a + b x^{3} \right)}}{6 b^{2}} + \frac{a p x^{3}}{6 b} + \frac{p x^{6} \log{\left(a + b x^{3} \right)}}{6} - \frac{p x^{6}}{12} + \frac{x^{6} \log{\left(c \right)}}{6} & \text{for}\: b \neq 0 \\\frac{x^{6} \log{\left(a^{p} c \right)}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*p*log(a + b*x**3)/(6*b**2) + a*p*x**3/(6*b) + p*x**6*log(a + b*x**3)/6 - p*x**6/12 + x**6*log(c)/6, Ne(b, 0)), (x**6*log(a**p*c)/6, True))","A",0
14,-1,0,0,0.000000," ","integrate(x**4*ln(c*(b*x**3+a)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate(x**3*ln(c*(b*x**3+a)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,1,56,0,4.701411," ","integrate(x**2*ln(c*(b*x**3+a)**p),x)","\begin{cases} \frac{a p \log{\left(a + b x^{3} \right)}}{3 b} + \frac{p x^{3} \log{\left(a + b x^{3} \right)}}{3} - \frac{p x^{3}}{3} + \frac{x^{3} \log{\left(c \right)}}{3} & \text{for}\: b \neq 0 \\\frac{x^{3} \log{\left(a^{p} c \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*p*log(a + b*x**3)/(3*b) + p*x**3*log(a + b*x**3)/3 - p*x**3/3 + x**3*log(c)/3, Ne(b, 0)), (x**3*log(a**p*c)/3, True))","A",0
17,1,260,0,142.411033," ","integrate(x*ln(c*(b*x**3+a)**p),x)","\begin{cases} \frac{x^{2} \log{\left(0^{p} c \right)}}{2} & \text{for}\: a = 0 \wedge b = 0 \\\frac{x^{2} \log{\left(a^{p} c \right)}}{2} & \text{for}\: b = 0 \\\frac{p x^{2} \log{\left(b \right)}}{2} + \frac{3 p x^{2} \log{\left(x \right)}}{2} - \frac{3 p x^{2}}{4} + \frac{x^{2} \log{\left(c \right)}}{2} & \text{for}\: a = 0 \\- \frac{\left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} p \left(\frac{1}{b}\right)^{\frac{2}{3}} \log{\left(a + b x^{3} \right)}}{2} + \frac{3 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} p \left(\frac{1}{b}\right)^{\frac{2}{3}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{4} - \frac{\left(-1\right)^{\frac{2}{3}} \sqrt{3} a^{\frac{2}{3}} p \left(\frac{1}{b}\right)^{\frac{2}{3}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} x}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{2} + \frac{p x^{2} \log{\left(a + b x^{3} \right)}}{2} - \frac{3 p x^{2}}{4} + \frac{x^{2} \log{\left(c \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2*log(0**p*c)/2, Eq(a, 0) & Eq(b, 0)), (x**2*log(a**p*c)/2, Eq(b, 0)), (p*x**2*log(b)/2 + 3*p*x**2*log(x)/2 - 3*p*x**2/4 + x**2*log(c)/2, Eq(a, 0)), (-(-1)**(2/3)*a**(2/3)*p*(1/b)**(2/3)*log(a + b*x**3)/2 + 3*(-1)**(2/3)*a**(2/3)*p*(1/b)**(2/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/4 - (-1)**(2/3)*sqrt(3)*a**(2/3)*p*(1/b)**(2/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x/(3*a**(1/3)*(1/b)**(1/3)))/2 + p*x**2*log(a + b*x**3)/2 - 3*p*x**2/4 + x**2*log(c)/2, True))","A",0
18,1,231,0,63.406924," ","integrate(ln(c*(b*x**3+a)**p),x)","\begin{cases} x \log{\left(0^{p} c \right)} & \text{for}\: a = 0 \wedge b = 0 \\x \log{\left(a^{p} c \right)} & \text{for}\: b = 0 \\p x \log{\left(b \right)} + 3 p x \log{\left(x \right)} - 3 p x + x \log{\left(c \right)} & \text{for}\: a = 0 \\- \sqrt[3]{-1} \sqrt[3]{a} b p \left(\frac{1}{b}\right)^{\frac{4}{3}} \log{\left(a + b x^{3} \right)} + \frac{3 \sqrt[3]{-1} \sqrt[3]{a} b p \left(\frac{1}{b}\right)^{\frac{4}{3}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{2} + \sqrt[3]{-1} \sqrt{3} \sqrt[3]{a} b p \left(\frac{1}{b}\right)^{\frac{4}{3}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} x}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)} + p x \log{\left(a + b x^{3} \right)} - 3 p x + x \log{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*log(0**p*c), Eq(a, 0) & Eq(b, 0)), (x*log(a**p*c), Eq(b, 0)), (p*x*log(b) + 3*p*x*log(x) - 3*p*x + x*log(c), Eq(a, 0)), (-(-1)**(1/3)*a**(1/3)*b*p*(1/b)**(4/3)*log(a + b*x**3) + 3*(-1)**(1/3)*a**(1/3)*b*p*(1/b)**(4/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/2 + (-1)**(1/3)*sqrt(3)*a**(1/3)*b*p*(1/b)**(4/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x/(3*a**(1/3)*(1/b)**(1/3))) + p*x*log(a + b*x**3) - 3*p*x + x*log(c), True))","A",0
19,0,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/x,x)","\int \frac{\log{\left(c \left(a + b x^{3}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(log(c*(a + b*x**3)**p)/x, x)","F",0
20,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,1,82,0,10.814523," ","integrate(ln(c*(b*x**3+a)**p)/x**4,x)","\begin{cases} - \frac{p \log{\left(a + b x^{3} \right)}}{3 x^{3}} - \frac{\log{\left(c \right)}}{3 x^{3}} + \frac{b p \log{\left(x \right)}}{a} - \frac{b p \log{\left(a + b x^{3} \right)}}{3 a} & \text{for}\: a \neq 0 \\- \frac{p \log{\left(b \right)}}{3 x^{3}} - \frac{p \log{\left(x \right)}}{x^{3}} - \frac{p}{3 x^{3}} - \frac{\log{\left(c \right)}}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-p*log(a + b*x**3)/(3*x**3) - log(c)/(3*x**3) + b*p*log(x)/a - b*p*log(a + b*x**3)/(3*a), Ne(a, 0)), (-p*log(b)/(3*x**3) - p*log(x)/x**3 - p/(3*x**3) - log(c)/(3*x**3), True))","A",0
23,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,1,102,0,45.917047," ","integrate(ln(c*(b*x**3+a)**p)/x**7,x)","\begin{cases} - \frac{p \log{\left(a + b x^{3} \right)}}{6 x^{6}} - \frac{\log{\left(c \right)}}{6 x^{6}} - \frac{b p}{6 a x^{3}} - \frac{b^{2} p \log{\left(x \right)}}{2 a^{2}} + \frac{b^{2} p \log{\left(a + b x^{3} \right)}}{6 a^{2}} & \text{for}\: a \neq 0 \\- \frac{p \log{\left(b \right)}}{6 x^{6}} - \frac{p \log{\left(x \right)}}{2 x^{6}} - \frac{p}{12 x^{6}} - \frac{\log{\left(c \right)}}{6 x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-p*log(a + b*x**3)/(6*x**6) - log(c)/(6*x**6) - b*p/(6*a*x**3) - b**2*p*log(x)/(2*a**2) + b**2*p*log(a + b*x**3)/(6*a**2), Ne(a, 0)), (-p*log(b)/(6*x**6) - p*log(x)/(2*x**6) - p/(12*x**6) - log(c)/(6*x**6), True))","A",0
26,1,122,0,12.376065," ","integrate(x**4*ln(c*(a+b/x)**p),x)","\begin{cases} \frac{p x^{5} \log{\left(a + \frac{b}{x} \right)}}{5} + \frac{x^{5} \log{\left(c \right)}}{5} + \frac{b p x^{4}}{20 a} - \frac{b^{2} p x^{3}}{15 a^{2}} + \frac{b^{3} p x^{2}}{10 a^{3}} - \frac{b^{4} p x}{5 a^{4}} + \frac{b^{5} p \log{\left(a x + b \right)}}{5 a^{5}} & \text{for}\: a \neq 0 \\\frac{p x^{5} \log{\left(b \right)}}{5} - \frac{p x^{5} \log{\left(x \right)}}{5} + \frac{p x^{5}}{25} + \frac{x^{5} \log{\left(c \right)}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x**5*log(a + b/x)/5 + x**5*log(c)/5 + b*p*x**4/(20*a) - b**2*p*x**3/(15*a**2) + b**3*p*x**2/(10*a**3) - b**4*p*x/(5*a**4) + b**5*p*log(a*x + b)/(5*a**5), Ne(a, 0)), (p*x**5*log(b)/5 - p*x**5*log(x)/5 + p*x**5/25 + x**5*log(c)/5, True))","A",0
27,1,109,0,7.247788," ","integrate(x**3*ln(c*(a+b/x)**p),x)","\begin{cases} \frac{p x^{4} \log{\left(a + \frac{b}{x} \right)}}{4} + \frac{x^{4} \log{\left(c \right)}}{4} + \frac{b p x^{3}}{12 a} - \frac{b^{2} p x^{2}}{8 a^{2}} + \frac{b^{3} p x}{4 a^{3}} - \frac{b^{4} p \log{\left(a x + b \right)}}{4 a^{4}} & \text{for}\: a \neq 0 \\\frac{p x^{4} \log{\left(b \right)}}{4} - \frac{p x^{4} \log{\left(x \right)}}{4} + \frac{p x^{4}}{16} + \frac{x^{4} \log{\left(c \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x**4*log(a + b/x)/4 + x**4*log(c)/4 + b*p*x**3/(12*a) - b**2*p*x**2/(8*a**2) + b**3*p*x/(4*a**3) - b**4*p*log(a*x + b)/(4*a**4), Ne(a, 0)), (p*x**4*log(b)/4 - p*x**4*log(x)/4 + p*x**4/16 + x**4*log(c)/4, True))","A",0
28,1,95,0,4.120530," ","integrate(x**2*ln(c*(a+b/x)**p),x)","\begin{cases} \frac{p x^{3} \log{\left(a + \frac{b}{x} \right)}}{3} + \frac{x^{3} \log{\left(c \right)}}{3} + \frac{b p x^{2}}{6 a} - \frac{b^{2} p x}{3 a^{2}} + \frac{b^{3} p \log{\left(a x + b \right)}}{3 a^{3}} & \text{for}\: a \neq 0 \\\frac{p x^{3} \log{\left(b \right)}}{3} - \frac{p x^{3} \log{\left(x \right)}}{3} + \frac{p x^{3}}{9} + \frac{x^{3} \log{\left(c \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x**3*log(a + b/x)/3 + x**3*log(c)/3 + b*p*x**2/(6*a) - b**2*p*x/(3*a**2) + b**3*p*log(a*x + b)/(3*a**3), Ne(a, 0)), (p*x**3*log(b)/3 - p*x**3*log(x)/3 + p*x**3/9 + x**3*log(c)/3, True))","A",0
29,1,82,0,2.186513," ","integrate(x*ln(c*(a+b/x)**p),x)","\begin{cases} \frac{p x^{2} \log{\left(a + \frac{b}{x} \right)}}{2} + \frac{x^{2} \log{\left(c \right)}}{2} + \frac{b p x}{2 a} - \frac{b^{2} p \log{\left(a x + b \right)}}{2 a^{2}} & \text{for}\: a \neq 0 \\\frac{p x^{2} \log{\left(b \right)}}{2} - \frac{p x^{2} \log{\left(x \right)}}{2} + \frac{p x^{2}}{4} + \frac{x^{2} \log{\left(c \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x**2*log(a + b/x)/2 + x**2*log(c)/2 + b*p*x/(2*a) - b**2*p*log(a*x + b)/(2*a**2), Ne(a, 0)), (p*x**2*log(b)/2 - p*x**2*log(x)/2 + p*x**2/4 + x**2*log(c)/2, True))","A",0
30,1,48,0,1.117758," ","integrate(ln(c*(a+b/x)**p),x)","\begin{cases} p x \log{\left(a + \frac{b}{x} \right)} + x \log{\left(c \right)} + \frac{b p \log{\left(a x + b \right)}}{a} & \text{for}\: a \neq 0 \\p x \log{\left(b \right)} - p x \log{\left(x \right)} + p x + x \log{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x*log(a + b/x) + x*log(c) + b*p*log(a*x + b)/a, Ne(a, 0)), (p*x*log(b) - p*x*log(x) + p*x + x*log(c), True))","A",0
31,0,0,0,0.000000," ","integrate(ln(c*(a+b/x)**p)/x,x)","\int \frac{\log{\left(c \left(a + \frac{b}{x}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(log(c*(a + b/x)**p)/x, x)","F",0
32,1,39,0,2.215389," ","integrate(ln(c*(a+b/x)**p)/x**2,x)","\begin{cases} - \frac{a p \log{\left(a + \frac{b}{x} \right)}}{b} - \frac{p \log{\left(a + \frac{b}{x} \right)}}{x} + \frac{p}{x} - \frac{\log{\left(c \right)}}{x} & \text{for}\: b \neq 0 \\- \frac{\log{\left(a^{p} c \right)}}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*p*log(a + b/x)/b - p*log(a + b/x)/x + p/x - log(c)/x, Ne(b, 0)), (-log(a**p*c)/x, True))","A",0
33,1,66,0,3.929060," ","integrate(ln(c*(a+b/x)**p)/x**3,x)","\begin{cases} \frac{a^{2} p \log{\left(a + \frac{b}{x} \right)}}{2 b^{2}} - \frac{a p}{2 b x} - \frac{p \log{\left(a + \frac{b}{x} \right)}}{2 x^{2}} + \frac{p}{4 x^{2}} - \frac{\log{\left(c \right)}}{2 x^{2}} & \text{for}\: b \neq 0 \\- \frac{\log{\left(a^{p} c \right)}}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*p*log(a + b/x)/(2*b**2) - a*p/(2*b*x) - p*log(a + b/x)/(2*x**2) + p/(4*x**2) - log(c)/(2*x**2), Ne(b, 0)), (-log(a**p*c)/(2*x**2), True))","A",0
34,1,80,0,6.434146," ","integrate(ln(c*(a+b/x)**p)/x**4,x)","\begin{cases} - \frac{a^{3} p \log{\left(a + \frac{b}{x} \right)}}{3 b^{3}} + \frac{a^{2} p}{3 b^{2} x} - \frac{a p}{6 b x^{2}} - \frac{p \log{\left(a + \frac{b}{x} \right)}}{3 x^{3}} + \frac{p}{9 x^{3}} - \frac{\log{\left(c \right)}}{3 x^{3}} & \text{for}\: b \neq 0 \\- \frac{\log{\left(a^{p} c \right)}}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*p*log(a + b/x)/(3*b**3) + a**2*p/(3*b**2*x) - a*p/(6*b*x**2) - p*log(a + b/x)/(3*x**3) + p/(9*x**3) - log(c)/(3*x**3), Ne(b, 0)), (-log(a**p*c)/(3*x**3), True))","A",0
35,1,94,0,10.470135," ","integrate(ln(c*(a+b/x)**p)/x**5,x)","\begin{cases} \frac{a^{4} p \log{\left(a + \frac{b}{x} \right)}}{4 b^{4}} - \frac{a^{3} p}{4 b^{3} x} + \frac{a^{2} p}{8 b^{2} x^{2}} - \frac{a p}{12 b x^{3}} - \frac{p \log{\left(a + \frac{b}{x} \right)}}{4 x^{4}} + \frac{p}{16 x^{4}} - \frac{\log{\left(c \right)}}{4 x^{4}} & \text{for}\: b \neq 0 \\- \frac{\log{\left(a^{p} c \right)}}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*p*log(a + b/x)/(4*b**4) - a**3*p/(4*b**3*x) + a**2*p/(8*b**2*x**2) - a*p/(12*b*x**3) - p*log(a + b/x)/(4*x**4) + p/(16*x**4) - log(c)/(4*x**4), Ne(b, 0)), (-log(a**p*c)/(4*x**4), True))","A",0
36,1,162,0,92.914195," ","integrate(x**4*ln(c*(a+b/x**2)**p),x)","\begin{cases} \frac{p x^{5} \log{\left(a + \frac{b}{x^{2}} \right)}}{5} + \frac{x^{5} \log{\left(c \right)}}{5} + \frac{2 b p x^{3}}{15 a} - \frac{2 b^{2} p x}{5 a^{2}} - \frac{i b^{\frac{5}{2}} p \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{5 a^{3} \sqrt{\frac{1}{a}}} + \frac{i b^{\frac{5}{2}} p \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{5 a^{3} \sqrt{\frac{1}{a}}} & \text{for}\: a \neq 0 \\\frac{p x^{5} \log{\left(b \right)}}{5} - \frac{2 p x^{5} \log{\left(x \right)}}{5} + \frac{2 p x^{5}}{25} + \frac{x^{5} \log{\left(c \right)}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x**5*log(a + b/x**2)/5 + x**5*log(c)/5 + 2*b*p*x**3/(15*a) - 2*b**2*p*x/(5*a**2) - I*b**(5/2)*p*log(-I*sqrt(b)*sqrt(1/a) + x)/(5*a**3*sqrt(1/a)) + I*b**(5/2)*p*log(I*sqrt(b)*sqrt(1/a) + x)/(5*a**3*sqrt(1/a)), Ne(a, 0)), (p*x**5*log(b)/5 - 2*p*x**5*log(x)/5 + 2*p*x**5/25 + x**5*log(c)/5, True))","A",0
37,1,87,0,9.549500," ","integrate(x**3*ln(c*(a+b/x**2)**p),x)","\begin{cases} \frac{p x^{4} \log{\left(a + \frac{b}{x^{2}} \right)}}{4} + \frac{x^{4} \log{\left(c \right)}}{4} + \frac{b p x^{2}}{4 a} - \frac{b^{2} p \log{\left(a x^{2} + b \right)}}{4 a^{2}} & \text{for}\: a \neq 0 \\\frac{p x^{4} \log{\left(b \right)}}{4} - \frac{p x^{4} \log{\left(x \right)}}{2} + \frac{p x^{4}}{8} + \frac{x^{4} \log{\left(c \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x**4*log(a + b/x**2)/4 + x**4*log(c)/4 + b*p*x**2/(4*a) - b**2*p*log(a*x**2 + b)/(4*a**2), Ne(a, 0)), (p*x**4*log(b)/4 - p*x**4*log(x)/2 + p*x**4/8 + x**4*log(c)/4, True))","A",0
38,1,146,0,33.144627," ","integrate(x**2*ln(c*(a+b/x**2)**p),x)","\begin{cases} \frac{p x^{3} \log{\left(a + \frac{b}{x^{2}} \right)}}{3} + \frac{x^{3} \log{\left(c \right)}}{3} + \frac{2 b p x}{3 a} + \frac{i b^{\frac{3}{2}} p \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{3 a^{2} \sqrt{\frac{1}{a}}} - \frac{i b^{\frac{3}{2}} p \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{3 a^{2} \sqrt{\frac{1}{a}}} & \text{for}\: a \neq 0 \\\frac{p x^{3} \log{\left(b \right)}}{3} - \frac{2 p x^{3} \log{\left(x \right)}}{3} + \frac{2 p x^{3}}{9} + \frac{x^{3} \log{\left(c \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x**3*log(a + b/x**2)/3 + x**3*log(c)/3 + 2*b*p*x/(3*a) + I*b**(3/2)*p*log(-I*sqrt(b)*sqrt(1/a) + x)/(3*a**2*sqrt(1/a)) - I*b**(3/2)*p*log(I*sqrt(b)*sqrt(1/a) + x)/(3*a**2*sqrt(1/a)), Ne(a, 0)), (p*x**3*log(b)/3 - 2*p*x**3*log(x)/3 + 2*p*x**3/9 + x**3*log(c)/3, True))","A",0
39,1,71,0,3.350590," ","integrate(x*ln(c*(a+b/x**2)**p),x)","\begin{cases} \frac{p x^{2} \log{\left(a + \frac{b}{x^{2}} \right)}}{2} + \frac{x^{2} \log{\left(c \right)}}{2} + \frac{b p \log{\left(a x^{2} + b \right)}}{2 a} & \text{for}\: a \neq 0 \\\frac{p x^{2} \log{\left(b \right)}}{2} - p x^{2} \log{\left(x \right)} + \frac{p x^{2}}{2} + \frac{x^{2} \log{\left(c \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x**2*log(a + b/x**2)/2 + x**2*log(c)/2 + b*p*log(a*x**2 + b)/(2*a), Ne(a, 0)), (p*x**2*log(b)/2 - p*x**2*log(x) + p*x**2/2 + x**2*log(c)/2, True))","A",0
40,1,109,0,11.317632," ","integrate(ln(c*(a+b/x**2)**p),x)","\begin{cases} p x \log{\left(a + \frac{b}{x^{2}} \right)} + x \log{\left(c \right)} - \frac{i \sqrt{b} p \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{a \sqrt{\frac{1}{a}}} + \frac{i \sqrt{b} p \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{a \sqrt{\frac{1}{a}}} & \text{for}\: a \neq 0 \\p x \log{\left(b \right)} - 2 p x \log{\left(x \right)} + 2 p x + x \log{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((p*x*log(a + b/x**2) + x*log(c) - I*sqrt(b)*p*log(-I*sqrt(b)*sqrt(1/a) + x)/(a*sqrt(1/a)) + I*sqrt(b)*p*log(I*sqrt(b)*sqrt(1/a) + x)/(a*sqrt(1/a)), Ne(a, 0)), (p*x*log(b) - 2*p*x*log(x) + 2*p*x + x*log(c), True))","A",0
41,0,0,0,0.000000," ","integrate(ln(c*(a+b/x**2)**p)/x,x)","\int \frac{\log{\left(c \left(a + \frac{b}{x^{2}}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(log(c*(a + b/x**2)**p)/x, x)","F",0
42,1,129,0,25.446795," ","integrate(ln(c*(a+b/x**2)**p)/x**2,x)","\begin{cases} - \frac{\log{\left(0^{p} c \right)}}{x} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{\log{\left(a^{p} c \right)}}{x} & \text{for}\: b = 0 \\- \frac{p \log{\left(b \right)}}{x} + \frac{2 p \log{\left(x \right)}}{x} + \frac{2 p}{x} - \frac{\log{\left(c \right)}}{x} & \text{for}\: a = 0 \\- \frac{p \log{\left(a + \frac{b}{x^{2}} \right)}}{x} + \frac{2 p}{x} - \frac{\log{\left(c \right)}}{x} - \frac{i p \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{\sqrt{b} \sqrt{\frac{1}{a}}} + \frac{i p \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{\sqrt{b} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(0**p*c)/x, Eq(a, 0) & Eq(b, 0)), (-log(a**p*c)/x, Eq(b, 0)), (-p*log(b)/x + 2*p*log(x)/x + 2*p/x - log(c)/x, Eq(a, 0)), (-p*log(a + b/x**2)/x + 2*p/x - log(c)/x - I*p*log(-I*sqrt(b)*sqrt(1/a) + x)/(sqrt(b)*sqrt(1/a)) + I*p*log(I*sqrt(b)*sqrt(1/a) + x)/(sqrt(b)*sqrt(1/a)), True))","A",0
43,1,58,0,5.647681," ","integrate(ln(c*(a+b/x**2)**p)/x**3,x)","\begin{cases} - \frac{a p \log{\left(a + \frac{b}{x^{2}} \right)}}{2 b} - \frac{p \log{\left(a + \frac{b}{x^{2}} \right)}}{2 x^{2}} + \frac{p}{2 x^{2}} - \frac{\log{\left(c \right)}}{2 x^{2}} & \text{for}\: b \neq 0 \\- \frac{\log{\left(a^{p} c \right)}}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*p*log(a + b/x**2)/(2*b) - p*log(a + b/x**2)/(2*x**2) + p/(2*x**2) - log(c)/(2*x**2), Ne(b, 0)), (-log(a**p*c)/(2*x**2), True))","A",0
44,1,177,0,72.059624," ","integrate(ln(c*(a+b/x**2)**p)/x**4,x)","\begin{cases} - \frac{\log{\left(0^{p} c \right)}}{3 x^{3}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{\log{\left(a^{p} c \right)}}{3 x^{3}} & \text{for}\: b = 0 \\- \frac{p \log{\left(b \right)}}{3 x^{3}} + \frac{2 p \log{\left(x \right)}}{3 x^{3}} + \frac{2 p}{9 x^{3}} - \frac{\log{\left(c \right)}}{3 x^{3}} & \text{for}\: a = 0 \\- \frac{2 a p}{3 b x} + \frac{i a p \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{3 b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{i a p \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} + x \right)}}{3 b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{p \log{\left(a + \frac{b}{x^{2}} \right)}}{3 x^{3}} + \frac{2 p}{9 x^{3}} - \frac{\log{\left(c \right)}}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(0**p*c)/(3*x**3), Eq(a, 0) & Eq(b, 0)), (-log(a**p*c)/(3*x**3), Eq(b, 0)), (-p*log(b)/(3*x**3) + 2*p*log(x)/(3*x**3) + 2*p/(9*x**3) - log(c)/(3*x**3), Eq(a, 0)), (-2*a*p/(3*b*x) + I*a*p*log(-I*sqrt(b)*sqrt(1/a) + x)/(3*b**(3/2)*sqrt(1/a)) - I*a*p*log(I*sqrt(b)*sqrt(1/a) + x)/(3*b**(3/2)*sqrt(1/a)) - p*log(a + b/x**2)/(3*x**3) + 2*p/(9*x**3) - log(c)/(3*x**3), True))","A",0
45,1,8,0,2.780492," ","integrate(ln(1+b/x)/x,x)","\operatorname{Li}_{2}\left(\frac{b e^{i \pi}}{x}\right)"," ",0,"polylog(2, b*exp_polar(I*pi)/x)","C",0
46,1,146,0,27.232818," ","integrate(x**3*ln(c*(a+b*x**(1/2))**p),x)","- \frac{b p \left(\frac{2 a^{8} \left(\begin{cases} \frac{\sqrt{x}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(a + b \sqrt{x} \right)}}{b} & \text{otherwise} \end{cases}\right)}{b^{8}} - \frac{2 a^{7} \sqrt{x}}{b^{8}} + \frac{a^{6} x}{b^{7}} - \frac{2 a^{5} x^{\frac{3}{2}}}{3 b^{6}} + \frac{a^{4} x^{2}}{2 b^{5}} - \frac{2 a^{3} x^{\frac{5}{2}}}{5 b^{4}} + \frac{a^{2} x^{3}}{3 b^{3}} - \frac{2 a x^{\frac{7}{2}}}{7 b^{2}} + \frac{x^{4}}{4 b}\right)}{8} + \frac{x^{4} \log{\left(c \left(a + b \sqrt{x}\right)^{p} \right)}}{4}"," ",0,"-b*p*(2*a**8*Piecewise((sqrt(x)/a, Eq(b, 0)), (log(a + b*sqrt(x))/b, True))/b**8 - 2*a**7*sqrt(x)/b**8 + a**6*x/b**7 - 2*a**5*x**(3/2)/(3*b**6) + a**4*x**2/(2*b**5) - 2*a**3*x**(5/2)/(5*b**4) + a**2*x**3/(3*b**3) - 2*a*x**(7/2)/(7*b**2) + x**4/(4*b))/8 + x**4*log(c*(a + b*sqrt(x))**p)/4","A",0
47,1,119,0,8.446168," ","integrate(x**2*ln(c*(a+b*x**(1/2))**p),x)","- \frac{b p \left(\frac{2 a^{6} \left(\begin{cases} \frac{\sqrt{x}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(a + b \sqrt{x} \right)}}{b} & \text{otherwise} \end{cases}\right)}{b^{6}} - \frac{2 a^{5} \sqrt{x}}{b^{6}} + \frac{a^{4} x}{b^{5}} - \frac{2 a^{3} x^{\frac{3}{2}}}{3 b^{4}} + \frac{a^{2} x^{2}}{2 b^{3}} - \frac{2 a x^{\frac{5}{2}}}{5 b^{2}} + \frac{x^{3}}{3 b}\right)}{6} + \frac{x^{3} \log{\left(c \left(a + b \sqrt{x}\right)^{p} \right)}}{3}"," ",0,"-b*p*(2*a**6*Piecewise((sqrt(x)/a, Eq(b, 0)), (log(a + b*sqrt(x))/b, True))/b**6 - 2*a**5*sqrt(x)/b**6 + a**4*x/b**5 - 2*a**3*x**(3/2)/(3*b**4) + a**2*x**2/(2*b**3) - 2*a*x**(5/2)/(5*b**2) + x**3/(3*b))/6 + x**3*log(c*(a + b*sqrt(x))**p)/3","A",0
48,1,92,0,2.910156," ","integrate(x*ln(c*(a+b*x**(1/2))**p),x)","- \frac{b p \left(\frac{2 a^{4} \left(\begin{cases} \frac{\sqrt{x}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(a + b \sqrt{x} \right)}}{b} & \text{otherwise} \end{cases}\right)}{b^{4}} - \frac{2 a^{3} \sqrt{x}}{b^{4}} + \frac{a^{2} x}{b^{3}} - \frac{2 a x^{\frac{3}{2}}}{3 b^{2}} + \frac{x^{2}}{2 b}\right)}{4} + \frac{x^{2} \log{\left(c \left(a + b \sqrt{x}\right)^{p} \right)}}{2}"," ",0,"-b*p*(2*a**4*Piecewise((sqrt(x)/a, Eq(b, 0)), (log(a + b*sqrt(x))/b, True))/b**4 - 2*a**3*sqrt(x)/b**4 + a**2*x/b**3 - 2*a*x**(3/2)/(3*b**2) + x**2/(2*b))/4 + x**2*log(c*(a + b*sqrt(x))**p)/2","A",0
49,1,61,0,1.501691," ","integrate(ln(c*(a+b*x**(1/2))**p),x)","- \frac{b p \left(\frac{2 a^{2} \left(\begin{cases} \frac{\sqrt{x}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(a + b \sqrt{x} \right)}}{b} & \text{otherwise} \end{cases}\right)}{b^{2}} - \frac{2 a \sqrt{x}}{b^{2}} + \frac{x}{b}\right)}{2} + x \log{\left(c \left(a + b \sqrt{x}\right)^{p} \right)}"," ",0,"-b*p*(2*a**2*Piecewise((sqrt(x)/a, Eq(b, 0)), (log(a + b*sqrt(x))/b, True))/b**2 - 2*a*sqrt(x)/b**2 + x/b)/2 + x*log(c*(a + b*sqrt(x))**p)","A",0
50,0,0,0,0.000000," ","integrate(ln(c*(a+b*x**(1/2))**p)/x,x)","\int \frac{\log{\left(c \left(a + b \sqrt{x}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(log(c*(a + b*sqrt(x))**p)/x, x)","F",0
51,1,461,0,40.890572," ","integrate(ln(c*(a+b*x**(1/2))**p)/x**2,x)","\begin{cases} - \frac{2 a^{3} p \sqrt{x} \log{\left(a + b \sqrt{x} \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} - \frac{2 a^{3} \sqrt{x} \log{\left(c \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} - \frac{2 a^{2} b p x \log{\left(a + b \sqrt{x} \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} - \frac{2 a^{2} b p x}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} - \frac{2 a^{2} b x \log{\left(c \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} - \frac{a b^{2} p x^{\frac{3}{2}} \log{\left(x \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} + \frac{2 a b^{2} p x^{\frac{3}{2}} \log{\left(a + b \sqrt{x} \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} - \frac{2 a b^{2} p x^{\frac{3}{2}}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} + \frac{2 a b^{2} x^{\frac{3}{2}} \log{\left(c \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} - \frac{b^{3} p x^{2} \log{\left(x \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} + \frac{2 b^{3} p x^{2} \log{\left(a + b \sqrt{x} \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} + \frac{2 b^{3} x^{2} \log{\left(c \right)}}{2 a^{3} x^{\frac{3}{2}} + 2 a^{2} b x^{2}} & \text{for}\: a \neq 0 \\- \frac{p \log{\left(b \right)}}{x} - \frac{p \log{\left(x \right)}}{2 x} - \frac{p}{2 x} - \frac{\log{\left(c \right)}}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*p*sqrt(x)*log(a + b*sqrt(x))/(2*a**3*x**(3/2) + 2*a**2*b*x**2) - 2*a**3*sqrt(x)*log(c)/(2*a**3*x**(3/2) + 2*a**2*b*x**2) - 2*a**2*b*p*x*log(a + b*sqrt(x))/(2*a**3*x**(3/2) + 2*a**2*b*x**2) - 2*a**2*b*p*x/(2*a**3*x**(3/2) + 2*a**2*b*x**2) - 2*a**2*b*x*log(c)/(2*a**3*x**(3/2) + 2*a**2*b*x**2) - a*b**2*p*x**(3/2)*log(x)/(2*a**3*x**(3/2) + 2*a**2*b*x**2) + 2*a*b**2*p*x**(3/2)*log(a + b*sqrt(x))/(2*a**3*x**(3/2) + 2*a**2*b*x**2) - 2*a*b**2*p*x**(3/2)/(2*a**3*x**(3/2) + 2*a**2*b*x**2) + 2*a*b**2*x**(3/2)*log(c)/(2*a**3*x**(3/2) + 2*a**2*b*x**2) - b**3*p*x**2*log(x)/(2*a**3*x**(3/2) + 2*a**2*b*x**2) + 2*b**3*p*x**2*log(a + b*sqrt(x))/(2*a**3*x**(3/2) + 2*a**2*b*x**2) + 2*b**3*x**2*log(c)/(2*a**3*x**(3/2) + 2*a**2*b*x**2), Ne(a, 0)), (-p*log(b)/x - p*log(x)/(2*x) - p/(2*x) - log(c)/x, True))","A",0
52,-1,0,0,0.000000," ","integrate(ln(c*(a+b*x**(1/2))**p)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-1,0,0,0.000000," ","integrate(ln(c*(a+b*x**(1/2))**p)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,1,133,0,0.714746," ","integrate(ln(a+b*x**(1/2))/x**(1/2),x)","\begin{cases} \frac{2 a^{2} \log{\left(a + b \sqrt{x} \right)}}{a b + b^{2} \sqrt{x}} + \frac{2 a^{2}}{a b + b^{2} \sqrt{x}} + \frac{4 a b \sqrt{x} \log{\left(a + b \sqrt{x} \right)}}{a b + b^{2} \sqrt{x}} + \frac{2 b^{2} x \log{\left(a + b \sqrt{x} \right)}}{a b + b^{2} \sqrt{x}} - \frac{2 b^{2} x}{a b + b^{2} \sqrt{x}} & \text{for}\: b \neq 0 \\2 \sqrt{x} \log{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*log(a + b*sqrt(x))/(a*b + b**2*sqrt(x)) + 2*a**2/(a*b + b**2*sqrt(x)) + 4*a*b*sqrt(x)*log(a + b*sqrt(x))/(a*b + b**2*sqrt(x)) + 2*b**2*x*log(a + b*sqrt(x))/(a*b + b**2*sqrt(x)) - 2*b**2*x/(a*b + b**2*sqrt(x)), Ne(b, 0)), (2*sqrt(x)*log(a), True))","A",0
55,-1,0,0,0.000000," ","integrate((f*x)**m*ln(c*(e*x**3+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,1,359,0,95.986571," ","integrate((f*x)**m*ln(c*(e*x**2+d)**p),x)","- 2 e p \left(\begin{cases} \frac{0^{m} \sqrt{- \frac{d}{e^{3}}} \log{\left(- e \sqrt{- \frac{d}{e^{3}}} + x \right)}}{2} - \frac{0^{m} \sqrt{- \frac{d}{e^{3}}} \log{\left(e \sqrt{- \frac{d}{e^{3}}} + x \right)}}{2} + \frac{0^{m} x}{e} & \text{for}\: \left(f = 0 \wedge m \neq -1\right) \vee f = 0 \\\frac{f f^{m} m x^{3} x^{m} \Phi\left(\frac{e x^{2} e^{i \pi}}{d}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 d f m \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 4 d f \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{3 f f^{m} x^{3} x^{m} \Phi\left(\frac{e x^{2} e^{i \pi}}{d}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 d f m \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 4 d f \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} & \text{for}\: m > -\infty \wedge m < \infty \wedge m \neq -1 \\- \frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{otherwise} \end{cases}}{2 e f} + \frac{\log{\left(f x \right)} \log{\left(d + e x^{2} \right)}}{2 e f} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0^{m} x & \text{for}\: f = 0 \\\frac{\begin{cases} \frac{\left(f x\right)^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(f x \right)} & \text{otherwise} \end{cases}}{f} & \text{otherwise} \end{cases}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}"," ",0,"-2*e*p*Piecewise((0**m*sqrt(-d/e**3)*log(-e*sqrt(-d/e**3) + x)/2 - 0**m*sqrt(-d/e**3)*log(e*sqrt(-d/e**3) + x)/2 + 0**m*x/e, Eq(f, 0) | (Eq(f, 0) & Ne(m, -1))), (f*f**m*m*x**3*x**m*lerchphi(e*x**2*exp_polar(I*pi)/d, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*d*f*m*gamma(m/2 + 5/2) + 4*d*f*gamma(m/2 + 5/2)) + 3*f*f**m*x**3*x**m*lerchphi(e*x**2*exp_polar(I*pi)/d, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*d*f*m*gamma(m/2 + 5/2) + 4*d*f*gamma(m/2 + 5/2)), (m > -oo) & (m < oo) & Ne(m, -1)), (-Piecewise((log(d)*log(x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, True))/(2*e*f) + log(f*x)*log(d + e*x**2)/(2*e*f), True)) + Piecewise((0**m*x, Eq(f, 0)), (Piecewise(((f*x)**(m + 1)/(m + 1), Ne(m, -1)), (log(f*x), True))/f, True))*log(c*(d + e*x**2)**p)","A",0
57,0,0,0,0.000000," ","integrate((f*x)**m*ln(c*(e*x+d)**p),x)","\int \left(f x\right)^{m} \log{\left(c \left(d + e x\right)^{p} \right)}\, dx"," ",0,"Integral((f*x)**m*log(c*(d + e*x)**p), x)","F",0
58,1,201,0,21.399930," ","integrate((f*x)**m*ln(c*(d+e/x)**p),x)","e p \left(\begin{cases} \frac{0^{m} \log{\left(d x + e \right)}}{d} & \text{for}\: \left(f = 0 \wedge m \neq -1\right) \vee f = 0 \\\frac{f^{m} m x^{m} \Phi\left(\frac{e e^{i \pi}}{d x}, 1, m e^{i \pi}\right) \Gamma\left(- m\right)}{d m \Gamma\left(1 - m\right) + d \Gamma\left(1 - m\right)} & \text{for}\: m > -\infty \wedge m < \infty \wedge m \neq -1 \\\frac{\begin{cases} - \frac{1}{d x} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} + \operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} + \operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + \operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}}{f} - \frac{\left(\begin{cases} \frac{1}{d x} & \text{for}\: e = 0 \\\frac{\log{\left(d + \frac{e}{x} \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(f x \right)}}{f} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0^{m} x & \text{for}\: f = 0 \\\frac{\begin{cases} \frac{\left(f x\right)^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(f x \right)} & \text{otherwise} \end{cases}}{f} & \text{otherwise} \end{cases}\right) \log{\left(c \left(d + \frac{e}{x}\right)^{p} \right)}"," ",0,"e*p*Piecewise((0**m*log(d*x + e)/d, Eq(f, 0) | (Eq(f, 0) & Ne(m, -1))), (f**m*m*x**m*lerchphi(e*exp_polar(I*pi)/(d*x), 1, m*exp_polar(I*pi))*gamma(-m)/(d*m*gamma(1 - m) + d*gamma(1 - m)), (m > -oo) & (m < oo) & Ne(m, -1)), (Piecewise((-1/(d*x), Eq(e, 0)), (Piecewise((log(d)*log(x) + polylog(2, e*exp_polar(I*pi)/(d*x)), Abs(x) < 1), (-log(d)*log(1/x) + polylog(2, e*exp_polar(I*pi)/(d*x)), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) + polylog(2, e*exp_polar(I*pi)/(d*x)), True))/e, True))/f - Piecewise((1/(d*x), Eq(e, 0)), (log(d + e/x)/e, True))*log(f*x)/f, True)) + Piecewise((0**m*x, Eq(f, 0)), (Piecewise(((f*x)**(m + 1)/(m + 1), Ne(m, -1)), (log(f*x), True))/f, True))*log(c*(d + e/x)**p)","A",0
59,1,348,0,77.641068," ","integrate((f*x)**m*ln(c*(d+e/x**2)**p),x)","2 e p \left(\begin{cases} - \frac{0^{m} \sqrt{- \frac{1}{d e}} \log{\left(- e \sqrt{- \frac{1}{d e}} + x \right)}}{2} + \frac{0^{m} \sqrt{- \frac{1}{d e}} \log{\left(e \sqrt{- \frac{1}{d e}} + x \right)}}{2} & \text{for}\: \left(f = 0 \wedge m \neq -1\right) \vee f = 0 \\\frac{f f^{m} m x^{m} \Phi\left(\frac{e e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{4 d f m x \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 4 d f x \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{f f^{m} x^{m} \Phi\left(\frac{e e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{4 d f m x \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 4 d f x \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} & \text{for}\: m > -\infty \wedge m < \infty \wedge m \neq -1 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} + \frac{\operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x^{2}}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} + \frac{\operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x^{2}}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + \frac{\operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x^{2}}\right)}{2} & \text{otherwise} \end{cases}}{2 e f} - \frac{\log{\left(f x \right)} \log{\left(d + \frac{e}{x^{2}} \right)}}{2 e f} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0^{m} x & \text{for}\: f = 0 \\\frac{\begin{cases} \frac{\left(f x\right)^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(f x \right)} & \text{otherwise} \end{cases}}{f} & \text{otherwise} \end{cases}\right) \log{\left(c \left(d + \frac{e}{x^{2}}\right)^{p} \right)}"," ",0,"2*e*p*Piecewise((-0**m*sqrt(-1/(d*e))*log(-e*sqrt(-1/(d*e)) + x)/2 + 0**m*sqrt(-1/(d*e))*log(e*sqrt(-1/(d*e)) + x)/2, Eq(f, 0) | (Eq(f, 0) & Ne(m, -1))), (f*f**m*m*x**m*lerchphi(e*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(4*d*f*m*x*gamma(3/2 - m/2) + 4*d*f*x*gamma(3/2 - m/2)) - f*f**m*x**m*lerchphi(e*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(4*d*f*m*x*gamma(3/2 - m/2) + 4*d*f*x*gamma(3/2 - m/2)), (m > -oo) & (m < oo) & Ne(m, -1)), (Piecewise((log(d)*log(x) + polylog(2, e*exp_polar(I*pi)/(d*x**2))/2, Abs(x) < 1), (-log(d)*log(1/x) + polylog(2, e*exp_polar(I*pi)/(d*x**2))/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) + polylog(2, e*exp_polar(I*pi)/(d*x**2))/2, True))/(2*e*f) - log(f*x)*log(d + e/x**2)/(2*e*f), True)) + Piecewise((0**m*x, Eq(f, 0)), (Piecewise(((f*x)**(m + 1)/(m + 1), Ne(m, -1)), (log(f*x), True))/f, True))*log(c*(d + e/x**2)**p)","A",0
60,-1,0,0,0.000000," ","integrate((f*x)**m*ln(c*(d+e/x**3)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,0,0,0,0.000000," ","integrate((f*x)**m*ln(c*(d+e*x**(1/2))**p),x)","\int \left(f x\right)^{m} \log{\left(c \left(d + e \sqrt{x}\right)^{p} \right)}\, dx"," ",0,"Integral((f*x)**m*log(c*(d + e*sqrt(x))**p), x)","F",0
62,0,0,0,0.000000," ","integrate((f*x)**m*ln(c*(d+e/x**(1/2))**p),x)","\int \left(f x\right)^{m} \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{p} \right)}\, dx"," ",0,"Integral((f*x)**m*log(c*(d + e/sqrt(x))**p), x)","F",0
63,0,0,0,0.000000," ","integrate((f*x)**m*ln(c*(d+e*x**n)**p),x)","\int \left(f x\right)^{m} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}\, dx"," ",0,"Integral((f*x)**m*log(c*(d + e*x**n)**p), x)","F",0
64,-1,0,0,0.000000," ","integrate((f*x)**(-1+3*n)*ln(c*(d+e*x**n)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate((f*x)**(-1+2*n)*ln(c*(d+e*x**n)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate((f*x)**(-1+n)*ln(c*(d+e*x**n)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/f/x,x)","\frac{\int \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx}{f}"," ",0,"Integral(log(c*(d + e*x**n)**p)/x, x)/f","F",0
68,-1,0,0,0.000000," ","integrate((f*x)**(-1-n)*ln(c*(d+e*x**n)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate((f*x)**(-1-2*n)*ln(c*(d+e*x**n)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,1,104,0,13.628165," ","integrate(x**2*ln(c*(d+e*x**n)**p),x)","\frac{x^{3} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{3} - \frac{e p x^{3} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{3}{n}\right) \Gamma\left(1 + \frac{3}{n}\right)}{3 d \Gamma\left(2 + \frac{3}{n}\right)} - \frac{e p x^{3} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{3}{n}\right) \Gamma\left(1 + \frac{3}{n}\right)}{d n \Gamma\left(2 + \frac{3}{n}\right)}"," ",0,"x**3*log(c*(d + e*x**n)**p)/3 - e*p*x**3*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 3/n)*gamma(1 + 3/n)/(3*d*gamma(2 + 3/n)) - e*p*x**3*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 3/n)*gamma(1 + 3/n)/(d*n*gamma(2 + 3/n))","C",0
71,1,104,0,6.630908," ","integrate(x*ln(c*(d+e*x**n)**p),x)","\frac{x^{2} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{2} - \frac{e p x^{2} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{2 d \Gamma\left(2 + \frac{2}{n}\right)} - \frac{e p x^{2} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{d n \Gamma\left(2 + \frac{2}{n}\right)}"," ",0,"x**2*log(c*(d + e*x**n)**p)/2 - e*p*x**2*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 2/n)*gamma(1 + 2/n)/(2*d*gamma(2 + 2/n)) - e*p*x**2*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 2/n)*gamma(1 + 2/n)/(d*n*gamma(2 + 2/n))","C",0
72,1,48,0,3.428959," ","integrate(ln(c*(d+e*x**n)**p),x)","x \log{\left(c \left(d + e x^{n}\right)^{p} \right)} + \frac{p x \Phi\left(\frac{d x^{- n} e^{i \pi}}{e}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"x*log(c*(d + e*x**n)**p) + p*x*lerchphi(d*x**(-n)*exp_polar(I*pi)/e, 1, exp_polar(I*pi)/n)*gamma(1/n)/(n*gamma(1 + 1/n))","C",0
73,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x,x)","\int \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(log(c*(d + e*x**n)**p)/x, x)","F",0
74,1,46,0,7.711329," ","integrate(ln(c*(d+e*x**n)**p)/x**2,x)","- \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x} + \frac{p \Phi\left(\frac{d x^{- n} e^{i \pi}}{e}, 1, \frac{1}{n}\right) \Gamma\left(- \frac{1}{n}\right)}{n x \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"-log(c*(d + e*x**n)**p)/x + p*lerchphi(d*x**(-n)*exp_polar(I*pi)/e, 1, 1/n)*gamma(-1/n)/(n*x*gamma(1 - 1/n))","C",0
75,1,51,0,15.285123," ","integrate(ln(c*(d+e*x**n)**p)/x**3,x)","- \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{2 x^{2}} + \frac{p \Phi\left(\frac{d x^{- n} e^{i \pi}}{e}, 1, \frac{2}{n}\right) \Gamma\left(- \frac{2}{n}\right)}{n x^{2} \Gamma\left(1 - \frac{2}{n}\right)}"," ",0,"-log(c*(d + e*x**n)**p)/(2*x**2) + p*lerchphi(d*x**(-n)*exp_polar(I*pi)/e, 1, 2/n)*gamma(-2/n)/(n*x**2*gamma(1 - 2/n))","C",0
76,1,51,0,32.217417," ","integrate(ln(c*(d+e*x**n)**p)/x**4,x)","- \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{3 x^{3}} + \frac{p \Phi\left(\frac{d x^{- n} e^{i \pi}}{e}, 1, \frac{3}{n}\right) \Gamma\left(- \frac{3}{n}\right)}{n x^{3} \Gamma\left(1 - \frac{3}{n}\right)}"," ",0,"-log(c*(d + e*x**n)**p)/(3*x**3) + p*lerchphi(d*x**(-n)*exp_polar(I*pi)/e, 1, 3/n)*gamma(-3/n)/(n*x**3*gamma(1 - 3/n))","C",0
77,1,267,0,22.718021," ","integrate(x**5*ln(c*(b*x**2+a)**p)**2,x)","\begin{cases} \frac{a^{3} p^{2} \log{\left(a + b x^{2} \right)}^{2}}{6 b^{3}} - \frac{11 a^{3} p^{2} \log{\left(a + b x^{2} \right)}}{18 b^{3}} + \frac{a^{3} p \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{3 b^{3}} - \frac{a^{2} p^{2} x^{2} \log{\left(a + b x^{2} \right)}}{3 b^{2}} + \frac{11 a^{2} p^{2} x^{2}}{18 b^{2}} - \frac{a^{2} p x^{2} \log{\left(c \right)}}{3 b^{2}} + \frac{a p^{2} x^{4} \log{\left(a + b x^{2} \right)}}{6 b} - \frac{5 a p^{2} x^{4}}{36 b} + \frac{a p x^{4} \log{\left(c \right)}}{6 b} + \frac{p^{2} x^{6} \log{\left(a + b x^{2} \right)}^{2}}{6} - \frac{p^{2} x^{6} \log{\left(a + b x^{2} \right)}}{9} + \frac{p^{2} x^{6}}{27} + \frac{p x^{6} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{3} - \frac{p x^{6} \log{\left(c \right)}}{9} + \frac{x^{6} \log{\left(c \right)}^{2}}{6} & \text{for}\: b \neq 0 \\\frac{x^{6} \log{\left(a^{p} c \right)}^{2}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*p**2*log(a + b*x**2)**2/(6*b**3) - 11*a**3*p**2*log(a + b*x**2)/(18*b**3) + a**3*p*log(c)*log(a + b*x**2)/(3*b**3) - a**2*p**2*x**2*log(a + b*x**2)/(3*b**2) + 11*a**2*p**2*x**2/(18*b**2) - a**2*p*x**2*log(c)/(3*b**2) + a*p**2*x**4*log(a + b*x**2)/(6*b) - 5*a*p**2*x**4/(36*b) + a*p*x**4*log(c)/(6*b) + p**2*x**6*log(a + b*x**2)**2/6 - p**2*x**6*log(a + b*x**2)/9 + p**2*x**6/27 + p*x**6*log(c)*log(a + b*x**2)/3 - p*x**6*log(c)/9 + x**6*log(c)**2/6, Ne(b, 0)), (x**6*log(a**p*c)**2/6, True))","A",0
78,1,209,0,8.638635," ","integrate(x**3*ln(c*(b*x**2+a)**p)**2,x)","\begin{cases} - \frac{a^{2} p^{2} \log{\left(a + b x^{2} \right)}^{2}}{4 b^{2}} + \frac{3 a^{2} p^{2} \log{\left(a + b x^{2} \right)}}{4 b^{2}} - \frac{a^{2} p \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{2 b^{2}} + \frac{a p^{2} x^{2} \log{\left(a + b x^{2} \right)}}{2 b} - \frac{3 a p^{2} x^{2}}{4 b} + \frac{a p x^{2} \log{\left(c \right)}}{2 b} + \frac{p^{2} x^{4} \log{\left(a + b x^{2} \right)}^{2}}{4} - \frac{p^{2} x^{4} \log{\left(a + b x^{2} \right)}}{4} + \frac{p^{2} x^{4}}{8} + \frac{p x^{4} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{2} - \frac{p x^{4} \log{\left(c \right)}}{4} + \frac{x^{4} \log{\left(c \right)}^{2}}{4} & \text{for}\: b \neq 0 \\\frac{x^{4} \log{\left(a^{p} c \right)}^{2}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*p**2*log(a + b*x**2)**2/(4*b**2) + 3*a**2*p**2*log(a + b*x**2)/(4*b**2) - a**2*p*log(c)*log(a + b*x**2)/(2*b**2) + a*p**2*x**2*log(a + b*x**2)/(2*b) - 3*a*p**2*x**2/(4*b) + a*p*x**2*log(c)/(2*b) + p**2*x**4*log(a + b*x**2)**2/4 - p**2*x**4*log(a + b*x**2)/4 + p**2*x**4/8 + p*x**4*log(c)*log(a + b*x**2)/2 - p*x**4*log(c)/4 + x**4*log(c)**2/4, Ne(b, 0)), (x**4*log(a**p*c)**2/4, True))","A",0
79,1,139,0,3.132061," ","integrate(x*ln(c*(b*x**2+a)**p)**2,x)","\begin{cases} \frac{a p^{2} \log{\left(a + b x^{2} \right)}^{2}}{2 b} - \frac{a p^{2} \log{\left(a + b x^{2} \right)}}{b} + \frac{a p \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{b} + \frac{p^{2} x^{2} \log{\left(a + b x^{2} \right)}^{2}}{2} - p^{2} x^{2} \log{\left(a + b x^{2} \right)} + p^{2} x^{2} + p x^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)} - p x^{2} \log{\left(c \right)} + \frac{x^{2} \log{\left(c \right)}^{2}}{2} & \text{for}\: b \neq 0 \\\frac{x^{2} \log{\left(a^{p} c \right)}^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*p**2*log(a + b*x**2)**2/(2*b) - a*p**2*log(a + b*x**2)/b + a*p*log(c)*log(a + b*x**2)/b + p**2*x**2*log(a + b*x**2)**2/2 - p**2*x**2*log(a + b*x**2) + p**2*x**2 + p*x**2*log(c)*log(a + b*x**2) - p*x**2*log(c) + x**2*log(c)**2/2, Ne(b, 0)), (x**2*log(a**p*c)**2/2, True))","A",0
80,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**2/x,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}{x}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**2/x, x)","F",0
81,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**2/x**3,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}{x^{3}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**2/x**3, x)","F",0
82,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**2/x**5,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}{x^{5}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**2/x**5, x)","F",0
83,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**2/x**7,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}{x^{7}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**2/x**7, x)","F",0
84,0,0,0,0.000000," ","integrate(x**4*ln(c*(b*x**2+a)**p)**2,x)","\int x^{4} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral(x**4*log(c*(a + b*x**2)**p)**2, x)","F",0
85,0,0,0,0.000000," ","integrate(x**2*ln(c*(b*x**2+a)**p)**2,x)","\int x^{2} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral(x**2*log(c*(a + b*x**2)**p)**2, x)","F",0
86,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**2,x)","\int \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**2, x)","F",0
87,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**2/x**2,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}{x^{2}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**2/x**2, x)","F",0
88,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**2/x**4,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}{x^{4}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**2/x**4, x)","F",0
89,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**2/x**6,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}{x^{6}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**2/x**6, x)","F",0
90,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**2/x**8,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}{x^{8}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**2/x**8, x)","F",0
91,1,561,0,37.187646," ","integrate(x**5*ln(c*(b*x**2+a)**p)**3,x)","\begin{cases} \frac{a^{3} p^{3} \log{\left(a + b x^{2} \right)}^{3}}{6 b^{3}} - \frac{11 a^{3} p^{3} \log{\left(a + b x^{2} \right)}^{2}}{12 b^{3}} + \frac{85 a^{3} p^{3} \log{\left(a + b x^{2} \right)}}{36 b^{3}} + \frac{a^{3} p^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}^{2}}{2 b^{3}} - \frac{11 a^{3} p^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{6 b^{3}} + \frac{a^{3} p \log{\left(c \right)}^{2} \log{\left(a + b x^{2} \right)}}{2 b^{3}} - \frac{a^{2} p^{3} x^{2} \log{\left(a + b x^{2} \right)}^{2}}{2 b^{2}} + \frac{11 a^{2} p^{3} x^{2} \log{\left(a + b x^{2} \right)}}{6 b^{2}} - \frac{85 a^{2} p^{3} x^{2}}{36 b^{2}} - \frac{a^{2} p^{2} x^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{b^{2}} + \frac{11 a^{2} p^{2} x^{2} \log{\left(c \right)}}{6 b^{2}} - \frac{a^{2} p x^{2} \log{\left(c \right)}^{2}}{2 b^{2}} + \frac{a p^{3} x^{4} \log{\left(a + b x^{2} \right)}^{2}}{4 b} - \frac{5 a p^{3} x^{4} \log{\left(a + b x^{2} \right)}}{12 b} + \frac{19 a p^{3} x^{4}}{72 b} + \frac{a p^{2} x^{4} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{2 b} - \frac{5 a p^{2} x^{4} \log{\left(c \right)}}{12 b} + \frac{a p x^{4} \log{\left(c \right)}^{2}}{4 b} + \frac{p^{3} x^{6} \log{\left(a + b x^{2} \right)}^{3}}{6} - \frac{p^{3} x^{6} \log{\left(a + b x^{2} \right)}^{2}}{6} + \frac{p^{3} x^{6} \log{\left(a + b x^{2} \right)}}{9} - \frac{p^{3} x^{6}}{27} + \frac{p^{2} x^{6} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}^{2}}{2} - \frac{p^{2} x^{6} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{3} + \frac{p^{2} x^{6} \log{\left(c \right)}}{9} + \frac{p x^{6} \log{\left(c \right)}^{2} \log{\left(a + b x^{2} \right)}}{2} - \frac{p x^{6} \log{\left(c \right)}^{2}}{6} + \frac{x^{6} \log{\left(c \right)}^{3}}{6} & \text{for}\: b \neq 0 \\\frac{x^{6} \log{\left(a^{p} c \right)}^{3}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*p**3*log(a + b*x**2)**3/(6*b**3) - 11*a**3*p**3*log(a + b*x**2)**2/(12*b**3) + 85*a**3*p**3*log(a + b*x**2)/(36*b**3) + a**3*p**2*log(c)*log(a + b*x**2)**2/(2*b**3) - 11*a**3*p**2*log(c)*log(a + b*x**2)/(6*b**3) + a**3*p*log(c)**2*log(a + b*x**2)/(2*b**3) - a**2*p**3*x**2*log(a + b*x**2)**2/(2*b**2) + 11*a**2*p**3*x**2*log(a + b*x**2)/(6*b**2) - 85*a**2*p**3*x**2/(36*b**2) - a**2*p**2*x**2*log(c)*log(a + b*x**2)/b**2 + 11*a**2*p**2*x**2*log(c)/(6*b**2) - a**2*p*x**2*log(c)**2/(2*b**2) + a*p**3*x**4*log(a + b*x**2)**2/(4*b) - 5*a*p**3*x**4*log(a + b*x**2)/(12*b) + 19*a*p**3*x**4/(72*b) + a*p**2*x**4*log(c)*log(a + b*x**2)/(2*b) - 5*a*p**2*x**4*log(c)/(12*b) + a*p*x**4*log(c)**2/(4*b) + p**3*x**6*log(a + b*x**2)**3/6 - p**3*x**6*log(a + b*x**2)**2/6 + p**3*x**6*log(a + b*x**2)/9 - p**3*x**6/27 + p**2*x**6*log(c)*log(a + b*x**2)**2/2 - p**2*x**6*log(c)*log(a + b*x**2)/3 + p**2*x**6*log(c)/9 + p*x**6*log(c)**2*log(a + b*x**2)/2 - p*x**6*log(c)**2/6 + x**6*log(c)**3/6, Ne(b, 0)), (x**6*log(a**p*c)**3/6, True))","A",0
92,1,450,0,15.109972," ","integrate(x**3*ln(c*(b*x**2+a)**p)**3,x)","\begin{cases} - \frac{a^{2} p^{3} \log{\left(a + b x^{2} \right)}^{3}}{4 b^{2}} + \frac{9 a^{2} p^{3} \log{\left(a + b x^{2} \right)}^{2}}{8 b^{2}} - \frac{21 a^{2} p^{3} \log{\left(a + b x^{2} \right)}}{8 b^{2}} - \frac{3 a^{2} p^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}^{2}}{4 b^{2}} + \frac{9 a^{2} p^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{4 b^{2}} - \frac{3 a^{2} p \log{\left(c \right)}^{2} \log{\left(a + b x^{2} \right)}}{4 b^{2}} + \frac{3 a p^{3} x^{2} \log{\left(a + b x^{2} \right)}^{2}}{4 b} - \frac{9 a p^{3} x^{2} \log{\left(a + b x^{2} \right)}}{4 b} + \frac{21 a p^{3} x^{2}}{8 b} + \frac{3 a p^{2} x^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{2 b} - \frac{9 a p^{2} x^{2} \log{\left(c \right)}}{4 b} + \frac{3 a p x^{2} \log{\left(c \right)}^{2}}{4 b} + \frac{p^{3} x^{4} \log{\left(a + b x^{2} \right)}^{3}}{4} - \frac{3 p^{3} x^{4} \log{\left(a + b x^{2} \right)}^{2}}{8} + \frac{3 p^{3} x^{4} \log{\left(a + b x^{2} \right)}}{8} - \frac{3 p^{3} x^{4}}{16} + \frac{3 p^{2} x^{4} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}^{2}}{4} - \frac{3 p^{2} x^{4} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{4} + \frac{3 p^{2} x^{4} \log{\left(c \right)}}{8} + \frac{3 p x^{4} \log{\left(c \right)}^{2} \log{\left(a + b x^{2} \right)}}{4} - \frac{3 p x^{4} \log{\left(c \right)}^{2}}{8} + \frac{x^{4} \log{\left(c \right)}^{3}}{4} & \text{for}\: b \neq 0 \\\frac{x^{4} \log{\left(a^{p} c \right)}^{3}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*p**3*log(a + b*x**2)**3/(4*b**2) + 9*a**2*p**3*log(a + b*x**2)**2/(8*b**2) - 21*a**2*p**3*log(a + b*x**2)/(8*b**2) - 3*a**2*p**2*log(c)*log(a + b*x**2)**2/(4*b**2) + 9*a**2*p**2*log(c)*log(a + b*x**2)/(4*b**2) - 3*a**2*p*log(c)**2*log(a + b*x**2)/(4*b**2) + 3*a*p**3*x**2*log(a + b*x**2)**2/(4*b) - 9*a*p**3*x**2*log(a + b*x**2)/(4*b) + 21*a*p**3*x**2/(8*b) + 3*a*p**2*x**2*log(c)*log(a + b*x**2)/(2*b) - 9*a*p**2*x**2*log(c)/(4*b) + 3*a*p*x**2*log(c)**2/(4*b) + p**3*x**4*log(a + b*x**2)**3/4 - 3*p**3*x**4*log(a + b*x**2)**2/8 + 3*p**3*x**4*log(a + b*x**2)/8 - 3*p**3*x**4/16 + 3*p**2*x**4*log(c)*log(a + b*x**2)**2/4 - 3*p**2*x**4*log(c)*log(a + b*x**2)/4 + 3*p**2*x**4*log(c)/8 + 3*p*x**4*log(c)**2*log(a + b*x**2)/4 - 3*p*x**4*log(c)**2/8 + x**4*log(c)**3/4, Ne(b, 0)), (x**4*log(a**p*c)**3/4, True))","A",0
93,1,301,0,5.332387," ","integrate(x*ln(c*(b*x**2+a)**p)**3,x)","\begin{cases} \frac{a p^{3} \log{\left(a + b x^{2} \right)}^{3}}{2 b} - \frac{3 a p^{3} \log{\left(a + b x^{2} \right)}^{2}}{2 b} + \frac{3 a p^{3} \log{\left(a + b x^{2} \right)}}{b} + \frac{3 a p^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}^{2}}{2 b} - \frac{3 a p^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}}{b} + \frac{3 a p \log{\left(c \right)}^{2} \log{\left(a + b x^{2} \right)}}{2 b} + \frac{p^{3} x^{2} \log{\left(a + b x^{2} \right)}^{3}}{2} - \frac{3 p^{3} x^{2} \log{\left(a + b x^{2} \right)}^{2}}{2} + 3 p^{3} x^{2} \log{\left(a + b x^{2} \right)} - 3 p^{3} x^{2} + \frac{3 p^{2} x^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)}^{2}}{2} - 3 p^{2} x^{2} \log{\left(c \right)} \log{\left(a + b x^{2} \right)} + 3 p^{2} x^{2} \log{\left(c \right)} + \frac{3 p x^{2} \log{\left(c \right)}^{2} \log{\left(a + b x^{2} \right)}}{2} - \frac{3 p x^{2} \log{\left(c \right)}^{2}}{2} + \frac{x^{2} \log{\left(c \right)}^{3}}{2} & \text{for}\: b \neq 0 \\\frac{x^{2} \log{\left(a^{p} c \right)}^{3}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*p**3*log(a + b*x**2)**3/(2*b) - 3*a*p**3*log(a + b*x**2)**2/(2*b) + 3*a*p**3*log(a + b*x**2)/b + 3*a*p**2*log(c)*log(a + b*x**2)**2/(2*b) - 3*a*p**2*log(c)*log(a + b*x**2)/b + 3*a*p*log(c)**2*log(a + b*x**2)/(2*b) + p**3*x**2*log(a + b*x**2)**3/2 - 3*p**3*x**2*log(a + b*x**2)**2/2 + 3*p**3*x**2*log(a + b*x**2) - 3*p**3*x**2 + 3*p**2*x**2*log(c)*log(a + b*x**2)**2/2 - 3*p**2*x**2*log(c)*log(a + b*x**2) + 3*p**2*x**2*log(c) + 3*p*x**2*log(c)**2*log(a + b*x**2)/2 - 3*p*x**2*log(c)**2/2 + x**2*log(c)**3/2, Ne(b, 0)), (x**2*log(a**p*c)**3/2, True))","A",0
94,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**3/x,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}{x}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**3/x, x)","F",0
95,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**3/x**3,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}{x^{3}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**3/x**3, x)","F",0
96,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**3/x**5,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}{x^{5}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**3/x**5, x)","F",0
97,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**3/x**7,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}{x^{7}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**3/x**7, x)","F",0
98,0,0,0,0.000000," ","integrate(x**2*ln(c*(b*x**2+a)**p)**3,x)","\int x^{2} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}\, dx"," ",0,"Integral(x**2*log(c*(a + b*x**2)**p)**3, x)","F",0
99,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**3,x)","\int \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**3, x)","F",0
100,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**3/x**2,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}{x^{2}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**3/x**2, x)","F",0
101,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)**3/x**4,x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}{x^{4}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**3/x**4, x)","F",0
102,0,0,0,0.000000," ","integrate(x**3/ln(c*(b*x**2+a)**p),x)","\int \frac{x^{3}}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral(x**3/log(c*(a + b*x**2)**p), x)","F",0
103,0,0,0,0.000000," ","integrate(x/ln(c*(b*x**2+a)**p),x)","\int \frac{x}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral(x/log(c*(a + b*x**2)**p), x)","F",0
104,0,0,0,0.000000," ","integrate(1/x/ln(c*(b*x**2+a)**p),x)","\int \frac{1}{x \log{\left(c \left(a + b x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/(x*log(c*(a + b*x**2)**p)), x)","F",0
105,0,0,0,0.000000," ","integrate(1/x**3/ln(c*(b*x**2+a)**p),x)","\int \frac{1}{x^{3} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/(x**3*log(c*(a + b*x**2)**p)), x)","F",0
106,0,0,0,0.000000," ","integrate(x**2/ln(c*(b*x**2+a)**p),x)","\int \frac{x^{2}}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral(x**2/log(c*(a + b*x**2)**p), x)","F",0
107,0,0,0,0.000000," ","integrate(1/ln(c*(b*x**2+a)**p),x)","\int \frac{1}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/log(c*(a + b*x**2)**p), x)","F",0
108,0,0,0,0.000000," ","integrate(1/x**2/ln(c*(b*x**2+a)**p),x)","\int \frac{1}{x^{2} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/(x**2*log(c*(a + b*x**2)**p)), x)","F",0
109,0,0,0,0.000000," ","integrate(x**3/ln(c*(b*x**2+a)**p)**2,x)","\int \frac{x^{3}}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(x**3/log(c*(a + b*x**2)**p)**2, x)","F",0
110,0,0,0,0.000000," ","integrate(x/ln(c*(b*x**2+a)**p)**2,x)","\int \frac{x}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(x/log(c*(a + b*x**2)**p)**2, x)","F",0
111,0,0,0,0.000000," ","integrate(1/x/ln(c*(b*x**2+a)**p)**2,x)","\int \frac{1}{x \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(1/(x*log(c*(a + b*x**2)**p)**2), x)","F",0
112,0,0,0,0.000000," ","integrate(1/x**3/ln(c*(b*x**2+a)**p)**2,x)","\int \frac{1}{x^{3} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(1/(x**3*log(c*(a + b*x**2)**p)**2), x)","F",0
113,0,0,0,0.000000," ","integrate(x**2/ln(c*(b*x**2+a)**p)**2,x)","\int \frac{x^{2}}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(x**2/log(c*(a + b*x**2)**p)**2, x)","F",0
114,0,0,0,0.000000," ","integrate(1/ln(c*(b*x**2+a)**p)**2,x)","\int \frac{1}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**(-2), x)","F",0
115,0,0,0,0.000000," ","integrate(1/x**2/ln(c*(b*x**2+a)**p)**2,x)","\int \frac{1}{x^{2} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(1/(x**2*log(c*(a + b*x**2)**p)**2), x)","F",0
116,0,0,0,0.000000," ","integrate(x**3/ln(c*(b*x**2+a)**p)**3,x)","\int \frac{x^{3}}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}\, dx"," ",0,"Integral(x**3/log(c*(a + b*x**2)**p)**3, x)","F",0
117,0,0,0,0.000000," ","integrate(x/ln(c*(b*x**2+a)**p)**3,x)","\int \frac{x}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}\, dx"," ",0,"Integral(x/log(c*(a + b*x**2)**p)**3, x)","F",0
118,0,0,0,0.000000," ","integrate(1/x/ln(c*(b*x**2+a)**p)**3,x)","\int \frac{1}{x \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}\, dx"," ",0,"Integral(1/(x*log(c*(a + b*x**2)**p)**3), x)","F",0
119,0,0,0,0.000000," ","integrate(1/x**3/ln(c*(b*x**2+a)**p)**3,x)","\int \frac{1}{x^{3} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}\, dx"," ",0,"Integral(1/(x**3*log(c*(a + b*x**2)**p)**3), x)","F",0
120,0,0,0,0.000000," ","integrate(x**2/ln(c*(b*x**2+a)**p)**3,x)","\int \frac{x^{2}}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}\, dx"," ",0,"Integral(x**2/log(c*(a + b*x**2)**p)**3, x)","F",0
121,0,0,0,0.000000," ","integrate(1/ln(c*(b*x**2+a)**p)**3,x)","\int \frac{1}{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)**(-3), x)","F",0
122,0,0,0,0.000000," ","integrate(1/x**2/ln(c*(b*x**2+a)**p)**3,x)","\int \frac{1}{x^{2} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}^{3}}\, dx"," ",0,"Integral(1/(x**2*log(c*(a + b*x**2)**p)**3), x)","F",0
123,0,0,0,0.000000," ","integrate(x**3/ln(c*(b*x**2+a)),x)","\int \frac{x^{3}}{\log{\left(a c + b c x^{2} \right)}}\, dx"," ",0,"Integral(x**3/log(a*c + b*c*x**2), x)","F",0
124,1,27,0,2.155389," ","integrate(x/ln(c*(b*x**2+a)),x)","\begin{cases} \frac{x^{2}}{2 \log{\left(a c \right)}} & \text{for}\: b = 0 \\0 & \text{for}\: c = 0 \\\frac{\operatorname{Ei}{\left(\log{\left(a c + b c x^{2} \right)} \right)}}{2 b c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2/(2*log(a*c)), Eq(b, 0)), (0, Eq(c, 0)), (Ei(log(a*c + b*c*x**2))/(2*b*c), True))","A",0
125,0,0,0,0.000000," ","integrate(x**3/ln(c*(b*x**2+a))**2,x)","\frac{- a x^{2} - b x^{4}}{2 b \log{\left(c \left(a + b x^{2}\right) \right)}} + \frac{\int \frac{a x}{\log{\left(a c + b c x^{2} \right)}}\, dx + \int \frac{2 b x^{3}}{\log{\left(a c + b c x^{2} \right)}}\, dx}{b}"," ",0,"(-a*x**2 - b*x**4)/(2*b*log(c*(a + b*x**2))) + (Integral(a*x/log(a*c + b*c*x**2), x) + Integral(2*b*x**3/log(a*c + b*c*x**2), x))/b","F",0
126,1,49,0,2.162686," ","integrate(x/ln(c*(b*x**2+a))**2,x)","\begin{cases} \frac{x^{2}}{2 \log{\left(a c \right)}} & \text{for}\: b = 0 \\0 & \text{for}\: c = 0 \\\frac{\operatorname{Ei}{\left(\log{\left(a c + b c x^{2} \right)} \right)}}{2 b c} & \text{otherwise} \end{cases} + \frac{- a - b x^{2}}{2 b \log{\left(c \left(a + b x^{2}\right) \right)}}"," ",0,"Piecewise((x**2/(2*log(a*c)), Eq(b, 0)), (0, Eq(c, 0)), (Ei(log(a*c + b*c*x**2))/(2*b*c), True)) + (-a - b*x**2)/(2*b*log(c*(a + b*x**2)))","A",0
127,0,0,0,0.000000," ","integrate(x**3/ln(c*(b*x**2+a))**3,x)","\frac{\int \frac{3 a x}{\log{\left(a c + b c x^{2} \right)}}\, dx + \int \frac{4 b x^{3}}{\log{\left(a c + b c x^{2} \right)}}\, dx}{2 b} + \frac{- a b x^{2} - b^{2} x^{4} + \left(- a^{2} - 3 a b x^{2} - 2 b^{2} x^{4}\right) \log{\left(c \left(a + b x^{2}\right) \right)}}{4 b^{2} \log{\left(c \left(a + b x^{2}\right) \right)}^{2}}"," ",0,"(Integral(3*a*x/log(a*c + b*c*x**2), x) + Integral(4*b*x**3/log(a*c + b*c*x**2), x))/(2*b) + (-a*b*x**2 - b**2*x**4 + (-a**2 - 3*a*b*x**2 - 2*b**2*x**4)*log(c*(a + b*x**2)))/(4*b**2*log(c*(a + b*x**2))**2)","F",0
128,1,70,0,2.194567," ","integrate(x/ln(c*(b*x**2+a))**3,x)","\frac{\begin{cases} \frac{x^{2}}{2 \log{\left(a c \right)}} & \text{for}\: b = 0 \\0 & \text{for}\: c = 0 \\\frac{\operatorname{Ei}{\left(\log{\left(a c + b c x^{2} \right)} \right)}}{2 b c} & \text{otherwise} \end{cases}}{2} + \frac{- a - b x^{2} + \left(- a - b x^{2}\right) \log{\left(c \left(a + b x^{2}\right) \right)}}{4 b \log{\left(c \left(a + b x^{2}\right) \right)}^{2}}"," ",0,"Piecewise((x**2/(2*log(a*c)), Eq(b, 0)), (0, Eq(c, 0)), (Ei(log(a*c + b*c*x**2))/(2*b*c), True))/2 + (-a - b*x**2 + (-a - b*x**2)*log(c*(a + b*x**2)))/(4*b*log(c*(a + b*x**2))**2)","A",0
129,1,206,0,31.917978," ","integrate(x**5*ln(c*(e*x**3+d)**p)**2,x)","\begin{cases} - \frac{d^{2} p^{2} \log{\left(d + e x^{3} \right)}^{2}}{6 e^{2}} + \frac{d^{2} p^{2} \log{\left(d + e x^{3} \right)}}{2 e^{2}} - \frac{d^{2} p \log{\left(c \right)} \log{\left(d + e x^{3} \right)}}{3 e^{2}} + \frac{d p^{2} x^{3} \log{\left(d + e x^{3} \right)}}{3 e} - \frac{d p^{2} x^{3}}{2 e} + \frac{d p x^{3} \log{\left(c \right)}}{3 e} + \frac{p^{2} x^{6} \log{\left(d + e x^{3} \right)}^{2}}{6} - \frac{p^{2} x^{6} \log{\left(d + e x^{3} \right)}}{6} + \frac{p^{2} x^{6}}{12} + \frac{p x^{6} \log{\left(c \right)} \log{\left(d + e x^{3} \right)}}{3} - \frac{p x^{6} \log{\left(c \right)}}{6} + \frac{x^{6} \log{\left(c \right)}^{2}}{6} & \text{for}\: e \neq 0 \\\frac{x^{6} \log{\left(c d^{p} \right)}^{2}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-d**2*p**2*log(d + e*x**3)**2/(6*e**2) + d**2*p**2*log(d + e*x**3)/(2*e**2) - d**2*p*log(c)*log(d + e*x**3)/(3*e**2) + d*p**2*x**3*log(d + e*x**3)/(3*e) - d*p**2*x**3/(2*e) + d*p*x**3*log(c)/(3*e) + p**2*x**6*log(d + e*x**3)**2/6 - p**2*x**6*log(d + e*x**3)/6 + p**2*x**6/12 + p*x**6*log(c)*log(d + e*x**3)/3 - p*x**6*log(c)/6 + x**6*log(c)**2/6, Ne(e, 0)), (x**6*log(c*d**p)**2/6, True))","A",0
130,1,160,0,7.878632," ","integrate(x**2*ln(c*(e*x**3+d)**p)**2,x)","\begin{cases} \frac{d p^{2} \log{\left(d + e x^{3} \right)}^{2}}{3 e} - \frac{2 d p^{2} \log{\left(d + e x^{3} \right)}}{3 e} + \frac{2 d p \log{\left(c \right)} \log{\left(d + e x^{3} \right)}}{3 e} + \frac{p^{2} x^{3} \log{\left(d + e x^{3} \right)}^{2}}{3} - \frac{2 p^{2} x^{3} \log{\left(d + e x^{3} \right)}}{3} + \frac{2 p^{2} x^{3}}{3} + \frac{2 p x^{3} \log{\left(c \right)} \log{\left(d + e x^{3} \right)}}{3} - \frac{2 p x^{3} \log{\left(c \right)}}{3} + \frac{x^{3} \log{\left(c \right)}^{2}}{3} & \text{for}\: e \neq 0 \\\frac{x^{3} \log{\left(c d^{p} \right)}^{2}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*p**2*log(d + e*x**3)**2/(3*e) - 2*d*p**2*log(d + e*x**3)/(3*e) + 2*d*p*log(c)*log(d + e*x**3)/(3*e) + p**2*x**3*log(d + e*x**3)**2/3 - 2*p**2*x**3*log(d + e*x**3)/3 + 2*p**2*x**3/3 + 2*p*x**3*log(c)*log(d + e*x**3)/3 - 2*p*x**3*log(c)/3 + x**3*log(c)**2/3, Ne(e, 0)), (x**3*log(c*d**p)**2/3, True))","A",0
131,0,0,0,0.000000," ","integrate(ln(c*(e*x**3+d)**p)**2/x,x)","\int \frac{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}{x}\, dx"," ",0,"Integral(log(c*(d + e*x**3)**p)**2/x, x)","F",0
132,0,0,0,0.000000," ","integrate(ln(c*(e*x**3+d)**p)**2/x**4,x)","\int \frac{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}{x^{4}}\, dx"," ",0,"Integral(log(c*(d + e*x**3)**p)**2/x**4, x)","F",0
133,0,0,0,0.000000," ","integrate(x*ln(c*(e*x**3+d)**p)**2,x)","\int x \log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral(x*log(c*(d + e*x**3)**p)**2, x)","F",0
134,0,0,0,0.000000," ","integrate(ln(c*(e*x**3+d)**p)**2,x)","\int \log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral(log(c*(d + e*x**3)**p)**2, x)","F",0
135,0,0,0,0.000000," ","integrate(ln(c*(e*x**3+d)**p)**2/x**2,x)","\int \frac{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}{x^{2}}\, dx"," ",0,"Integral(log(c*(d + e*x**3)**p)**2/x**2, x)","F",0
136,0,0,0,0.000000," ","integrate(ln(c*(e*x**3+d)**p)**2/x**3,x)","\int \frac{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}{x^{3}}\, dx"," ",0,"Integral(log(c*(d + e*x**3)**p)**2/x**3, x)","F",0
137,-1,0,0,0.000000," ","integrate(ln(c*(e*x**3+d)**p)**2/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,0,0,0,0.000000," ","integrate(x**8/ln(c*(e*x**3+d)**p),x)","\int \frac{x^{8}}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(x**8/log(c*(d + e*x**3)**p), x)","F",0
139,0,0,0,0.000000," ","integrate(x**5/ln(c*(e*x**3+d)**p),x)","\int \frac{x^{5}}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(x**5/log(c*(d + e*x**3)**p), x)","F",0
140,0,0,0,0.000000," ","integrate(x**2/ln(c*(e*x**3+d)**p),x)","\int \frac{x^{2}}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(x**2/log(c*(d + e*x**3)**p), x)","F",0
141,0,0,0,0.000000," ","integrate(1/x/ln(c*(e*x**3+d)**p),x)","\int \frac{1}{x \log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/(x*log(c*(d + e*x**3)**p)), x)","F",0
142,0,0,0,0.000000," ","integrate(1/x**4/ln(c*(e*x**3+d)**p),x)","\int \frac{1}{x^{4} \log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/(x**4*log(c*(d + e*x**3)**p)), x)","F",0
143,0,0,0,0.000000," ","integrate(x**3/ln(c*(e*x**3+d)**p),x)","\int \frac{x^{3}}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(x**3/log(c*(d + e*x**3)**p), x)","F",0
144,0,0,0,0.000000," ","integrate(x/ln(c*(e*x**3+d)**p),x)","\int \frac{x}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(x/log(c*(d + e*x**3)**p), x)","F",0
145,0,0,0,0.000000," ","integrate(1/ln(c*(e*x**3+d)**p),x)","\int \frac{1}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/log(c*(d + e*x**3)**p), x)","F",0
146,0,0,0,0.000000," ","integrate(1/x**2/ln(c*(e*x**3+d)**p),x)","\int \frac{1}{x^{2} \log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/(x**2*log(c*(d + e*x**3)**p)), x)","F",0
147,0,0,0,0.000000," ","integrate(1/x**3/ln(c*(e*x**3+d)**p),x)","\int \frac{1}{x^{3} \log{\left(c \left(d + e x^{3}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/(x**3*log(c*(d + e*x**3)**p)), x)","F",0
148,0,0,0,0.000000," ","integrate(x**8/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{x^{8}}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(x**8/log(c*(d + e*x**3)**p)**2, x)","F",0
149,0,0,0,0.000000," ","integrate(x**5/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{x^{5}}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(x**5/log(c*(d + e*x**3)**p)**2, x)","F",0
150,0,0,0,0.000000," ","integrate(x**2/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{x^{2}}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(x**2/log(c*(d + e*x**3)**p)**2, x)","F",0
151,0,0,0,0.000000," ","integrate(1/x/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{1}{x \log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(1/(x*log(c*(d + e*x**3)**p)**2), x)","F",0
152,0,0,0,0.000000," ","integrate(1/x**4/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{1}{x^{4} \log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(1/(x**4*log(c*(d + e*x**3)**p)**2), x)","F",0
153,0,0,0,0.000000," ","integrate(x**3/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{x^{3}}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(x**3/log(c*(d + e*x**3)**p)**2, x)","F",0
154,0,0,0,0.000000," ","integrate(x/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{x}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(x/log(c*(d + e*x**3)**p)**2, x)","F",0
155,0,0,0,0.000000," ","integrate(1/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{1}{\log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(log(c*(d + e*x**3)**p)**(-2), x)","F",0
156,0,0,0,0.000000," ","integrate(1/x**2/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{1}{x^{2} \log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(1/(x**2*log(c*(d + e*x**3)**p)**2), x)","F",0
157,0,0,0,0.000000," ","integrate(1/x**3/ln(c*(e*x**3+d)**p)**2,x)","\int \frac{1}{x^{3} \log{\left(c \left(d + e x^{3}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(1/(x**3*log(c*(d + e*x**3)**p)**2), x)","F",0
158,-1,0,0,0.000000," ","integrate((f*x)**m*ln(c*(e*x**2+d)**p)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,0,0,0,0.000000," ","integrate((f*x)**m*ln(c*(e*x**2+d)**p)**2,x)","\int \left(f x\right)^{m} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral((f*x)**m*log(c*(d + e*x**2)**p)**2, x)","F",0
160,1,359,0,94.765586," ","integrate((f*x)**m*ln(c*(e*x**2+d)**p),x)","- 2 e p \left(\begin{cases} \frac{0^{m} \sqrt{- \frac{d}{e^{3}}} \log{\left(- e \sqrt{- \frac{d}{e^{3}}} + x \right)}}{2} - \frac{0^{m} \sqrt{- \frac{d}{e^{3}}} \log{\left(e \sqrt{- \frac{d}{e^{3}}} + x \right)}}{2} + \frac{0^{m} x}{e} & \text{for}\: \left(f = 0 \wedge m \neq -1\right) \vee f = 0 \\\frac{f f^{m} m x^{3} x^{m} \Phi\left(\frac{e x^{2} e^{i \pi}}{d}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 d f m \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 4 d f \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{3 f f^{m} x^{3} x^{m} \Phi\left(\frac{e x^{2} e^{i \pi}}{d}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 d f m \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 4 d f \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} & \text{for}\: m > -\infty \wedge m < \infty \wedge m \neq -1 \\- \frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{otherwise} \end{cases}}{2 e f} + \frac{\log{\left(f x \right)} \log{\left(d + e x^{2} \right)}}{2 e f} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0^{m} x & \text{for}\: f = 0 \\\frac{\begin{cases} \frac{\left(f x\right)^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(f x \right)} & \text{otherwise} \end{cases}}{f} & \text{otherwise} \end{cases}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}"," ",0,"-2*e*p*Piecewise((0**m*sqrt(-d/e**3)*log(-e*sqrt(-d/e**3) + x)/2 - 0**m*sqrt(-d/e**3)*log(e*sqrt(-d/e**3) + x)/2 + 0**m*x/e, Eq(f, 0) | (Eq(f, 0) & Ne(m, -1))), (f*f**m*m*x**3*x**m*lerchphi(e*x**2*exp_polar(I*pi)/d, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*d*f*m*gamma(m/2 + 5/2) + 4*d*f*gamma(m/2 + 5/2)) + 3*f*f**m*x**3*x**m*lerchphi(e*x**2*exp_polar(I*pi)/d, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*d*f*m*gamma(m/2 + 5/2) + 4*d*f*gamma(m/2 + 5/2)), (m > -oo) & (m < oo) & Ne(m, -1)), (-Piecewise((log(d)*log(x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, True))/(2*e*f) + log(f*x)*log(d + e*x**2)/(2*e*f), True)) + Piecewise((0**m*x, Eq(f, 0)), (Piecewise(((f*x)**(m + 1)/(m + 1), Ne(m, -1)), (log(f*x), True))/f, True))*log(c*(d + e*x**2)**p)","A",0
161,0,0,0,0.000000," ","integrate((f*x)**m/ln(c*(e*x**2+d)**p),x)","\int \frac{\left(f x\right)^{m}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral((f*x)**m/log(c*(d + e*x**2)**p), x)","F",0
162,0,0,0,0.000000," ","integrate((f*x)**m/ln(c*(e*x**2+d)**p)**2,x)","\int \frac{\left(f x\right)^{m}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral((f*x)**m/log(c*(d + e*x**2)**p)**2, x)","F",0
163,-1,0,0,0.000000," ","integrate((f*x)**(-1+3*n)*ln(c*(d+e*x**n)**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate((f*x)**(-1+2*n)*ln(c*(d+e*x**n)**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((f*x)**(-1+n)*ln(c*(d+e*x**n)**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)**2/f/x,x)","\frac{\int \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}^{2}}{x}\, dx}{f}"," ",0,"Integral(log(c*(d + e*x**n)**p)**2/x, x)/f","F",0
167,-1,0,0,0.000000," ","integrate((f*x)**(-1-n)*ln(c*(d+e*x**n)**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate((f*x)**(-1-2*n)*ln(c*(d+e*x**n)**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,1,14,0,3.115532," ","integrate(ln(1+e*x**n)/x,x)","- \frac{\operatorname{Li}_{2}\left(e x^{n} e^{i \pi}\right)}{n}"," ",0,"-polylog(2, e*x**n*exp_polar(I*pi))/n","C",0
170,1,78,0,3.723301," ","integrate(ln(2+e*x**n)/x,x)","\begin{cases} \log{\left(2 \right)} \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{n} e^{i \pi}}{2}\right)}{n} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(2 \right)} \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{n} e^{i \pi}}{2}\right)}{n} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{n} e^{i \pi}}{2}\right)}{n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(2)*log(x) - polylog(2, e*x**n*exp_polar(I*pi)/2)/n, Abs(x) < 1), (-log(2)*log(1/x) - polylog(2, e*x**n*exp_polar(I*pi)/2)/n, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(2) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(2) - polylog(2, e*x**n*exp_polar(I*pi)/2)/n, True))","C",0
171,1,78,0,3.868329," ","integrate(ln(6+2*e*x**n)/x,x)","\begin{cases} \log{\left(6 \right)} \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{n} e^{i \pi}}{3}\right)}{n} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(6 \right)} \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{n} e^{i \pi}}{3}\right)}{n} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(6 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(6 \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{n} e^{i \pi}}{3}\right)}{n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(6)*log(x) - polylog(2, e*x**n*exp_polar(I*pi)/3)/n, Abs(x) < 1), (-log(6)*log(1/x) - polylog(2, e*x**n*exp_polar(I*pi)/3)/n, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(6) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(6) - polylog(2, e*x**n*exp_polar(I*pi)/3)/n, True))","C",0
172,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n))/x,x)","\int \frac{\log{\left(c d + c e x^{n} \right)}}{x}\, dx"," ",0,"Integral(log(c*d + c*e*x**n)/x, x)","F",0
173,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x,x)","\int \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(log(c*(d + e*x**n)**p)/x, x)","F",0
174,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)**2/x,x)","\int \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}^{2}}{x}\, dx"," ",0,"Integral(log(c*(d + e*x**n)**p)**2/x, x)","F",0
175,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)**3/x,x)","\int \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}^{3}}{x}\, dx"," ",0,"Integral(log(c*(d + e*x**n)**p)**3/x, x)","F",0
176,1,369,0,6.403831," ","integrate((e*x+d)**3*ln(c*(b*x+a)**p),x)","\begin{cases} - \frac{a^{4} e^{3} p \log{\left(a + b x \right)}}{4 b^{4}} + \frac{a^{3} d e^{2} p \log{\left(a + b x \right)}}{b^{3}} + \frac{a^{3} e^{3} p x}{4 b^{3}} - \frac{3 a^{2} d^{2} e p \log{\left(a + b x \right)}}{2 b^{2}} - \frac{a^{2} d e^{2} p x}{b^{2}} - \frac{a^{2} e^{3} p x^{2}}{8 b^{2}} + \frac{a d^{3} p \log{\left(a + b x \right)}}{b} + \frac{3 a d^{2} e p x}{2 b} + \frac{a d e^{2} p x^{2}}{2 b} + \frac{a e^{3} p x^{3}}{12 b} + d^{3} p x \log{\left(a + b x \right)} - d^{3} p x + d^{3} x \log{\left(c \right)} + \frac{3 d^{2} e p x^{2} \log{\left(a + b x \right)}}{2} - \frac{3 d^{2} e p x^{2}}{4} + \frac{3 d^{2} e x^{2} \log{\left(c \right)}}{2} + d e^{2} p x^{3} \log{\left(a + b x \right)} - \frac{d e^{2} p x^{3}}{3} + d e^{2} x^{3} \log{\left(c \right)} + \frac{e^{3} p x^{4} \log{\left(a + b x \right)}}{4} - \frac{e^{3} p x^{4}}{16} + \frac{e^{3} x^{4} \log{\left(c \right)}}{4} & \text{for}\: b \neq 0 \\\left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) \log{\left(a^{p} c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*e**3*p*log(a + b*x)/(4*b**4) + a**3*d*e**2*p*log(a + b*x)/b**3 + a**3*e**3*p*x/(4*b**3) - 3*a**2*d**2*e*p*log(a + b*x)/(2*b**2) - a**2*d*e**2*p*x/b**2 - a**2*e**3*p*x**2/(8*b**2) + a*d**3*p*log(a + b*x)/b + 3*a*d**2*e*p*x/(2*b) + a*d*e**2*p*x**2/(2*b) + a*e**3*p*x**3/(12*b) + d**3*p*x*log(a + b*x) - d**3*p*x + d**3*x*log(c) + 3*d**2*e*p*x**2*log(a + b*x)/2 - 3*d**2*e*p*x**2/4 + 3*d**2*e*x**2*log(c)/2 + d*e**2*p*x**3*log(a + b*x) - d*e**2*p*x**3/3 + d*e**2*x**3*log(c) + e**3*p*x**4*log(a + b*x)/4 - e**3*p*x**4/16 + e**3*x**4*log(c)/4, Ne(b, 0)), ((d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4)*log(a**p*c), True))","A",0
177,1,223,0,3.019203," ","integrate((e*x+d)**2*ln(c*(b*x+a)**p),x)","\begin{cases} \frac{a^{3} e^{2} p \log{\left(a + b x \right)}}{3 b^{3}} - \frac{a^{2} d e p \log{\left(a + b x \right)}}{b^{2}} - \frac{a^{2} e^{2} p x}{3 b^{2}} + \frac{a d^{2} p \log{\left(a + b x \right)}}{b} + \frac{a d e p x}{b} + \frac{a e^{2} p x^{2}}{6 b} + d^{2} p x \log{\left(a + b x \right)} - d^{2} p x + d^{2} x \log{\left(c \right)} + d e p x^{2} \log{\left(a + b x \right)} - \frac{d e p x^{2}}{2} + d e x^{2} \log{\left(c \right)} + \frac{e^{2} p x^{3} \log{\left(a + b x \right)}}{3} - \frac{e^{2} p x^{3}}{9} + \frac{e^{2} x^{3} \log{\left(c \right)}}{3} & \text{for}\: b \neq 0 \\\left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) \log{\left(a^{p} c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*e**2*p*log(a + b*x)/(3*b**3) - a**2*d*e*p*log(a + b*x)/b**2 - a**2*e**2*p*x/(3*b**2) + a*d**2*p*log(a + b*x)/b + a*d*e*p*x/b + a*e**2*p*x**2/(6*b) + d**2*p*x*log(a + b*x) - d**2*p*x + d**2*x*log(c) + d*e*p*x**2*log(a + b*x) - d*e*p*x**2/2 + d*e*x**2*log(c) + e**2*p*x**3*log(a + b*x)/3 - e**2*p*x**3/9 + e**2*x**3*log(c)/3, Ne(b, 0)), ((d**2*x + d*e*x**2 + e**2*x**3/3)*log(a**p*c), True))","A",0
178,1,116,0,1.377255," ","integrate((e*x+d)*ln(c*(b*x+a)**p),x)","\begin{cases} - \frac{a^{2} e p \log{\left(a + b x \right)}}{2 b^{2}} + \frac{a d p \log{\left(a + b x \right)}}{b} + \frac{a e p x}{2 b} + d p x \log{\left(a + b x \right)} - d p x + d x \log{\left(c \right)} + \frac{e p x^{2} \log{\left(a + b x \right)}}{2} - \frac{e p x^{2}}{4} + \frac{e x^{2} \log{\left(c \right)}}{2} & \text{for}\: b \neq 0 \\\left(d x + \frac{e x^{2}}{2}\right) \log{\left(a^{p} c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*e*p*log(a + b*x)/(2*b**2) + a*d*p*log(a + b*x)/b + a*e*p*x/(2*b) + d*p*x*log(a + b*x) - d*p*x + d*x*log(c) + e*p*x**2*log(a + b*x)/2 - e*p*x**2/4 + e*x**2*log(c)/2, Ne(b, 0)), ((d*x + e*x**2/2)*log(a**p*c), True))","A",0
179,1,37,0,0.459110," ","integrate(ln(c*(b*x+a)**p),x)","\begin{cases} \frac{a p \log{\left(a + b x \right)}}{b} + p x \log{\left(a + b x \right)} - p x + x \log{\left(c \right)} & \text{for}\: b \neq 0 \\x \log{\left(a^{p} c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*p*log(a + b*x)/b + p*x*log(a + b*x) - p*x + x*log(c), Ne(b, 0)), (x*log(a**p*c), True))","A",0
180,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**p)/(e*x+d),x)","\int \frac{\log{\left(c \left(a + b x\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(log(c*(a + b*x)**p)/(d + e*x), x)","F",0
181,-2,0,0,0.000000," ","integrate(ln(c*(b*x+a)**p)/(e*x+d)**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
182,-2,0,0,0.000000," ","integrate(ln(c*(b*x+a)**p)/(e*x+d)**3,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
183,1,6069,0,39.660703," ","integrate(ln(c*(b*x+a)**p)/(e*x+d)**4,x)","\begin{cases} - \frac{3 p \log{\left(\frac{b d}{e} + b x \right)}}{9 d^{3} e + 27 d^{2} e^{2} x + 27 d e^{3} x^{2} + 9 e^{4} x^{3}} - \frac{p}{9 d^{3} e + 27 d^{2} e^{2} x + 27 d e^{3} x^{2} + 9 e^{4} x^{3}} - \frac{3 \log{\left(c \right)}}{9 d^{3} e + 27 d^{2} e^{2} x + 27 d e^{3} x^{2} + 9 e^{4} x^{3}} & \text{for}\: a = \frac{b d}{e} \\\frac{\frac{a p \log{\left(a + b x \right)}}{b} + p x \log{\left(a + b x \right)} - p x + x \log{\left(c \right)}}{d^{4}} & \text{for}\: e = 0 \\- \frac{2 a^{3} e^{3} p \log{\left(a + b x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{2 a^{3} e^{3} \log{\left(c \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} + \frac{6 a^{2} b d e^{2} p \log{\left(a + b x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{a^{2} b d e^{2} p}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} + \frac{6 a^{2} b d e^{2} \log{\left(c \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{a^{2} b e^{3} p x}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{6 a b^{2} d^{2} e p \log{\left(a + b x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} + \frac{4 a b^{2} d^{2} e p}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{6 a b^{2} d^{2} e \log{\left(c \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} + \frac{6 a b^{2} d e^{2} p x}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} + \frac{2 a b^{2} e^{3} p x^{2}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} + \frac{2 b^{3} d^{3} p \log{\left(\frac{d}{e} + x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{3 b^{3} d^{3} p}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{6 b^{3} d^{2} e p x \log{\left(a + b x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} + \frac{6 b^{3} d^{2} e p x \log{\left(\frac{d}{e} + x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{5 b^{3} d^{2} e p x}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{6 b^{3} d^{2} e x \log{\left(c \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{6 b^{3} d e^{2} p x^{2} \log{\left(a + b x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} + \frac{6 b^{3} d e^{2} p x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{2 b^{3} d e^{2} p x^{2}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{6 b^{3} d e^{2} x^{2} \log{\left(c \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{2 b^{3} e^{3} p x^{3} \log{\left(a + b x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} + \frac{2 b^{3} e^{3} p x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} - \frac{2 b^{3} e^{3} x^{3} \log{\left(c \right)}}{6 a^{3} d^{3} e^{4} + 18 a^{3} d^{2} e^{5} x + 18 a^{3} d e^{6} x^{2} + 6 a^{3} e^{7} x^{3} - 18 a^{2} b d^{4} e^{3} - 54 a^{2} b d^{3} e^{4} x - 54 a^{2} b d^{2} e^{5} x^{2} - 18 a^{2} b d e^{6} x^{3} + 18 a b^{2} d^{5} e^{2} + 54 a b^{2} d^{4} e^{3} x + 54 a b^{2} d^{3} e^{4} x^{2} + 18 a b^{2} d^{2} e^{5} x^{3} - 6 b^{3} d^{6} e - 18 b^{3} d^{5} e^{2} x - 18 b^{3} d^{4} e^{3} x^{2} - 6 b^{3} d^{3} e^{4} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*p*log(b*d/e + b*x)/(9*d**3*e + 27*d**2*e**2*x + 27*d*e**3*x**2 + 9*e**4*x**3) - p/(9*d**3*e + 27*d**2*e**2*x + 27*d*e**3*x**2 + 9*e**4*x**3) - 3*log(c)/(9*d**3*e + 27*d**2*e**2*x + 27*d*e**3*x**2 + 9*e**4*x**3), Eq(a, b*d/e)), ((a*p*log(a + b*x)/b + p*x*log(a + b*x) - p*x + x*log(c))/d**4, Eq(e, 0)), (-2*a**3*e**3*p*log(a + b*x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 2*a**3*e**3*log(c)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) + 6*a**2*b*d*e**2*p*log(a + b*x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - a**2*b*d*e**2*p/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) + 6*a**2*b*d*e**2*log(c)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - a**2*b*e**3*p*x/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 6*a*b**2*d**2*e*p*log(a + b*x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) + 4*a*b**2*d**2*e*p/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 6*a*b**2*d**2*e*log(c)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) + 6*a*b**2*d*e**2*p*x/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) + 2*a*b**2*e**3*p*x**2/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) + 2*b**3*d**3*p*log(d/e + x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 3*b**3*d**3*p/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 6*b**3*d**2*e*p*x*log(a + b*x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) + 6*b**3*d**2*e*p*x*log(d/e + x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 5*b**3*d**2*e*p*x/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 6*b**3*d**2*e*x*log(c)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 6*b**3*d*e**2*p*x**2*log(a + b*x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) + 6*b**3*d*e**2*p*x**2*log(d/e + x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 2*b**3*d*e**2*p*x**2/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 6*b**3*d*e**2*x**2*log(c)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 2*b**3*e**3*p*x**3*log(a + b*x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) + 2*b**3*e**3*p*x**3*log(d/e + x)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3) - 2*b**3*e**3*x**3*log(c)/(6*a**3*d**3*e**4 + 18*a**3*d**2*e**5*x + 18*a**3*d*e**6*x**2 + 6*a**3*e**7*x**3 - 18*a**2*b*d**4*e**3 - 54*a**2*b*d**3*e**4*x - 54*a**2*b*d**2*e**5*x**2 - 18*a**2*b*d*e**6*x**3 + 18*a*b**2*d**5*e**2 + 54*a*b**2*d**4*e**3*x + 54*a*b**2*d**3*e**4*x**2 + 18*a*b**2*d**2*e**5*x**3 - 6*b**3*d**6*e - 18*b**3*d**5*e**2*x - 18*b**3*d**4*e**3*x**2 - 6*b**3*d**3*e**4*x**3), True))","A",0
184,1,422,0,47.872727," ","integrate((e*x+d)**3*ln(c*(b*x**2+a)**p),x)","\begin{cases} - \frac{i a^{\frac{3}{2}} d e^{2} p \log{\left(a + b x^{2} \right)}}{b^{2} \sqrt{\frac{1}{b}}} + \frac{2 i a^{\frac{3}{2}} d e^{2} p \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{b^{2} \sqrt{\frac{1}{b}}} + \frac{i \sqrt{a} d^{3} p \log{\left(a + b x^{2} \right)}}{b \sqrt{\frac{1}{b}}} - \frac{2 i \sqrt{a} d^{3} p \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{b \sqrt{\frac{1}{b}}} - \frac{a^{2} e^{3} p \log{\left(a + b x^{2} \right)}}{4 b^{2}} + \frac{3 a d^{2} e p \log{\left(a + b x^{2} \right)}}{2 b} + \frac{2 a d e^{2} p x}{b} + \frac{a e^{3} p x^{2}}{4 b} + d^{3} p x \log{\left(a + b x^{2} \right)} - 2 d^{3} p x + d^{3} x \log{\left(c \right)} + \frac{3 d^{2} e p x^{2} \log{\left(a + b x^{2} \right)}}{2} - \frac{3 d^{2} e p x^{2}}{2} + \frac{3 d^{2} e x^{2} \log{\left(c \right)}}{2} + d e^{2} p x^{3} \log{\left(a + b x^{2} \right)} - \frac{2 d e^{2} p x^{3}}{3} + d e^{2} x^{3} \log{\left(c \right)} + \frac{e^{3} p x^{4} \log{\left(a + b x^{2} \right)}}{4} - \frac{e^{3} p x^{4}}{8} + \frac{e^{3} x^{4} \log{\left(c \right)}}{4} & \text{for}\: b \neq 0 \\\left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) \log{\left(a^{p} c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**(3/2)*d*e**2*p*log(a + b*x**2)/(b**2*sqrt(1/b)) + 2*I*a**(3/2)*d*e**2*p*log(-I*sqrt(a)*sqrt(1/b) + x)/(b**2*sqrt(1/b)) + I*sqrt(a)*d**3*p*log(a + b*x**2)/(b*sqrt(1/b)) - 2*I*sqrt(a)*d**3*p*log(-I*sqrt(a)*sqrt(1/b) + x)/(b*sqrt(1/b)) - a**2*e**3*p*log(a + b*x**2)/(4*b**2) + 3*a*d**2*e*p*log(a + b*x**2)/(2*b) + 2*a*d*e**2*p*x/b + a*e**3*p*x**2/(4*b) + d**3*p*x*log(a + b*x**2) - 2*d**3*p*x + d**3*x*log(c) + 3*d**2*e*p*x**2*log(a + b*x**2)/2 - 3*d**2*e*p*x**2/2 + 3*d**2*e*x**2*log(c)/2 + d*e**2*p*x**3*log(a + b*x**2) - 2*d*e**2*p*x**3/3 + d*e**2*x**3*log(c) + e**3*p*x**4*log(a + b*x**2)/4 - e**3*p*x**4/8 + e**3*x**4*log(c)/4, Ne(b, 0)), ((d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4)*log(a**p*c), True))","A",0
185,1,309,0,24.022755," ","integrate((e*x+d)**2*ln(c*(b*x**2+a)**p),x)","\begin{cases} - \frac{i a^{\frac{3}{2}} e^{2} p \log{\left(a + b x^{2} \right)}}{3 b^{2} \sqrt{\frac{1}{b}}} + \frac{2 i a^{\frac{3}{2}} e^{2} p \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{3 b^{2} \sqrt{\frac{1}{b}}} + \frac{i \sqrt{a} d^{2} p \log{\left(a + b x^{2} \right)}}{b \sqrt{\frac{1}{b}}} - \frac{2 i \sqrt{a} d^{2} p \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{b \sqrt{\frac{1}{b}}} + \frac{a d e p \log{\left(a + b x^{2} \right)}}{b} + \frac{2 a e^{2} p x}{3 b} + d^{2} p x \log{\left(a + b x^{2} \right)} - 2 d^{2} p x + d^{2} x \log{\left(c \right)} + d e p x^{2} \log{\left(a + b x^{2} \right)} - d e p x^{2} + d e x^{2} \log{\left(c \right)} + \frac{e^{2} p x^{3} \log{\left(a + b x^{2} \right)}}{3} - \frac{2 e^{2} p x^{3}}{9} + \frac{e^{2} x^{3} \log{\left(c \right)}}{3} & \text{for}\: b \neq 0 \\\left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) \log{\left(a^{p} c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**(3/2)*e**2*p*log(a + b*x**2)/(3*b**2*sqrt(1/b)) + 2*I*a**(3/2)*e**2*p*log(-I*sqrt(a)*sqrt(1/b) + x)/(3*b**2*sqrt(1/b)) + I*sqrt(a)*d**2*p*log(a + b*x**2)/(b*sqrt(1/b)) - 2*I*sqrt(a)*d**2*p*log(-I*sqrt(a)*sqrt(1/b) + x)/(b*sqrt(1/b)) + a*d*e*p*log(a + b*x**2)/b + 2*a*e**2*p*x/(3*b) + d**2*p*x*log(a + b*x**2) - 2*d**2*p*x + d**2*x*log(c) + d*e*p*x**2*log(a + b*x**2) - d*e*p*x**2 + d*e*x**2*log(c) + e**2*p*x**3*log(a + b*x**2)/3 - 2*e**2*p*x**3/9 + e**2*x**3*log(c)/3, Ne(b, 0)), ((d**2*x + d*e*x**2 + e**2*x**3/3)*log(a**p*c), True))","A",0
186,1,160,0,11.676859," ","integrate((e*x+d)*ln(c*(b*x**2+a)**p),x)","\begin{cases} \frac{i \sqrt{a} d p \log{\left(a + b x^{2} \right)}}{b \sqrt{\frac{1}{b}}} - \frac{2 i \sqrt{a} d p \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{b \sqrt{\frac{1}{b}}} + \frac{a e p \log{\left(a + b x^{2} \right)}}{2 b} + d p x \log{\left(a + b x^{2} \right)} - 2 d p x + d x \log{\left(c \right)} + \frac{e p x^{2} \log{\left(a + b x^{2} \right)}}{2} - \frac{e p x^{2}}{2} + \frac{e x^{2} \log{\left(c \right)}}{2} & \text{for}\: b \neq 0 \\\left(d x + \frac{e x^{2}}{2}\right) \log{\left(a^{p} c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*sqrt(a)*d*p*log(a + b*x**2)/(b*sqrt(1/b)) - 2*I*sqrt(a)*d*p*log(-I*sqrt(a)*sqrt(1/b) + x)/(b*sqrt(1/b)) + a*e*p*log(a + b*x**2)/(2*b) + d*p*x*log(a + b*x**2) - 2*d*p*x + d*x*log(c) + e*p*x**2*log(a + b*x**2)/2 - e*p*x**2/2 + e*x**2*log(c)/2, Ne(b, 0)), ((d*x + e*x**2/2)*log(a**p*c), True))","A",0
187,1,90,0,5.841509," ","integrate(ln(c*(b*x**2+a)**p),x)","\begin{cases} \frac{i \sqrt{a} p \log{\left(a + b x^{2} \right)}}{b \sqrt{\frac{1}{b}}} - \frac{2 i \sqrt{a} p \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{b \sqrt{\frac{1}{b}}} + p x \log{\left(a + b x^{2} \right)} - 2 p x + x \log{\left(c \right)} & \text{for}\: b \neq 0 \\x \log{\left(a^{p} c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*sqrt(a)*p*log(a + b*x**2)/(b*sqrt(1/b)) - 2*I*sqrt(a)*p*log(-I*sqrt(a)*sqrt(1/b) + x)/(b*sqrt(1/b)) + p*x*log(a + b*x**2) - 2*p*x + x*log(c), Ne(b, 0)), (x*log(a**p*c), True))","A",0
188,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)/(e*x+d),x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)/(d + e*x), x)","F",0
189,-1,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,1,265,0,79.675411," ","integrate((e*x+d)**3*ln(c*(b*x**3+a)**p),x)","- \frac{3 a^{2} e^{3} p \operatorname{RootSum} {\left(27 t^{3} a^{2} b - 1, \left( t \mapsto t \log{\left(3 t a + x \right)} \right)\right)}}{4 b} + 3 a d^{3} p \operatorname{RootSum} {\left(27 t^{3} a^{2} b - 1, \left( t \mapsto t \log{\left(3 t a + x \right)} \right)\right)} + \frac{9 a d^{2} e p \operatorname{RootSum} {\left(27 t^{3} a b^{2} + 1, \left( t \mapsto t \log{\left(9 t^{2} a b + x \right)} \right)\right)}}{2} + a d e^{2} p \left(\begin{cases} \frac{x^{3}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(a + b x^{3} \right)}}{b} & \text{otherwise} \end{cases}\right) + \frac{3 a e^{3} p x}{4 b} - 3 d^{3} p x + d^{3} x \log{\left(c \left(a + b x^{3}\right)^{p} \right)} - \frac{9 d^{2} e p x^{2}}{4} + \frac{3 d^{2} e x^{2} \log{\left(c \left(a + b x^{3}\right)^{p} \right)}}{2} - d e^{2} p x^{3} + d e^{2} x^{3} \log{\left(c \left(a + b x^{3}\right)^{p} \right)} - \frac{3 e^{3} p x^{4}}{16} + \frac{e^{3} x^{4} \log{\left(c \left(a + b x^{3}\right)^{p} \right)}}{4}"," ",0,"-3*a**2*e**3*p*RootSum(27*_t**3*a**2*b - 1, Lambda(_t, _t*log(3*_t*a + x)))/(4*b) + 3*a*d**3*p*RootSum(27*_t**3*a**2*b - 1, Lambda(_t, _t*log(3*_t*a + x))) + 9*a*d**2*e*p*RootSum(27*_t**3*a*b**2 + 1, Lambda(_t, _t*log(9*_t**2*a*b + x)))/2 + a*d*e**2*p*Piecewise((x**3/a, Eq(b, 0)), (log(a + b*x**3)/b, True)) + 3*a*e**3*p*x/(4*b) - 3*d**3*p*x + d**3*x*log(c*(a + b*x**3)**p) - 9*d**2*e*p*x**2/4 + 3*d**2*e*x**2*log(c*(a + b*x**3)**p)/2 - d*e**2*p*x**3 + d*e**2*x**3*log(c*(a + b*x**3)**p) - 3*e**3*p*x**4/16 + e**3*x**4*log(c*(a + b*x**3)**p)/4","A",0
192,-1,0,0,0.000000," ","integrate((e*x+d)**2*ln(c*(b*x**3+a)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,1,520,0,141.242423," ","integrate((e*x+d)*ln(c*(b*x**3+a)**p),x)","\begin{cases} \left(d x + \frac{e x^{2}}{2}\right) \log{\left(0^{p} c \right)} & \text{for}\: a = 0 \wedge b = 0 \\\left(d x + \frac{e x^{2}}{2}\right) \log{\left(a^{p} c \right)} & \text{for}\: b = 0 \\d p x \log{\left(b \right)} + 3 d p x \log{\left(x \right)} - 3 d p x + d x \log{\left(c \right)} + \frac{e p x^{2} \log{\left(b \right)}}{2} + \frac{3 e p x^{2} \log{\left(x \right)}}{2} - \frac{3 e p x^{2}}{4} + \frac{e x^{2} \log{\left(c \right)}}{2} & \text{for}\: a = 0 \\- \frac{\left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} e p \left(\frac{1}{b}\right)^{\frac{2}{3}} \log{\left(a + b x^{3} \right)}}{2} + \frac{3 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} e p \left(\frac{1}{b}\right)^{\frac{2}{3}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{4} - \frac{\left(-1\right)^{\frac{2}{3}} \sqrt{3} a^{\frac{2}{3}} e p \left(\frac{1}{b}\right)^{\frac{2}{3}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} x}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{2} + \frac{3 \sqrt[3]{-1} \sqrt[3]{a} b d p \left(\frac{1}{b}\right)^{\frac{4}{3}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{2} + \sqrt[3]{-1} \sqrt{3} \sqrt[3]{a} b d p \left(\frac{1}{b}\right)^{\frac{4}{3}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} x}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)} - \sqrt[3]{-1} \sqrt[3]{a} d p \sqrt[3]{\frac{1}{b}} \log{\left(a + b x^{3} \right)} + d p x \log{\left(a + b x^{3} \right)} - 3 d p x + d x \log{\left(c \right)} + \frac{e p x^{2} \log{\left(a + b x^{3} \right)}}{2} - \frac{3 e p x^{2}}{4} + \frac{e x^{2} \log{\left(c \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((d*x + e*x**2/2)*log(0**p*c), Eq(a, 0) & Eq(b, 0)), ((d*x + e*x**2/2)*log(a**p*c), Eq(b, 0)), (d*p*x*log(b) + 3*d*p*x*log(x) - 3*d*p*x + d*x*log(c) + e*p*x**2*log(b)/2 + 3*e*p*x**2*log(x)/2 - 3*e*p*x**2/4 + e*x**2*log(c)/2, Eq(a, 0)), (-(-1)**(2/3)*a**(2/3)*e*p*(1/b)**(2/3)*log(a + b*x**3)/2 + 3*(-1)**(2/3)*a**(2/3)*e*p*(1/b)**(2/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/4 - (-1)**(2/3)*sqrt(3)*a**(2/3)*e*p*(1/b)**(2/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x/(3*a**(1/3)*(1/b)**(1/3)))/2 + 3*(-1)**(1/3)*a**(1/3)*b*d*p*(1/b)**(4/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/2 + (-1)**(1/3)*sqrt(3)*a**(1/3)*b*d*p*(1/b)**(4/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x/(3*a**(1/3)*(1/b)**(1/3))) - (-1)**(1/3)*a**(1/3)*d*p*(1/b)**(1/3)*log(a + b*x**3) + d*p*x*log(a + b*x**3) - 3*d*p*x + d*x*log(c) + e*p*x**2*log(a + b*x**3)/2 - 3*e*p*x**2/4 + e*x**2*log(c)/2, True))","A",0
194,1,231,0,60.148056," ","integrate(ln(c*(b*x**3+a)**p),x)","\begin{cases} x \log{\left(0^{p} c \right)} & \text{for}\: a = 0 \wedge b = 0 \\x \log{\left(a^{p} c \right)} & \text{for}\: b = 0 \\p x \log{\left(b \right)} + 3 p x \log{\left(x \right)} - 3 p x + x \log{\left(c \right)} & \text{for}\: a = 0 \\- \sqrt[3]{-1} \sqrt[3]{a} b p \left(\frac{1}{b}\right)^{\frac{4}{3}} \log{\left(a + b x^{3} \right)} + \frac{3 \sqrt[3]{-1} \sqrt[3]{a} b p \left(\frac{1}{b}\right)^{\frac{4}{3}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{2} + \sqrt[3]{-1} \sqrt{3} \sqrt[3]{a} b p \left(\frac{1}{b}\right)^{\frac{4}{3}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} x}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)} + p x \log{\left(a + b x^{3} \right)} - 3 p x + x \log{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*log(0**p*c), Eq(a, 0) & Eq(b, 0)), (x*log(a**p*c), Eq(b, 0)), (p*x*log(b) + 3*p*x*log(x) - 3*p*x + x*log(c), Eq(a, 0)), (-(-1)**(1/3)*a**(1/3)*b*p*(1/b)**(4/3)*log(a + b*x**3) + 3*(-1)**(1/3)*a**(1/3)*b*p*(1/b)**(4/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/2 + (-1)**(1/3)*sqrt(3)*a**(1/3)*b*p*(1/b)**(4/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x/(3*a**(1/3)*(1/b)**(1/3))) + p*x*log(a + b*x**3) - 3*p*x + x*log(c), True))","A",0
195,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,1,484,0,9.450994," ","integrate((e*x+d)**3*ln(c*(a+b/x)**p),x)","\begin{cases} d^{3} p x \log{\left(a + \frac{b}{x} \right)} + d^{3} x \log{\left(c \right)} + \frac{3 d^{2} e p x^{2} \log{\left(a + \frac{b}{x} \right)}}{2} + \frac{3 d^{2} e x^{2} \log{\left(c \right)}}{2} + d e^{2} p x^{3} \log{\left(a + \frac{b}{x} \right)} + d e^{2} x^{3} \log{\left(c \right)} + \frac{e^{3} p x^{4} \log{\left(a + \frac{b}{x} \right)}}{4} + \frac{e^{3} x^{4} \log{\left(c \right)}}{4} + \frac{b d^{3} p \log{\left(x + \frac{b}{a} \right)}}{a} + \frac{3 b d^{2} e p x}{2 a} + \frac{b d e^{2} p x^{2}}{2 a} + \frac{b e^{3} p x^{3}}{12 a} - \frac{3 b^{2} d^{2} e p \log{\left(x + \frac{b}{a} \right)}}{2 a^{2}} - \frac{b^{2} d e^{2} p x}{a^{2}} - \frac{b^{2} e^{3} p x^{2}}{8 a^{2}} + \frac{b^{3} d e^{2} p \log{\left(x + \frac{b}{a} \right)}}{a^{3}} + \frac{b^{3} e^{3} p x}{4 a^{3}} - \frac{b^{4} e^{3} p \log{\left(x + \frac{b}{a} \right)}}{4 a^{4}} & \text{for}\: a \neq 0 \\d^{3} p x \log{\left(b \right)} - d^{3} p x \log{\left(x \right)} + d^{3} p x + d^{3} x \log{\left(c \right)} + \frac{3 d^{2} e p x^{2} \log{\left(b \right)}}{2} - \frac{3 d^{2} e p x^{2} \log{\left(x \right)}}{2} + \frac{3 d^{2} e p x^{2}}{4} + \frac{3 d^{2} e x^{2} \log{\left(c \right)}}{2} + d e^{2} p x^{3} \log{\left(b \right)} - d e^{2} p x^{3} \log{\left(x \right)} + \frac{d e^{2} p x^{3}}{3} + d e^{2} x^{3} \log{\left(c \right)} + \frac{e^{3} p x^{4} \log{\left(b \right)}}{4} - \frac{e^{3} p x^{4} \log{\left(x \right)}}{4} + \frac{e^{3} p x^{4}}{16} + \frac{e^{3} x^{4} \log{\left(c \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**3*p*x*log(a + b/x) + d**3*x*log(c) + 3*d**2*e*p*x**2*log(a + b/x)/2 + 3*d**2*e*x**2*log(c)/2 + d*e**2*p*x**3*log(a + b/x) + d*e**2*x**3*log(c) + e**3*p*x**4*log(a + b/x)/4 + e**3*x**4*log(c)/4 + b*d**3*p*log(x + b/a)/a + 3*b*d**2*e*p*x/(2*a) + b*d*e**2*p*x**2/(2*a) + b*e**3*p*x**3/(12*a) - 3*b**2*d**2*e*p*log(x + b/a)/(2*a**2) - b**2*d*e**2*p*x/a**2 - b**2*e**3*p*x**2/(8*a**2) + b**3*d*e**2*p*log(x + b/a)/a**3 + b**3*e**3*p*x/(4*a**3) - b**4*e**3*p*log(x + b/a)/(4*a**4), Ne(a, 0)), (d**3*p*x*log(b) - d**3*p*x*log(x) + d**3*p*x + d**3*x*log(c) + 3*d**2*e*p*x**2*log(b)/2 - 3*d**2*e*p*x**2*log(x)/2 + 3*d**2*e*p*x**2/4 + 3*d**2*e*x**2*log(c)/2 + d*e**2*p*x**3*log(b) - d*e**2*p*x**3*log(x) + d*e**2*p*x**3/3 + d*e**2*x**3*log(c) + e**3*p*x**4*log(b)/4 - e**3*p*x**4*log(x)/4 + e**3*p*x**4/16 + e**3*x**4*log(c)/4, True))","A",0
199,1,298,0,4.942535," ","integrate((e*x+d)**2*ln(c*(a+b/x)**p),x)","\begin{cases} d^{2} p x \log{\left(a + \frac{b}{x} \right)} + d^{2} x \log{\left(c \right)} + d e p x^{2} \log{\left(a + \frac{b}{x} \right)} + d e x^{2} \log{\left(c \right)} + \frac{e^{2} p x^{3} \log{\left(a + \frac{b}{x} \right)}}{3} + \frac{e^{2} x^{3} \log{\left(c \right)}}{3} + \frac{b d^{2} p \log{\left(x + \frac{b}{a} \right)}}{a} + \frac{b d e p x}{a} + \frac{b e^{2} p x^{2}}{6 a} - \frac{b^{2} d e p \log{\left(x + \frac{b}{a} \right)}}{a^{2}} - \frac{b^{2} e^{2} p x}{3 a^{2}} + \frac{b^{3} e^{2} p \log{\left(x + \frac{b}{a} \right)}}{3 a^{3}} & \text{for}\: a \neq 0 \\d^{2} p x \log{\left(b \right)} - d^{2} p x \log{\left(x \right)} + d^{2} p x + d^{2} x \log{\left(c \right)} + d e p x^{2} \log{\left(b \right)} - d e p x^{2} \log{\left(x \right)} + \frac{d e p x^{2}}{2} + d e x^{2} \log{\left(c \right)} + \frac{e^{2} p x^{3} \log{\left(b \right)}}{3} - \frac{e^{2} p x^{3} \log{\left(x \right)}}{3} + \frac{e^{2} p x^{3}}{9} + \frac{e^{2} x^{3} \log{\left(c \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**2*p*x*log(a + b/x) + d**2*x*log(c) + d*e*p*x**2*log(a + b/x) + d*e*x**2*log(c) + e**2*p*x**3*log(a + b/x)/3 + e**2*x**3*log(c)/3 + b*d**2*p*log(x + b/a)/a + b*d*e*p*x/a + b*e**2*p*x**2/(6*a) - b**2*d*e*p*log(x + b/a)/a**2 - b**2*e**2*p*x/(3*a**2) + b**3*e**2*p*log(x + b/a)/(3*a**3), Ne(a, 0)), (d**2*p*x*log(b) - d**2*p*x*log(x) + d**2*p*x + d**2*x*log(c) + d*e*p*x**2*log(b) - d*e*p*x**2*log(x) + d*e*p*x**2/2 + d*e*x**2*log(c) + e**2*p*x**3*log(b)/3 - e**2*p*x**3*log(x)/3 + e**2*p*x**3/9 + e**2*x**3*log(c)/3, True))","A",0
200,1,156,0,2.353825," ","integrate((e*x+d)*ln(c*(a+b/x)**p),x)","\begin{cases} d p x \log{\left(a + \frac{b}{x} \right)} + d x \log{\left(c \right)} + \frac{e p x^{2} \log{\left(a + \frac{b}{x} \right)}}{2} + \frac{e x^{2} \log{\left(c \right)}}{2} + \frac{b d p \log{\left(x + \frac{b}{a} \right)}}{a} + \frac{b e p x}{2 a} - \frac{b^{2} e p \log{\left(x + \frac{b}{a} \right)}}{2 a^{2}} & \text{for}\: a \neq 0 \\d p x \log{\left(b \right)} - d p x \log{\left(x \right)} + d p x + d x \log{\left(c \right)} + \frac{e p x^{2} \log{\left(b \right)}}{2} - \frac{e p x^{2} \log{\left(x \right)}}{2} + \frac{e p x^{2}}{4} + \frac{e x^{2} \log{\left(c \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*p*x*log(a + b/x) + d*x*log(c) + e*p*x**2*log(a + b/x)/2 + e*x**2*log(c)/2 + b*d*p*log(x + b/a)/a + b*e*p*x/(2*a) - b**2*e*p*log(x + b/a)/(2*a**2), Ne(a, 0)), (d*p*x*log(b) - d*p*x*log(x) + d*p*x + d*x*log(c) + e*p*x**2*log(b)/2 - e*p*x**2*log(x)/2 + e*p*x**2/4 + e*x**2*log(c)/2, True))","A",0
201,0,0,0,0.000000," ","integrate(ln(c*(a+b/x)**p)/(e*x+d),x)","\int \frac{\log{\left(c \left(a + \frac{b}{x}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(log(c*(a + b/x)**p)/(d + e*x), x)","F",0
202,1,585,0,7.622769," ","integrate(ln(c*(a+b/x)**p)/(e*x+d)**2,x)","\begin{cases} \frac{d p \log{\left(\frac{d}{e} + x \right)}}{d^{2} e + d e^{2} x} + \frac{e p x \log{\left(b \right)}}{d^{2} e + d e^{2} x} - \frac{e p x \log{\left(x \right)}}{d^{2} e + d e^{2} x} + \frac{e p x \log{\left(\frac{d}{e} + x \right)}}{d^{2} e + d e^{2} x} + \frac{e x \log{\left(c \right)}}{d^{2} e + d e^{2} x} & \text{for}\: a = 0 \\- \frac{d p}{d^{2} e + d e^{2} x} + \frac{e p x \log{\left(\frac{b}{x} + \frac{b e}{d} \right)}}{d^{2} e + d e^{2} x} + \frac{e x \log{\left(c \right)}}{d^{2} e + d e^{2} x} & \text{for}\: a = \frac{b e}{d} \\\frac{- \frac{a p \log{\left(a + \frac{b}{x} \right)}}{b} - \frac{p \log{\left(a + \frac{b}{x} \right)}}{x} + \frac{p}{x} - \frac{\log{\left(c \right)}}{x}}{e^{2}} & \text{for}\: d = 0 \\\tilde{\infty} \left(p x \log{\left(a + \frac{b}{x} \right)} + x \log{\left(c \right)} + \frac{b p \log{\left(a x + b \right)}}{a}\right) & \text{for}\: d = - e x \\\frac{p x \log{\left(a + \frac{b}{x} \right)} + x \log{\left(c \right)} + \frac{b p \log{\left(a x + b \right)}}{a}}{d^{2}} & \text{for}\: e = 0 \\\frac{a d p x \log{\left(a + \frac{b}{x} \right)}}{a d^{3} + a d^{2} e x - b d^{2} e - b d e^{2} x} + \frac{a d x \log{\left(c \right)}}{a d^{3} + a d^{2} e x - b d^{2} e - b d e^{2} x} + \frac{b d p \log{\left(x + \frac{b}{a} \right)}}{a d^{3} + a d^{2} e x - b d^{2} e - b d e^{2} x} - \frac{b d p \log{\left(\frac{d}{e} + x \right)}}{a d^{3} + a d^{2} e x - b d^{2} e - b d e^{2} x} - \frac{b e p x \log{\left(a + \frac{b}{x} \right)}}{a d^{3} + a d^{2} e x - b d^{2} e - b d e^{2} x} + \frac{b e p x \log{\left(x + \frac{b}{a} \right)}}{a d^{3} + a d^{2} e x - b d^{2} e - b d e^{2} x} - \frac{b e p x \log{\left(\frac{d}{e} + x \right)}}{a d^{3} + a d^{2} e x - b d^{2} e - b d e^{2} x} - \frac{b e x \log{\left(c \right)}}{a d^{3} + a d^{2} e x - b d^{2} e - b d e^{2} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*p*log(d/e + x)/(d**2*e + d*e**2*x) + e*p*x*log(b)/(d**2*e + d*e**2*x) - e*p*x*log(x)/(d**2*e + d*e**2*x) + e*p*x*log(d/e + x)/(d**2*e + d*e**2*x) + e*x*log(c)/(d**2*e + d*e**2*x), Eq(a, 0)), (-d*p/(d**2*e + d*e**2*x) + e*p*x*log(b/x + b*e/d)/(d**2*e + d*e**2*x) + e*x*log(c)/(d**2*e + d*e**2*x), Eq(a, b*e/d)), ((-a*p*log(a + b/x)/b - p*log(a + b/x)/x + p/x - log(c)/x)/e**2, Eq(d, 0)), (zoo*(p*x*log(a + b/x) + x*log(c) + b*p*log(a*x + b)/a), Eq(d, -e*x)), ((p*x*log(a + b/x) + x*log(c) + b*p*log(a*x + b)/a)/d**2, Eq(e, 0)), (a*d*p*x*log(a + b/x)/(a*d**3 + a*d**2*e*x - b*d**2*e - b*d*e**2*x) + a*d*x*log(c)/(a*d**3 + a*d**2*e*x - b*d**2*e - b*d*e**2*x) + b*d*p*log(x + b/a)/(a*d**3 + a*d**2*e*x - b*d**2*e - b*d*e**2*x) - b*d*p*log(d/e + x)/(a*d**3 + a*d**2*e*x - b*d**2*e - b*d*e**2*x) - b*e*p*x*log(a + b/x)/(a*d**3 + a*d**2*e*x - b*d**2*e - b*d*e**2*x) + b*e*p*x*log(x + b/a)/(a*d**3 + a*d**2*e*x - b*d**2*e - b*d*e**2*x) - b*e*p*x*log(d/e + x)/(a*d**3 + a*d**2*e*x - b*d**2*e - b*d*e**2*x) - b*e*x*log(c)/(a*d**3 + a*d**2*e*x - b*d**2*e - b*d*e**2*x), True))","A",0
203,1,4527,0,23.003215," ","integrate(ln(c*(a+b/x)**p)/(e*x+d)**3,x)","\begin{cases} \frac{d^{2} p \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} - \frac{d^{2} p}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{2 d e p x \log{\left(b \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} - \frac{2 d e p x \log{\left(x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{2 d e p x \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} - \frac{d e p x}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{2 d e x \log{\left(c \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{e^{2} p x^{2} \log{\left(b \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} - \frac{e^{2} p x^{2} \log{\left(x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{e^{2} p x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{e^{2} x^{2} \log{\left(c \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} & \text{for}\: a = 0 \\\frac{p x \log{\left(a + \frac{b}{x} \right)} + x \log{\left(c \right)} + \frac{b p \log{\left(a x + b \right)}}{a}}{d^{3}} & \text{for}\: e = 0 \\- \frac{3 d^{2} p}{4 d^{4} e + 8 d^{3} e^{2} x + 4 d^{2} e^{3} x^{2}} + \frac{4 d e p x \log{\left(\frac{b}{x} + \frac{b e}{d} \right)}}{4 d^{4} e + 8 d^{3} e^{2} x + 4 d^{2} e^{3} x^{2}} - \frac{2 d e p x}{4 d^{4} e + 8 d^{3} e^{2} x + 4 d^{2} e^{3} x^{2}} + \frac{4 d e x \log{\left(c \right)}}{4 d^{4} e + 8 d^{3} e^{2} x + 4 d^{2} e^{3} x^{2}} + \frac{2 e^{2} p x^{2} \log{\left(\frac{b}{x} + \frac{b e}{d} \right)}}{4 d^{4} e + 8 d^{3} e^{2} x + 4 d^{2} e^{3} x^{2}} + \frac{2 e^{2} x^{2} \log{\left(c \right)}}{4 d^{4} e + 8 d^{3} e^{2} x + 4 d^{2} e^{3} x^{2}} & \text{for}\: a = \frac{b e}{d} \\\frac{\frac{a^{2} p \log{\left(a + \frac{b}{x} \right)}}{2 b^{2}} - \frac{a p}{2 b x} - \frac{p \log{\left(a + \frac{b}{x} \right)}}{2 x^{2}} + \frac{p}{4 x^{2}} - \frac{\log{\left(c \right)}}{2 x^{2}}}{e^{3}} & \text{for}\: d = 0 \\\tilde{\infty} \left(p x \log{\left(a + \frac{b}{x} \right)} + x \log{\left(c \right)} + \frac{b p \log{\left(a x + b \right)}}{a}\right) & \text{for}\: d = - e x \\\frac{2 a^{2} d^{3} p x \log{\left(a + \frac{b}{x} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{2 a^{2} d^{3} x \log{\left(c \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{a^{2} d^{2} e p x^{2} \log{\left(a + \frac{b}{x} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{a^{2} d^{2} e x^{2} \log{\left(c \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{2 a b d^{3} p \log{\left(x + \frac{b}{a} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{2 a b d^{3} p \log{\left(\frac{d}{e} + x \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{a b d^{3} p}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{4 a b d^{2} e p x \log{\left(a + \frac{b}{x} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{4 a b d^{2} e p x \log{\left(x + \frac{b}{a} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{4 a b d^{2} e p x \log{\left(\frac{d}{e} + x \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{a b d^{2} e p x}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{4 a b d^{2} e x \log{\left(c \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{2 a b d e^{2} p x^{2} \log{\left(a + \frac{b}{x} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{2 a b d e^{2} p x^{2} \log{\left(x + \frac{b}{a} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{2 a b d e^{2} p x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{2 a b d e^{2} x^{2} \log{\left(c \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{b^{2} d^{2} e p \log{\left(x + \frac{b}{a} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{b^{2} d^{2} e p \log{\left(\frac{d}{e} + x \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{b^{2} d^{2} e p}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{2 b^{2} d e^{2} p x \log{\left(a + \frac{b}{x} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{2 b^{2} d e^{2} p x \log{\left(x + \frac{b}{a} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{2 b^{2} d e^{2} p x \log{\left(\frac{d}{e} + x \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{b^{2} d e^{2} p x}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{2 b^{2} d e^{2} x \log{\left(c \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{b^{2} e^{3} p x^{2} \log{\left(a + \frac{b}{x} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} - \frac{b^{2} e^{3} p x^{2} \log{\left(x + \frac{b}{a} \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{b^{2} e^{3} p x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} + \frac{b^{2} e^{3} x^{2} \log{\left(c \right)}}{2 a^{2} d^{6} + 4 a^{2} d^{5} e x + 2 a^{2} d^{4} e^{2} x^{2} - 4 a b d^{5} e - 8 a b d^{4} e^{2} x - 4 a b d^{3} e^{3} x^{2} + 2 b^{2} d^{4} e^{2} + 4 b^{2} d^{3} e^{3} x + 2 b^{2} d^{2} e^{4} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**2*p*log(d/e + x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) - d**2*p/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + 2*d*e*p*x*log(b)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) - 2*d*e*p*x*log(x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + 2*d*e*p*x*log(d/e + x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) - d*e*p*x/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + 2*d*e*x*log(c)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + e**2*p*x**2*log(b)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) - e**2*p*x**2*log(x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + e**2*p*x**2*log(d/e + x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + e**2*x**2*log(c)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2), Eq(a, 0)), ((p*x*log(a + b/x) + x*log(c) + b*p*log(a*x + b)/a)/d**3, Eq(e, 0)), (-3*d**2*p/(4*d**4*e + 8*d**3*e**2*x + 4*d**2*e**3*x**2) + 4*d*e*p*x*log(b/x + b*e/d)/(4*d**4*e + 8*d**3*e**2*x + 4*d**2*e**3*x**2) - 2*d*e*p*x/(4*d**4*e + 8*d**3*e**2*x + 4*d**2*e**3*x**2) + 4*d*e*x*log(c)/(4*d**4*e + 8*d**3*e**2*x + 4*d**2*e**3*x**2) + 2*e**2*p*x**2*log(b/x + b*e/d)/(4*d**4*e + 8*d**3*e**2*x + 4*d**2*e**3*x**2) + 2*e**2*x**2*log(c)/(4*d**4*e + 8*d**3*e**2*x + 4*d**2*e**3*x**2), Eq(a, b*e/d)), ((a**2*p*log(a + b/x)/(2*b**2) - a*p/(2*b*x) - p*log(a + b/x)/(2*x**2) + p/(4*x**2) - log(c)/(2*x**2))/e**3, Eq(d, 0)), (zoo*(p*x*log(a + b/x) + x*log(c) + b*p*log(a*x + b)/a), Eq(d, -e*x)), (2*a**2*d**3*p*x*log(a + b/x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + 2*a**2*d**3*x*log(c)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + a**2*d**2*e*p*x**2*log(a + b/x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + a**2*d**2*e*x**2*log(c)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + 2*a*b*d**3*p*log(x + b/a)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - 2*a*b*d**3*p*log(d/e + x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + a*b*d**3*p/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - 4*a*b*d**2*e*p*x*log(a + b/x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + 4*a*b*d**2*e*p*x*log(x + b/a)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - 4*a*b*d**2*e*p*x*log(d/e + x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + a*b*d**2*e*p*x/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - 4*a*b*d**2*e*x*log(c)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - 2*a*b*d*e**2*p*x**2*log(a + b/x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + 2*a*b*d*e**2*p*x**2*log(x + b/a)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - 2*a*b*d*e**2*p*x**2*log(d/e + x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - 2*a*b*d*e**2*x**2*log(c)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - b**2*d**2*e*p*log(x + b/a)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + b**2*d**2*e*p*log(d/e + x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - b**2*d**2*e*p/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + 2*b**2*d*e**2*p*x*log(a + b/x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - 2*b**2*d*e**2*p*x*log(x + b/a)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + 2*b**2*d*e**2*p*x*log(d/e + x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - b**2*d*e**2*p*x/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + 2*b**2*d*e**2*x*log(c)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + b**2*e**3*p*x**2*log(a + b/x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) - b**2*e**3*p*x**2*log(x + b/a)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + b**2*e**3*p*x**2*log(d/e + x)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2) + b**2*e**3*x**2*log(c)/(2*a**2*d**6 + 4*a**2*d**5*e*x + 2*a**2*d**4*e**2*x**2 - 4*a*b*d**5*e - 8*a*b*d**4*e**2*x - 4*a*b*d**3*e**3*x**2 + 2*b**2*d**4*e**2 + 4*b**2*d**3*e**3*x + 2*b**2*d**2*e**4*x**2), True))","A",0
204,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x)**p)/(e*x+d)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,0,0,0,0.000000," ","integrate(ln(a+b/x)/(d*x+c),x)","\int \frac{\log{\left(a + \frac{b}{x} \right)}}{c + d x}\, dx"," ",0,"Integral(log(a + b/x)/(c + d*x), x)","F",0
206,-1,0,0,0.000000," ","integrate((e*x+d)**m*ln(c*(b*x**3+a)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate((e*x+d)**m*ln(c*(b*x**2+a)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-2,0,0,0.000000," ","integrate((e*x+d)**m*ln(c*(b*x+a)**p),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
209,0,0,0,0.000000," ","integrate((e*x+d)**m*ln(c*(a+b/x)**p),x)","\int \left(d + e x\right)^{m} \log{\left(c \left(a + \frac{b}{x}\right)^{p} \right)}\, dx"," ",0,"Integral((d + e*x)**m*log(c*(a + b/x)**p), x)","F",0
210,-1,0,0,0.000000," ","integrate((e*x+d)**m*ln(c*(a+b/x**2)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate((g*x+f)**m*ln(c*(d+e*x**n)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,1,415,0,32.590508," ","integrate((g*x+f)**3*ln(c*(d+e*x**n)**p),x)","f^{3} x \log{\left(c \left(d + e x^{n}\right)^{p} \right)} + \frac{f^{3} p x \Phi\left(\frac{d x^{- n} e^{i \pi}}{e}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{n \Gamma\left(1 + \frac{1}{n}\right)} + \frac{3 f^{2} g x^{2} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{2} + f g^{2} x^{3} \log{\left(c \left(d + e x^{n}\right)^{p} \right)} + \frac{g^{3} x^{4} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{4} - \frac{3 e f^{2} g p x^{2} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{2 d \Gamma\left(2 + \frac{2}{n}\right)} - \frac{3 e f^{2} g p x^{2} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{d n \Gamma\left(2 + \frac{2}{n}\right)} - \frac{e f g^{2} p x^{3} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{3}{n}\right) \Gamma\left(1 + \frac{3}{n}\right)}{d \Gamma\left(2 + \frac{3}{n}\right)} - \frac{3 e f g^{2} p x^{3} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{3}{n}\right) \Gamma\left(1 + \frac{3}{n}\right)}{d n \Gamma\left(2 + \frac{3}{n}\right)} - \frac{e g^{3} p x^{4} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{4}{n}\right) \Gamma\left(1 + \frac{4}{n}\right)}{4 d \Gamma\left(2 + \frac{4}{n}\right)} - \frac{e g^{3} p x^{4} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{4}{n}\right) \Gamma\left(1 + \frac{4}{n}\right)}{d n \Gamma\left(2 + \frac{4}{n}\right)}"," ",0,"f**3*x*log(c*(d + e*x**n)**p) + f**3*p*x*lerchphi(d*x**(-n)*exp_polar(I*pi)/e, 1, exp_polar(I*pi)/n)*gamma(1/n)/(n*gamma(1 + 1/n)) + 3*f**2*g*x**2*log(c*(d + e*x**n)**p)/2 + f*g**2*x**3*log(c*(d + e*x**n)**p) + g**3*x**4*log(c*(d + e*x**n)**p)/4 - 3*e*f**2*g*p*x**2*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 2/n)*gamma(1 + 2/n)/(2*d*gamma(2 + 2/n)) - 3*e*f**2*g*p*x**2*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 2/n)*gamma(1 + 2/n)/(d*n*gamma(2 + 2/n)) - e*f*g**2*p*x**3*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 3/n)*gamma(1 + 3/n)/(d*gamma(2 + 3/n)) - 3*e*f*g**2*p*x**3*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 3/n)*gamma(1 + 3/n)/(d*n*gamma(2 + 3/n)) - e*g**3*p*x**4*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 4/n)*gamma(1 + 4/n)/(4*d*gamma(2 + 4/n)) - e*g**3*p*x**4*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 4/n)*gamma(1 + 4/n)/(d*n*gamma(2 + 4/n))","C",0
213,1,284,0,20.057633," ","integrate((g*x+f)**2*ln(c*(d+e*x**n)**p),x)","f^{2} x \log{\left(c \left(d + e x^{n}\right)^{p} \right)} + \frac{f^{2} p x \Phi\left(\frac{d x^{- n} e^{i \pi}}{e}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{n \Gamma\left(1 + \frac{1}{n}\right)} + f g x^{2} \log{\left(c \left(d + e x^{n}\right)^{p} \right)} + \frac{g^{2} x^{3} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{3} - \frac{e f g p x^{2} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{d \Gamma\left(2 + \frac{2}{n}\right)} - \frac{2 e f g p x^{2} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{d n \Gamma\left(2 + \frac{2}{n}\right)} - \frac{e g^{2} p x^{3} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{3}{n}\right) \Gamma\left(1 + \frac{3}{n}\right)}{3 d \Gamma\left(2 + \frac{3}{n}\right)} - \frac{e g^{2} p x^{3} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{3}{n}\right) \Gamma\left(1 + \frac{3}{n}\right)}{d n \Gamma\left(2 + \frac{3}{n}\right)}"," ",0,"f**2*x*log(c*(d + e*x**n)**p) + f**2*p*x*lerchphi(d*x**(-n)*exp_polar(I*pi)/e, 1, exp_polar(I*pi)/n)*gamma(1/n)/(n*gamma(1 + 1/n)) + f*g*x**2*log(c*(d + e*x**n)**p) + g**2*x**3*log(c*(d + e*x**n)**p)/3 - e*f*g*p*x**2*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 2/n)*gamma(1 + 2/n)/(d*gamma(2 + 2/n)) - 2*e*f*g*p*x**2*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 2/n)*gamma(1 + 2/n)/(d*n*gamma(2 + 2/n)) - e*g**2*p*x**3*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 3/n)*gamma(1 + 3/n)/(3*d*gamma(2 + 3/n)) - e*g**2*p*x**3*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 3/n)*gamma(1 + 3/n)/(d*n*gamma(2 + 3/n))","C",0
214,1,162,0,12.861969," ","integrate((g*x+f)*ln(c*(d+e*x**n)**p),x)","f x \log{\left(c \left(d + e x^{n}\right)^{p} \right)} + \frac{f p x \Phi\left(\frac{d x^{- n} e^{i \pi}}{e}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{n \Gamma\left(1 + \frac{1}{n}\right)} + \frac{g x^{2} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{2} - \frac{e g p x^{2} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{2 d \Gamma\left(2 + \frac{2}{n}\right)} - \frac{e g p x^{2} x^{n} \Phi\left(\frac{e x^{n} e^{i \pi}}{d}, 1, 1 + \frac{2}{n}\right) \Gamma\left(1 + \frac{2}{n}\right)}{d n \Gamma\left(2 + \frac{2}{n}\right)}"," ",0,"f*x*log(c*(d + e*x**n)**p) + f*p*x*lerchphi(d*x**(-n)*exp_polar(I*pi)/e, 1, exp_polar(I*pi)/n)*gamma(1/n)/(n*gamma(1 + 1/n)) + g*x**2*log(c*(d + e*x**n)**p)/2 - e*g*p*x**2*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 2/n)*gamma(1 + 2/n)/(2*d*gamma(2 + 2/n)) - e*g*p*x**2*x**n*lerchphi(e*x**n*exp_polar(I*pi)/d, 1, 1 + 2/n)*gamma(1 + 2/n)/(d*n*gamma(2 + 2/n))","C",0
215,1,48,0,3.434128," ","integrate(ln(c*(d+e*x**n)**p),x)","x \log{\left(c \left(d + e x^{n}\right)^{p} \right)} + \frac{p x \Phi\left(\frac{d x^{- n} e^{i \pi}}{e}, 1, \frac{e^{i \pi}}{n}\right) \Gamma\left(\frac{1}{n}\right)}{n \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"x*log(c*(d + e*x**n)**p) + p*x*lerchphi(d*x**(-n)*exp_polar(I*pi)/e, 1, exp_polar(I*pi)/n)*gamma(1/n)/(n*gamma(1 + 1/n))","C",0
216,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/(g*x+f),x)","\int \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{f + g x}\, dx"," ",0,"Integral(log(c*(d + e*x**n)**p)/(f + g*x), x)","F",0
217,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/(g*x+f)**2,x)","\int \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral(log(c*(d + e*x**n)**p)/(f + g*x)**2, x)","F",0
218,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/(g*x+f)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,0,0,0,0.000000," ","integrate(x**3*ln(c*(b*x+a)**p)/(e*x+d),x)","\int \frac{x^{3} \log{\left(c \left(a + b x\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x**3*log(c*(a + b*x)**p)/(d + e*x), x)","F",0
220,0,0,0,0.000000," ","integrate(x**2*ln(c*(b*x+a)**p)/(e*x+d),x)","\int \frac{x^{2} \log{\left(c \left(a + b x\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x**2*log(c*(a + b*x)**p)/(d + e*x), x)","F",0
221,0,0,0,0.000000," ","integrate(x*ln(c*(b*x+a)**p)/(e*x+d),x)","\int \frac{x \log{\left(c \left(a + b x\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x*log(c*(a + b*x)**p)/(d + e*x), x)","F",0
222,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**p)/(e*x+d),x)","\int \frac{\log{\left(c \left(a + b x\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(log(c*(a + b*x)**p)/(d + e*x), x)","F",0
223,0,0,0,0.000000," ","integrate(ln(c*(b*x+a)**p)/x/(e*x+d),x)","\int \frac{\log{\left(c \left(a + b x\right)^{p} \right)}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(log(c*(a + b*x)**p)/(x*(d + e*x)), x)","F",0
224,-1,0,0,0.000000," ","integrate(ln(c*(b*x+a)**p)/x**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate(ln(c*(b*x+a)**p)/x**3/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,-1,0,0,0.000000," ","integrate(x**3*ln(c*(b*x**2+a)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,0,0,0,0.000000," ","integrate(x**2*ln(c*(b*x**2+a)**p)/(e*x+d),x)","\int \frac{x^{2} \log{\left(c \left(a + b x^{2}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x**2*log(c*(a + b*x**2)**p)/(d + e*x), x)","F",0
228,0,0,0,0.000000," ","integrate(x*ln(c*(b*x**2+a)**p)/(e*x+d),x)","\int \frac{x \log{\left(c \left(a + b x^{2}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x*log(c*(a + b*x**2)**p)/(d + e*x), x)","F",0
229,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)/(e*x+d),x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)/(d + e*x), x)","F",0
230,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)/x/(e*x+d),x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{p} \right)}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**p)/(x*(d + e*x)), x)","F",0
231,-1,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)/x**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**p)/x**3/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate(x**3*ln(c*(b*x**3+a)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate(x**2*ln(c*(b*x**3+a)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,-1,0,0,0.000000," ","integrate(x*ln(c*(b*x**3+a)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/x/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/x**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate(ln(c*(b*x**3+a)**p)/x**3/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,0,0,0,0.000000," ","integrate(x**3*ln(c*(a+b/x)**p)/(e*x+d),x)","\int \frac{x^{3} \log{\left(c \left(a + \frac{b}{x}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x**3*log(c*(a + b/x)**p)/(d + e*x), x)","F",0
241,0,0,0,0.000000," ","integrate(x**2*ln(c*(a+b/x)**p)/(e*x+d),x)","\int \frac{x^{2} \log{\left(c \left(a + \frac{b}{x}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x**2*log(c*(a + b/x)**p)/(d + e*x), x)","F",0
242,0,0,0,0.000000," ","integrate(x*ln(c*(a+b/x)**p)/(e*x+d),x)","\int \frac{x \log{\left(c \left(a + \frac{b}{x}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x*log(c*(a + b/x)**p)/(d + e*x), x)","F",0
243,0,0,0,0.000000," ","integrate(ln(c*(a+b/x)**p)/(e*x+d),x)","\int \frac{\log{\left(c \left(a + \frac{b}{x}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(log(c*(a + b/x)**p)/(d + e*x), x)","F",0
244,0,0,0,0.000000," ","integrate(ln(c*(a+b/x)**p)/x/(e*x+d),x)","\int \frac{\log{\left(c \left(a + \frac{b}{x}\right)^{p} \right)}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(log(c*(a + b/x)**p)/(x*(d + e*x)), x)","F",0
245,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x)**p)/x**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x)**p)/x**3/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,0,0,0,0.000000," ","integrate(x**3*ln(c*(a+b/x**2)**p)/(e*x+d),x)","\int \frac{x^{3} \log{\left(c \left(a + \frac{b}{x^{2}}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x**3*log(c*(a + b/x**2)**p)/(d + e*x), x)","F",0
248,0,0,0,0.000000," ","integrate(x**2*ln(c*(a+b/x**2)**p)/(e*x+d),x)","\int \frac{x^{2} \log{\left(c \left(a + \frac{b}{x^{2}}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x**2*log(c*(a + b/x**2)**p)/(d + e*x), x)","F",0
249,0,0,0,0.000000," ","integrate(x*ln(c*(a+b/x**2)**p)/(e*x+d),x)","\int \frac{x \log{\left(c \left(a + \frac{b}{x^{2}}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(x*log(c*(a + b/x**2)**p)/(d + e*x), x)","F",0
250,0,0,0,0.000000," ","integrate(ln(c*(a+b/x**2)**p)/(e*x+d),x)","\int \frac{\log{\left(c \left(a + \frac{b}{x^{2}}\right)^{p} \right)}}{d + e x}\, dx"," ",0,"Integral(log(c*(a + b/x**2)**p)/(d + e*x), x)","F",0
251,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x**2)**p)/x/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x**2)**p)/x**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x**2)**p)/x**3/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate(x**3*ln(c*(a+b/x**3)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,-1,0,0,0.000000," ","integrate(x**2*ln(c*(a+b/x**3)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,-1,0,0,0.000000," ","integrate(x*ln(c*(a+b/x**3)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x**3)**p)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x**3)**p)/x/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x**3)**p)/x**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate(ln(c*(a+b/x**3)**p)/x**3/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,-1,0,0,0.000000," ","integrate(ln(c*(e*x**3+d)**p)/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
262,0,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/(g*x**2+f),x)","\int \frac{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(log(c*(d + e*x**2)**p)/(f + g*x**2), x)","F",0
263,0,0,0,0.000000," ","integrate(ln(c*(e*x+d)**p)/(g*x**2+f),x)","\int \frac{\log{\left(c \left(d + e x\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(log(c*(d + e*x)**p)/(f + g*x**2), x)","F",0
264,0,0,0,0.000000," ","integrate(ln(c*(d+e/x)**p)/(g*x**2+f),x)","\int \frac{\log{\left(c \left(d + \frac{e}{x}\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(log(c*(d + e/x)**p)/(f + g*x**2), x)","F",0
265,-1,0,0,0.000000," ","integrate(ln(c*(d+e/x**2)**p)/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**(1/2))**p)/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,-1,0,0,0.000000," ","integrate(ln(c*(d+e/x**(1/2))**p)/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
268,-1,0,0,0.000000," ","integrate((g*x**2+f)**3*ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,1,415,0,89.769115," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p),x)","\begin{cases} \frac{i d^{\frac{5}{2}} g^{2} p \log{\left(d + e x^{2} \right)}}{5 e^{3} \sqrt{\frac{1}{e}}} - \frac{2 i d^{\frac{5}{2}} g^{2} p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{5 e^{3} \sqrt{\frac{1}{e}}} - \frac{2 i d^{\frac{3}{2}} f g p \log{\left(d + e x^{2} \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{4 i d^{\frac{3}{2}} f g p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{i \sqrt{d} f^{2} p \log{\left(d + e x^{2} \right)}}{e \sqrt{\frac{1}{e}}} - \frac{2 i \sqrt{d} f^{2} p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{e \sqrt{\frac{1}{e}}} - \frac{2 d^{2} g^{2} p x}{5 e^{2}} + \frac{4 d f g p x}{3 e} + \frac{2 d g^{2} p x^{3}}{15 e} + f^{2} p x \log{\left(d + e x^{2} \right)} - 2 f^{2} p x + f^{2} x \log{\left(c \right)} + \frac{2 f g p x^{3} \log{\left(d + e x^{2} \right)}}{3} - \frac{4 f g p x^{3}}{9} + \frac{2 f g x^{3} \log{\left(c \right)}}{3} + \frac{g^{2} p x^{5} \log{\left(d + e x^{2} \right)}}{5} - \frac{2 g^{2} p x^{5}}{25} + \frac{g^{2} x^{5} \log{\left(c \right)}}{5} & \text{for}\: e \neq 0 \\\left(f^{2} x + \frac{2 f g x^{3}}{3} + \frac{g^{2} x^{5}}{5}\right) \log{\left(c d^{p} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*d**(5/2)*g**2*p*log(d + e*x**2)/(5*e**3*sqrt(1/e)) - 2*I*d**(5/2)*g**2*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(5*e**3*sqrt(1/e)) - 2*I*d**(3/2)*f*g*p*log(d + e*x**2)/(3*e**2*sqrt(1/e)) + 4*I*d**(3/2)*f*g*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*e**2*sqrt(1/e)) + I*sqrt(d)*f**2*p*log(d + e*x**2)/(e*sqrt(1/e)) - 2*I*sqrt(d)*f**2*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(e*sqrt(1/e)) - 2*d**2*g**2*p*x/(5*e**2) + 4*d*f*g*p*x/(3*e) + 2*d*g**2*p*x**3/(15*e) + f**2*p*x*log(d + e*x**2) - 2*f**2*p*x + f**2*x*log(c) + 2*f*g*p*x**3*log(d + e*x**2)/3 - 4*f*g*p*x**3/9 + 2*f*g*x**3*log(c)/3 + g**2*p*x**5*log(d + e*x**2)/5 - 2*g**2*p*x**5/25 + g**2*x**5*log(c)/5, Ne(e, 0)), ((f**2*x + 2*f*g*x**3/3 + g**2*x**5/5)*log(c*d**p), True))","A",0
270,1,228,0,23.522754," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p),x)","\begin{cases} - \frac{i d^{\frac{3}{2}} g p \log{\left(d + e x^{2} \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{2 i d^{\frac{3}{2}} g p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{i \sqrt{d} f p \log{\left(d + e x^{2} \right)}}{e \sqrt{\frac{1}{e}}} - \frac{2 i \sqrt{d} f p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{e \sqrt{\frac{1}{e}}} + \frac{2 d g p x}{3 e} + f p x \log{\left(d + e x^{2} \right)} - 2 f p x + f x \log{\left(c \right)} + \frac{g p x^{3} \log{\left(d + e x^{2} \right)}}{3} - \frac{2 g p x^{3}}{9} + \frac{g x^{3} \log{\left(c \right)}}{3} & \text{for}\: e \neq 0 \\\left(f x + \frac{g x^{3}}{3}\right) \log{\left(c d^{p} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*d**(3/2)*g*p*log(d + e*x**2)/(3*e**2*sqrt(1/e)) + 2*I*d**(3/2)*g*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*e**2*sqrt(1/e)) + I*sqrt(d)*f*p*log(d + e*x**2)/(e*sqrt(1/e)) - 2*I*sqrt(d)*f*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(e*sqrt(1/e)) + 2*d*g*p*x/(3*e) + f*p*x*log(d + e*x**2) - 2*f*p*x + f*x*log(c) + g*p*x**3*log(d + e*x**2)/3 - 2*g*p*x**3/9 + g*x**3*log(c)/3, Ne(e, 0)), ((f*x + g*x**3/3)*log(c*d**p), True))","A",0
271,0,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/(g*x**2+f),x)","\int \frac{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(log(c*(d + e*x**2)**p)/(f + g*x**2), x)","F",0
272,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,0,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)**2,x)","\int \left(f + g x^{2}\right)^{2} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral((f + g*x**2)**2*log(c*(d + e*x**2)**p)**2, x)","F",0
274,0,0,0,0.000000," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)**2,x)","\int \left(f + g x^{2}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral((f + g*x**2)*log(c*(d + e*x**2)**p)**2, x)","F",0
275,0,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)**2/(g*x**2+f),x)","\int \frac{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}}{f + g x^{2}}\, dx"," ",0,"Integral(log(c*(d + e*x**2)**p)**2/(f + g*x**2), x)","F",0
276,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,0,0,0,0.000000," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)**3,x)","\int \left(f + g x^{2}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{3}\, dx"," ",0,"Integral((f + g*x**2)*log(c*(d + e*x**2)**p)**3, x)","F",0
278,0,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)**3/(g*x**2+f),x)","\int \frac{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{3}}{f + g x^{2}}\, dx"," ",0,"Integral(log(c*(d + e*x**2)**p)**3/(f + g*x**2), x)","F",0
279,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)**3/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,0,0,0,0.000000," ","integrate((g*x**2+f)**2/ln(c*(e*x**2+d)**p),x)","\int \frac{\left(f + g x^{2}\right)^{2}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral((f + g*x**2)**2/log(c*(d + e*x**2)**p), x)","F",0
281,0,0,0,0.000000," ","integrate((g*x**2+f)/ln(c*(e*x**2+d)**p),x)","\int \frac{f + g x^{2}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral((f + g*x**2)/log(c*(d + e*x**2)**p), x)","F",0
282,0,0,0,0.000000," ","integrate(1/(g*x**2+f)/ln(c*(e*x**2+d)**p),x)","\int \frac{1}{\left(f + g x^{2}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/((f + g*x**2)*log(c*(d + e*x**2)**p)), x)","F",0
283,-1,0,0,0.000000," ","integrate(1/(g*x**2+f)**2/ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,0,0,0,0.000000," ","integrate((g*x**2+f)**2/ln(c*(e*x**2+d)**p)**2,x)","\int \frac{\left(f + g x^{2}\right)^{2}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral((f + g*x**2)**2/log(c*(d + e*x**2)**p)**2, x)","F",0
285,0,0,0,0.000000," ","integrate((g*x**2+f)/ln(c*(e*x**2+d)**p)**2,x)","\int \frac{f + g x^{2}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral((f + g*x**2)/log(c*(d + e*x**2)**p)**2, x)","F",0
286,0,0,0,0.000000," ","integrate(1/(g*x**2+f)/ln(c*(e*x**2+d)**p)**2,x)","\int \frac{1}{\left(f + g x^{2}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral(1/((f + g*x**2)*log(c*(d + e*x**2)**p)**2), x)","F",0
287,-1,0,0,0.000000," ","integrate(1/(g*x**2+f)**2/ln(c*(e*x**2+d)**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate((g*x**3+f)**3*ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate((g*x**3+f)**2*ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,1,175,0,48.265476," ","integrate((g*x**3+f)*ln(c*(e*x**2+d)**p),x)","\begin{cases} \frac{i \sqrt{d} f p \log{\left(d + e x^{2} \right)}}{e \sqrt{\frac{1}{e}}} - \frac{2 i \sqrt{d} f p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{e \sqrt{\frac{1}{e}}} - \frac{d^{2} g p \log{\left(d + e x^{2} \right)}}{4 e^{2}} + \frac{d g p x^{2}}{4 e} + f p x \log{\left(d + e x^{2} \right)} - 2 f p x + f x \log{\left(c \right)} + \frac{g p x^{4} \log{\left(d + e x^{2} \right)}}{4} - \frac{g p x^{4}}{8} + \frac{g x^{4} \log{\left(c \right)}}{4} & \text{for}\: e \neq 0 \\\left(f x + \frac{g x^{4}}{4}\right) \log{\left(c d^{p} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*sqrt(d)*f*p*log(d + e*x**2)/(e*sqrt(1/e)) - 2*I*sqrt(d)*f*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(e*sqrt(1/e)) - d**2*g*p*log(d + e*x**2)/(4*e**2) + d*g*p*x**2/(4*e) + f*p*x*log(d + e*x**2) - 2*f*p*x + f*x*log(c) + g*p*x**4*log(d + e*x**2)/4 - g*p*x**4/8 + g*x**4*log(c)/4, Ne(e, 0)), ((f*x + g*x**4/4)*log(c*d**p), True))","A",0
291,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/(g*x**3+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/(g*x**3+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate((g*x**3+f)**3*ln(c*(e*x**2+d)**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,0,0,0,0.000000," ","integrate((g*x**3+f)**2*ln(c*(e*x**2+d)**p)**2,x)","\int \left(f + g x^{3}\right)^{2} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral((f + g*x**3)**2*log(c*(d + e*x**2)**p)**2, x)","F",0
295,0,0,0,0.000000," ","integrate((g*x**3+f)*ln(c*(e*x**2+d)**p)**2,x)","\int \left(f + g x^{3}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}\, dx"," ",0,"Integral((f + g*x**3)*log(c*(d + e*x**2)**p)**2, x)","F",0
296,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)**2/(g*x**3+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)**2/(g*x**3+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,0,0,0,0.000000," ","integrate((g*x**3+f)**2*ln(c*(e*x**2+d)**p)**3,x)","\int \left(f + g x^{3}\right)^{2} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{3}\, dx"," ",0,"Integral((f + g*x**3)**2*log(c*(d + e*x**2)**p)**3, x)","F",0
299,0,0,0,0.000000," ","integrate((g*x**3+f)*ln(c*(e*x**2+d)**p)**3,x)","\int \left(f + g x^{3}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{3}\, dx"," ",0,"Integral((f + g*x**3)*log(c*(d + e*x**2)**p)**3, x)","F",0
300,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)**3/(g*x**3+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)**3/(g*x**3+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,0,0,0,0.000000," ","integrate((g*x**3+f)**2/ln(c*(e*x**2+d)**p),x)","\int \frac{\left(f + g x^{3}\right)^{2}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral((f + g*x**3)**2/log(c*(d + e*x**2)**p), x)","F",0
303,0,0,0,0.000000," ","integrate((g*x**3+f)/ln(c*(e*x**2+d)**p),x)","\int \frac{f + g x^{3}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}}\, dx"," ",0,"Integral((f + g*x**3)/log(c*(d + e*x**2)**p), x)","F",0
304,-1,0,0,0.000000," ","integrate(1/(g*x**3+f)/ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate(1/(g*x**3+f)**2/ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,0,0,0,0.000000," ","integrate((g*x**3+f)**2/ln(c*(e*x**2+d)**p)**2,x)","\int \frac{\left(f + g x^{3}\right)^{2}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral((f + g*x**3)**2/log(c*(d + e*x**2)**p)**2, x)","F",0
307,0,0,0,0.000000," ","integrate((g*x**3+f)/ln(c*(e*x**2+d)**p)**2,x)","\int \frac{f + g x^{3}}{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}^{2}}\, dx"," ",0,"Integral((f + g*x**3)/log(c*(d + e*x**2)**p)**2, x)","F",0
308,-1,0,0,0.000000," ","integrate(1/(g*x**3+f)/ln(c*(e*x**2+d)**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,-1,0,0,0.000000," ","integrate(1/(g*x**3+f)**2/ln(c*(e*x**2+d)**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate(x**5*(g*x**2+f)*ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,1,170,0,162.651902," ","integrate(x**3*(g*x**2+f)*ln(c*(e*x**2+d)**p),x)","\begin{cases} \frac{d^{3} g p \log{\left(d + e x^{2} \right)}}{6 e^{3}} - \frac{d^{2} f p \log{\left(d + e x^{2} \right)}}{4 e^{2}} - \frac{d^{2} g p x^{2}}{6 e^{2}} + \frac{d f p x^{2}}{4 e} + \frac{d g p x^{4}}{12 e} + \frac{f p x^{4} \log{\left(d + e x^{2} \right)}}{4} - \frac{f p x^{4}}{8} + \frac{f x^{4} \log{\left(c \right)}}{4} + \frac{g p x^{6} \log{\left(d + e x^{2} \right)}}{6} - \frac{g p x^{6}}{18} + \frac{g x^{6} \log{\left(c \right)}}{6} & \text{for}\: e \neq 0 \\\left(\frac{f x^{4}}{4} + \frac{g x^{6}}{6}\right) \log{\left(c d^{p} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**3*g*p*log(d + e*x**2)/(6*e**3) - d**2*f*p*log(d + e*x**2)/(4*e**2) - d**2*g*p*x**2/(6*e**2) + d*f*p*x**2/(4*e) + d*g*p*x**4/(12*e) + f*p*x**4*log(d + e*x**2)/4 - f*p*x**4/8 + f*x**4*log(c)/4 + g*p*x**6*log(d + e*x**2)/6 - g*p*x**6/18 + g*x**6*log(c)/6, Ne(e, 0)), ((f*x**4/4 + g*x**6/6)*log(c*d**p), True))","A",0
312,1,139,0,44.851873," ","integrate(x*(g*x**2+f)*ln(c*(e*x**2+d)**p),x)","\begin{cases} - \frac{d^{2} g p \log{\left(d + e x^{2} \right)}}{4 e^{2}} + \frac{d f p \log{\left(d + e x^{2} \right)}}{2 e} + \frac{d g p x^{2}}{4 e} + \frac{f p x^{2} \log{\left(d + e x^{2} \right)}}{2} - \frac{f p x^{2}}{2} + \frac{f x^{2} \log{\left(c \right)}}{2} + \frac{g p x^{4} \log{\left(d + e x^{2} \right)}}{4} - \frac{g p x^{4}}{8} + \frac{g x^{4} \log{\left(c \right)}}{4} & \text{for}\: e \neq 0 \\\left(\frac{f x^{2}}{2} + \frac{g x^{4}}{4}\right) \log{\left(c d^{p} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-d**2*g*p*log(d + e*x**2)/(4*e**2) + d*f*p*log(d + e*x**2)/(2*e) + d*g*p*x**2/(4*e) + f*p*x**2*log(d + e*x**2)/2 - f*p*x**2/2 + f*x**2*log(c)/2 + g*p*x**4*log(d + e*x**2)/4 - g*p*x**4/8 + g*x**4*log(c)/4, Ne(e, 0)), ((f*x**2/2 + g*x**4/4)*log(c*d**p), True))","A",0
313,0,0,0,0.000000," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)/x,x)","\int \frac{\left(f + g x^{2}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral((f + g*x**2)*log(c*(d + e*x**2)**p)/x, x)","F",0
314,0,0,0,0.000000," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)/x**3,x)","\int \frac{\left(f + g x^{2}\right) \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{x^{3}}\, dx"," ",0,"Integral((f + g*x**2)*log(c*(d + e*x**2)**p)/x**3, x)","F",0
315,-1,0,0,0.000000," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)/x**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,1,277,0,90.172038," ","integrate(x**2*(g*x**2+f)*ln(c*(e*x**2+d)**p),x)","\begin{cases} \frac{i d^{\frac{5}{2}} g p \log{\left(d + e x^{2} \right)}}{5 e^{3} \sqrt{\frac{1}{e}}} - \frac{2 i d^{\frac{5}{2}} g p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{5 e^{3} \sqrt{\frac{1}{e}}} - \frac{i d^{\frac{3}{2}} f p \log{\left(d + e x^{2} \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{2 i d^{\frac{3}{2}} f p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} - \frac{2 d^{2} g p x}{5 e^{2}} + \frac{2 d f p x}{3 e} + \frac{2 d g p x^{3}}{15 e} + \frac{f p x^{3} \log{\left(d + e x^{2} \right)}}{3} - \frac{2 f p x^{3}}{9} + \frac{f x^{3} \log{\left(c \right)}}{3} + \frac{g p x^{5} \log{\left(d + e x^{2} \right)}}{5} - \frac{2 g p x^{5}}{25} + \frac{g x^{5} \log{\left(c \right)}}{5} & \text{for}\: e \neq 0 \\\left(\frac{f x^{3}}{3} + \frac{g x^{5}}{5}\right) \log{\left(c d^{p} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*d**(5/2)*g*p*log(d + e*x**2)/(5*e**3*sqrt(1/e)) - 2*I*d**(5/2)*g*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(5*e**3*sqrt(1/e)) - I*d**(3/2)*f*p*log(d + e*x**2)/(3*e**2*sqrt(1/e)) + 2*I*d**(3/2)*f*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*e**2*sqrt(1/e)) - 2*d**2*g*p*x/(5*e**2) + 2*d*f*p*x/(3*e) + 2*d*g*p*x**3/(15*e) + f*p*x**3*log(d + e*x**2)/3 - 2*f*p*x**3/9 + f*x**3*log(c)/3 + g*p*x**5*log(d + e*x**2)/5 - 2*g*p*x**5/25 + g*x**5*log(c)/5, Ne(e, 0)), ((f*x**3/3 + g*x**5/5)*log(c*d**p), True))","A",0
319,1,228,0,24.130399," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p),x)","\begin{cases} - \frac{i d^{\frac{3}{2}} g p \log{\left(d + e x^{2} \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{2 i d^{\frac{3}{2}} g p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{i \sqrt{d} f p \log{\left(d + e x^{2} \right)}}{e \sqrt{\frac{1}{e}}} - \frac{2 i \sqrt{d} f p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{e \sqrt{\frac{1}{e}}} + \frac{2 d g p x}{3 e} + f p x \log{\left(d + e x^{2} \right)} - 2 f p x + f x \log{\left(c \right)} + \frac{g p x^{3} \log{\left(d + e x^{2} \right)}}{3} - \frac{2 g p x^{3}}{9} + \frac{g x^{3} \log{\left(c \right)}}{3} & \text{for}\: e \neq 0 \\\left(f x + \frac{g x^{3}}{3}\right) \log{\left(c d^{p} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*d**(3/2)*g*p*log(d + e*x**2)/(3*e**2*sqrt(1/e)) + 2*I*d**(3/2)*g*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*e**2*sqrt(1/e)) + I*sqrt(d)*f*p*log(d + e*x**2)/(e*sqrt(1/e)) - 2*I*sqrt(d)*f*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(e*sqrt(1/e)) + 2*d*g*p*x/(3*e) + f*p*x*log(d + e*x**2) - 2*f*p*x + f*x*log(c) + g*p*x**3*log(d + e*x**2)/3 - 2*g*p*x**3/9 + g*x**3*log(c)/3, Ne(e, 0)), ((f*x + g*x**3/3)*log(c*d**p), True))","A",0
320,1,262,0,45.995087," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)/x**2,x)","\begin{cases} \left(- \frac{f}{x} + g x\right) \log{\left(0^{p} c \right)} & \text{for}\: d = 0 \wedge e = 0 \\- \frac{f p \log{\left(e \right)}}{x} - \frac{2 f p \log{\left(x \right)}}{x} - \frac{2 f p}{x} - \frac{f \log{\left(c \right)}}{x} + g p x \log{\left(e \right)} + 2 g p x \log{\left(x \right)} - 2 g p x + g x \log{\left(c \right)} & \text{for}\: d = 0 \\\left(- \frac{f}{x} + g x\right) \log{\left(c d^{p} \right)} & \text{for}\: e = 0 \\\frac{i \sqrt{d} g p \log{\left(d + e x^{2} \right)}}{e \sqrt{\frac{1}{e}}} - \frac{2 i \sqrt{d} g p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{e \sqrt{\frac{1}{e}}} - \frac{f p \log{\left(d + e x^{2} \right)}}{x} - \frac{f \log{\left(c \right)}}{x} + g p x \log{\left(d + e x^{2} \right)} - 2 g p x + g x \log{\left(c \right)} + \frac{i f p \log{\left(d + e x^{2} \right)}}{\sqrt{d} \sqrt{\frac{1}{e}}} - \frac{2 i f p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{\sqrt{d} \sqrt{\frac{1}{e}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-f/x + g*x)*log(0**p*c), Eq(d, 0) & Eq(e, 0)), (-f*p*log(e)/x - 2*f*p*log(x)/x - 2*f*p/x - f*log(c)/x + g*p*x*log(e) + 2*g*p*x*log(x) - 2*g*p*x + g*x*log(c), Eq(d, 0)), ((-f/x + g*x)*log(c*d**p), Eq(e, 0)), (I*sqrt(d)*g*p*log(d + e*x**2)/(e*sqrt(1/e)) - 2*I*sqrt(d)*g*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(e*sqrt(1/e)) - f*p*log(d + e*x**2)/x - f*log(c)/x + g*p*x*log(d + e*x**2) - 2*g*p*x + g*x*log(c) + I*f*p*log(d + e*x**2)/(sqrt(d)*sqrt(1/e)) - 2*I*f*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(sqrt(d)*sqrt(1/e)), True))","A",0
321,1,1454,0,105.074763," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)/x**4,x)","\begin{cases} \left(- \frac{f}{3 x^{3}} - \frac{g}{x}\right) \log{\left(0^{p} c \right)} & \text{for}\: d = 0 \wedge e = 0 \\\left(- \frac{f}{3 x^{3}} - \frac{g}{x}\right) \log{\left(c d^{p} \right)} & \text{for}\: e = 0 \\- \frac{f p \log{\left(e \right)}}{3 x^{3}} - \frac{2 f p \log{\left(x \right)}}{3 x^{3}} - \frac{2 f p}{9 x^{3}} - \frac{f \log{\left(c \right)}}{3 x^{3}} - \frac{g p \log{\left(e \right)}}{x} - \frac{2 g p \log{\left(x \right)}}{x} - \frac{2 g p}{x} - \frac{g \log{\left(c \right)}}{x} & \text{for}\: d = 0 \\- \frac{i d^{\frac{5}{2}} f p \sqrt{\frac{1}{e}} \log{\left(d + e x^{2} \right)}}{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}} + 3 i d^{\frac{3}{2}} e x^{5} \sqrt{\frac{1}{e}}} - \frac{i d^{\frac{5}{2}} f \sqrt{\frac{1}{e}} \log{\left(c \right)}}{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}} + 3 i d^{\frac{3}{2}} e x^{5} \sqrt{\frac{1}{e}}} - \frac{3 i d^{\frac{5}{2}} g p x^{2} \sqrt{\frac{1}{e}} \log{\left(d + e x^{2} \right)}}{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}} + 3 i d^{\frac{3}{2}} e x^{5} \sqrt{\frac{1}{e}}} - \frac{3 i d^{\frac{5}{2}} g x^{2} \sqrt{\frac{1}{e}} \log{\left(c \right)}}{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}} + 3 i d^{\frac{3}{2}} e x^{5} \sqrt{\frac{1}{e}}} - \frac{i d^{\frac{3}{2}} f p x^{2} \sqrt{\frac{1}{e}} \log{\left(d + e x^{2} \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{2 i d^{\frac{3}{2}} f p x^{2} \sqrt{\frac{1}{e}}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{i d^{\frac{3}{2}} f x^{2} \sqrt{\frac{1}{e}} \log{\left(c \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{3 i d^{\frac{3}{2}} g p x^{4} \sqrt{\frac{1}{e}} \log{\left(d + e x^{2} \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{3 i d^{\frac{3}{2}} g x^{4} \sqrt{\frac{1}{e}} \log{\left(c \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{2 i \sqrt{d} e f p x^{4} \sqrt{\frac{1}{e}}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{3 d^{2} g p x^{3} \log{\left(d + e x^{2} \right)}}{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}} + 3 i d^{\frac{3}{2}} e x^{5} \sqrt{\frac{1}{e}}} + \frac{6 d^{2} g p x^{3} \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}} + 3 i d^{\frac{3}{2}} e x^{5} \sqrt{\frac{1}{e}}} - \frac{3 d^{2} g x^{3} \log{\left(c \right)}}{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}} + 3 i d^{\frac{3}{2}} e x^{5} \sqrt{\frac{1}{e}}} + \frac{d f p x^{3} \log{\left(d + e x^{2} \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{2 d f p x^{3} \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} + \frac{d f x^{3} \log{\left(c \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{3 d g p x^{5} \log{\left(d + e x^{2} \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} + \frac{6 d g p x^{5} \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{3 d g x^{5} \log{\left(c \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} + \frac{e f p x^{5} \log{\left(d + e x^{2} \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} - \frac{2 e f p x^{5} \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} + \frac{e f x^{5} \log{\left(c \right)}}{\frac{3 i d^{\frac{5}{2}} x^{3} \sqrt{\frac{1}{e}}}{e} + 3 i d^{\frac{3}{2}} x^{5} \sqrt{\frac{1}{e}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-f/(3*x**3) - g/x)*log(0**p*c), Eq(d, 0) & Eq(e, 0)), ((-f/(3*x**3) - g/x)*log(c*d**p), Eq(e, 0)), (-f*p*log(e)/(3*x**3) - 2*f*p*log(x)/(3*x**3) - 2*f*p/(9*x**3) - f*log(c)/(3*x**3) - g*p*log(e)/x - 2*g*p*log(x)/x - 2*g*p/x - g*log(c)/x, Eq(d, 0)), (-I*d**(5/2)*f*p*sqrt(1/e)*log(d + e*x**2)/(3*I*d**(5/2)*x**3*sqrt(1/e) + 3*I*d**(3/2)*e*x**5*sqrt(1/e)) - I*d**(5/2)*f*sqrt(1/e)*log(c)/(3*I*d**(5/2)*x**3*sqrt(1/e) + 3*I*d**(3/2)*e*x**5*sqrt(1/e)) - 3*I*d**(5/2)*g*p*x**2*sqrt(1/e)*log(d + e*x**2)/(3*I*d**(5/2)*x**3*sqrt(1/e) + 3*I*d**(3/2)*e*x**5*sqrt(1/e)) - 3*I*d**(5/2)*g*x**2*sqrt(1/e)*log(c)/(3*I*d**(5/2)*x**3*sqrt(1/e) + 3*I*d**(3/2)*e*x**5*sqrt(1/e)) - I*d**(3/2)*f*p*x**2*sqrt(1/e)*log(d + e*x**2)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - 2*I*d**(3/2)*f*p*x**2*sqrt(1/e)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - I*d**(3/2)*f*x**2*sqrt(1/e)*log(c)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - 3*I*d**(3/2)*g*p*x**4*sqrt(1/e)*log(d + e*x**2)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - 3*I*d**(3/2)*g*x**4*sqrt(1/e)*log(c)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - 2*I*sqrt(d)*e*f*p*x**4*sqrt(1/e)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - 3*d**2*g*p*x**3*log(d + e*x**2)/(3*I*d**(5/2)*x**3*sqrt(1/e) + 3*I*d**(3/2)*e*x**5*sqrt(1/e)) + 6*d**2*g*p*x**3*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*I*d**(5/2)*x**3*sqrt(1/e) + 3*I*d**(3/2)*e*x**5*sqrt(1/e)) - 3*d**2*g*x**3*log(c)/(3*I*d**(5/2)*x**3*sqrt(1/e) + 3*I*d**(3/2)*e*x**5*sqrt(1/e)) + d*f*p*x**3*log(d + e*x**2)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - 2*d*f*p*x**3*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) + d*f*x**3*log(c)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - 3*d*g*p*x**5*log(d + e*x**2)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) + 6*d*g*p*x**5*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - 3*d*g*x**5*log(c)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) + e*f*p*x**5*log(d + e*x**2)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) - 2*e*f*p*x**5*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)) + e*f*x**5*log(c)/(3*I*d**(5/2)*x**3*sqrt(1/e)/e + 3*I*d**(3/2)*x**5*sqrt(1/e)), True))","A",0
322,-1,0,0,0.000000," ","integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate(x**5*(g*x**2+f)**2*ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate(x**3*(g*x**2+f)**2*ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,1,260,0,173.995499," ","integrate(x*(g*x**2+f)**2*ln(c*(e*x**2+d)**p),x)","\begin{cases} \frac{d^{3} g^{2} p \log{\left(d + e x^{2} \right)}}{6 e^{3}} - \frac{d^{2} f g p \log{\left(d + e x^{2} \right)}}{2 e^{2}} - \frac{d^{2} g^{2} p x^{2}}{6 e^{2}} + \frac{d f^{2} p \log{\left(d + e x^{2} \right)}}{2 e} + \frac{d f g p x^{2}}{2 e} + \frac{d g^{2} p x^{4}}{12 e} + \frac{f^{2} p x^{2} \log{\left(d + e x^{2} \right)}}{2} - \frac{f^{2} p x^{2}}{2} + \frac{f^{2} x^{2} \log{\left(c \right)}}{2} + \frac{f g p x^{4} \log{\left(d + e x^{2} \right)}}{2} - \frac{f g p x^{4}}{4} + \frac{f g x^{4} \log{\left(c \right)}}{2} + \frac{g^{2} p x^{6} \log{\left(d + e x^{2} \right)}}{6} - \frac{g^{2} p x^{6}}{18} + \frac{g^{2} x^{6} \log{\left(c \right)}}{6} & \text{for}\: e \neq 0 \\\left(\frac{f^{2} x^{2}}{2} + \frac{f g x^{4}}{2} + \frac{g^{2} x^{6}}{6}\right) \log{\left(c d^{p} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**3*g**2*p*log(d + e*x**2)/(6*e**3) - d**2*f*g*p*log(d + e*x**2)/(2*e**2) - d**2*g**2*p*x**2/(6*e**2) + d*f**2*p*log(d + e*x**2)/(2*e) + d*f*g*p*x**2/(2*e) + d*g**2*p*x**4/(12*e) + f**2*p*x**2*log(d + e*x**2)/2 - f**2*p*x**2/2 + f**2*x**2*log(c)/2 + f*g*p*x**4*log(d + e*x**2)/2 - f*g*p*x**4/4 + f*g*x**4*log(c)/2 + g**2*p*x**6*log(d + e*x**2)/6 - g**2*p*x**6/18 + g**2*x**6*log(c)/6, Ne(e, 0)), ((f**2*x**2/2 + f*g*x**4/2 + g**2*x**6/6)*log(c*d**p), True))","A",0
326,0,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x,x)","\int \frac{\left(f + g x^{2}\right)^{2} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral((f + g*x**2)**2*log(c*(d + e*x**2)**p)/x, x)","F",0
327,0,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x**3,x)","\int \frac{\left(f + g x^{2}\right)^{2} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{x^{3}}\, dx"," ",0,"Integral((f + g*x**2)**2*log(c*(d + e*x**2)**p)/x**3, x)","F",0
328,0,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x**5,x)","\int \frac{\left(f + g x^{2}\right)^{2} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{x^{5}}\, dx"," ",0,"Integral((f + g*x**2)**2*log(c*(d + e*x**2)**p)/x**5, x)","F",0
329,-1,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,-1,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(x**2*(g*x**2+f)**2*ln(c*(e*x**2+d)**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,1,415,0,95.793755," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p),x)","\begin{cases} \frac{i d^{\frac{5}{2}} g^{2} p \log{\left(d + e x^{2} \right)}}{5 e^{3} \sqrt{\frac{1}{e}}} - \frac{2 i d^{\frac{5}{2}} g^{2} p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{5 e^{3} \sqrt{\frac{1}{e}}} - \frac{2 i d^{\frac{3}{2}} f g p \log{\left(d + e x^{2} \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{4 i d^{\frac{3}{2}} f g p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{i \sqrt{d} f^{2} p \log{\left(d + e x^{2} \right)}}{e \sqrt{\frac{1}{e}}} - \frac{2 i \sqrt{d} f^{2} p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{e \sqrt{\frac{1}{e}}} - \frac{2 d^{2} g^{2} p x}{5 e^{2}} + \frac{4 d f g p x}{3 e} + \frac{2 d g^{2} p x^{3}}{15 e} + f^{2} p x \log{\left(d + e x^{2} \right)} - 2 f^{2} p x + f^{2} x \log{\left(c \right)} + \frac{2 f g p x^{3} \log{\left(d + e x^{2} \right)}}{3} - \frac{4 f g p x^{3}}{9} + \frac{2 f g x^{3} \log{\left(c \right)}}{3} + \frac{g^{2} p x^{5} \log{\left(d + e x^{2} \right)}}{5} - \frac{2 g^{2} p x^{5}}{25} + \frac{g^{2} x^{5} \log{\left(c \right)}}{5} & \text{for}\: e \neq 0 \\\left(f^{2} x + \frac{2 f g x^{3}}{3} + \frac{g^{2} x^{5}}{5}\right) \log{\left(c d^{p} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*d**(5/2)*g**2*p*log(d + e*x**2)/(5*e**3*sqrt(1/e)) - 2*I*d**(5/2)*g**2*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(5*e**3*sqrt(1/e)) - 2*I*d**(3/2)*f*g*p*log(d + e*x**2)/(3*e**2*sqrt(1/e)) + 4*I*d**(3/2)*f*g*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*e**2*sqrt(1/e)) + I*sqrt(d)*f**2*p*log(d + e*x**2)/(e*sqrt(1/e)) - 2*I*sqrt(d)*f**2*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(e*sqrt(1/e)) - 2*d**2*g**2*p*x/(5*e**2) + 4*d*f*g*p*x/(3*e) + 2*d*g**2*p*x**3/(15*e) + f**2*p*x*log(d + e*x**2) - 2*f**2*p*x + f**2*x*log(c) + 2*f*g*p*x**3*log(d + e*x**2)/3 - 4*f*g*p*x**3/9 + 2*f*g*x**3*log(c)/3 + g**2*p*x**5*log(d + e*x**2)/5 - 2*g**2*p*x**5/25 + g**2*x**5*log(c)/5, Ne(e, 0)), ((f**2*x + 2*f*g*x**3/3 + g**2*x**5/5)*log(c*d**p), True))","A",0
334,1,510,0,172.738771," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x**2,x)","\begin{cases} \left(- \frac{f^{2}}{x} + 2 f g x + \frac{g^{2} x^{3}}{3}\right) \log{\left(0^{p} c \right)} & \text{for}\: d = 0 \wedge e = 0 \\- \frac{f^{2} p \log{\left(e \right)}}{x} - \frac{2 f^{2} p \log{\left(x \right)}}{x} - \frac{2 f^{2} p}{x} - \frac{f^{2} \log{\left(c \right)}}{x} + 2 f g p x \log{\left(e \right)} + 4 f g p x \log{\left(x \right)} - 4 f g p x + 2 f g x \log{\left(c \right)} + \frac{g^{2} p x^{3} \log{\left(e \right)}}{3} + \frac{2 g^{2} p x^{3} \log{\left(x \right)}}{3} - \frac{2 g^{2} p x^{3}}{9} + \frac{g^{2} x^{3} \log{\left(c \right)}}{3} & \text{for}\: d = 0 \\\left(- \frac{f^{2}}{x} + 2 f g x + \frac{g^{2} x^{3}}{3}\right) \log{\left(c d^{p} \right)} & \text{for}\: e = 0 \\- \frac{i d^{\frac{3}{2}} g^{2} p \log{\left(d + e x^{2} \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{2 i d^{\frac{3}{2}} g^{2} p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{3 e^{2} \sqrt{\frac{1}{e}}} + \frac{2 i \sqrt{d} f g p \log{\left(d + e x^{2} \right)}}{e \sqrt{\frac{1}{e}}} - \frac{4 i \sqrt{d} f g p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{e \sqrt{\frac{1}{e}}} + \frac{2 d g^{2} p x}{3 e} - \frac{f^{2} p \log{\left(d + e x^{2} \right)}}{x} - \frac{f^{2} \log{\left(c \right)}}{x} + 2 f g p x \log{\left(d + e x^{2} \right)} - 4 f g p x + 2 f g x \log{\left(c \right)} + \frac{g^{2} p x^{3} \log{\left(d + e x^{2} \right)}}{3} - \frac{2 g^{2} p x^{3}}{9} + \frac{g^{2} x^{3} \log{\left(c \right)}}{3} + \frac{i f^{2} p \log{\left(d + e x^{2} \right)}}{\sqrt{d} \sqrt{\frac{1}{e}}} - \frac{2 i f^{2} p \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{\sqrt{d} \sqrt{\frac{1}{e}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-f**2/x + 2*f*g*x + g**2*x**3/3)*log(0**p*c), Eq(d, 0) & Eq(e, 0)), (-f**2*p*log(e)/x - 2*f**2*p*log(x)/x - 2*f**2*p/x - f**2*log(c)/x + 2*f*g*p*x*log(e) + 4*f*g*p*x*log(x) - 4*f*g*p*x + 2*f*g*x*log(c) + g**2*p*x**3*log(e)/3 + 2*g**2*p*x**3*log(x)/3 - 2*g**2*p*x**3/9 + g**2*x**3*log(c)/3, Eq(d, 0)), ((-f**2/x + 2*f*g*x + g**2*x**3/3)*log(c*d**p), Eq(e, 0)), (-I*d**(3/2)*g**2*p*log(d + e*x**2)/(3*e**2*sqrt(1/e)) + 2*I*d**(3/2)*g**2*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(3*e**2*sqrt(1/e)) + 2*I*sqrt(d)*f*g*p*log(d + e*x**2)/(e*sqrt(1/e)) - 4*I*sqrt(d)*f*g*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(e*sqrt(1/e)) + 2*d*g**2*p*x/(3*e) - f**2*p*log(d + e*x**2)/x - f**2*log(c)/x + 2*f*g*p*x*log(d + e*x**2) - 4*f*g*p*x + 2*f*g*x*log(c) + g**2*p*x**3*log(d + e*x**2)/3 - 2*g**2*p*x**3/9 + g**2*x**3*log(c)/3 + I*f**2*p*log(d + e*x**2)/(sqrt(d)*sqrt(1/e)) - 2*I*f**2*p*log(-I*sqrt(d)*sqrt(1/e) + x)/(sqrt(d)*sqrt(1/e)), True))","A",0
335,-1,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate((g*x**2+f)**2*ln(c*(e*x**2+d)**p)/x**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,0,0,0,0.000000," ","integrate(x**5*ln(c*(e*x**2+d)**p)/(g*x**2+f),x)","\int \frac{x^{5} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(x**5*log(c*(d + e*x**2)**p)/(f + g*x**2), x)","F",0
339,0,0,0,0.000000," ","integrate(x**3*ln(c*(e*x**2+d)**p)/(g*x**2+f),x)","\int \frac{x^{3} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(x**3*log(c*(d + e*x**2)**p)/(f + g*x**2), x)","F",0
340,0,0,0,0.000000," ","integrate(x*ln(c*(e*x**2+d)**p)/(g*x**2+f),x)","\int \frac{x \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(x*log(c*(d + e*x**2)**p)/(f + g*x**2), x)","F",0
341,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/x/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/x**3/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,0,0,0,0.000000," ","integrate(x**4*ln(c*(e*x**2+d)**p)/(g*x**2+f),x)","\int \frac{x^{4} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(x**4*log(c*(d + e*x**2)**p)/(f + g*x**2), x)","F",0
344,0,0,0,0.000000," ","integrate(x**2*ln(c*(e*x**2+d)**p)/(g*x**2+f),x)","\int \frac{x^{2} \log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(x**2*log(c*(d + e*x**2)**p)/(f + g*x**2), x)","F",0
345,0,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/(g*x**2+f),x)","\int \frac{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{f + g x^{2}}\, dx"," ",0,"Integral(log(c*(d + e*x**2)**p)/(f + g*x**2), x)","F",0
346,0,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/x**2/(g*x**2+f),x)","\int \frac{\log{\left(c \left(d + e x^{2}\right)^{p} \right)}}{x^{2} \left(f + g x^{2}\right)}\, dx"," ",0,"Integral(log(c*(d + e*x**2)**p)/(x**2*(f + g*x**2)), x)","F",0
347,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/x**4/(g*x**2+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate(x**5*ln(c*(e*x**2+d)**p)/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate(x**3*ln(c*(e*x**2+d)**p)/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,-1,0,0,0.000000," ","integrate(x*ln(c*(e*x**2+d)**p)/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/x/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/x**3/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-1,0,0,0.000000," ","integrate(x**4*ln(c*(e*x**2+d)**p)/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate(x**2*ln(c*(e*x**2+d)**p)/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,-1,0,0,0.000000," ","integrate(ln(c*(e*x**2+d)**p)/x**2/(g*x**2+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,0,0,0,0.000000," ","integrate(ln(c*(b*x**2+a)**n)/(b*x**2+a),x)","\int \frac{\log{\left(c \left(a + b x^{2}\right)^{n} \right)}}{a + b x^{2}}\, dx"," ",0,"Integral(log(c*(a + b*x**2)**n)/(a + b*x**2), x)","F",0
358,0,0,0,0.000000," ","integrate(ln(-x**2+1)/(-x**2+2),x)","- \int \frac{\log{\left(1 - x^{2} \right)}}{x^{2} - 2}\, dx"," ",0,"-Integral(log(1 - x**2)/(x**2 - 2), x)","F",0
359,0,0,0,0.000000," ","integrate(ln(e*x**2+d)/(-x**2+1),x)","- \int \frac{\log{\left(d + e x^{2} \right)}}{x^{2} - 1}\, dx"," ",0,"-Integral(log(d + e*x**2)/(x**2 - 1), x)","F",0
360,0,0,0,0.000000," ","integrate((f+g*x**(3*n))*ln(c*(d+e*x**n)**p)/x,x)","\int \frac{\left(f + g x^{3 n}\right) \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral((f + g*x**(3*n))*log(c*(d + e*x**n)**p)/x, x)","F",0
361,0,0,0,0.000000," ","integrate((f+g*x**(2*n))*ln(c*(d+e*x**n)**p)/x,x)","\int \frac{\left(f + g x^{2 n}\right) \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral((f + g*x**(2*n))*log(c*(d + e*x**n)**p)/x, x)","F",0
362,0,0,0,0.000000," ","integrate((f+g*x**n)*ln(c*(d+e*x**n)**p)/x,x)","\int \frac{\left(f + g x^{n}\right) \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral((f + g*x**n)*log(c*(d + e*x**n)**p)/x, x)","F",0
363,0,0,0,0.000000," ","integrate((f+g/(x**n))*ln(c*(d+e*x**n)**p)/x,x)","\int \frac{x^{- n} \left(f x^{n} + g\right) \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(x**(-n)*(f*x**n + g)*log(c*(d + e*x**n)**p)/x, x)","F",0
364,0,0,0,0.000000," ","integrate((f+g/(x**(2*n)))*ln(c*(d+e*x**n)**p)/x,x)","\int \frac{x^{- 2 n} \left(f x^{2 n} + g\right) \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(x**(-2*n)*(f*x**(2*n) + g)*log(c*(d + e*x**n)**p)/x, x)","F",0
365,-1,0,0,0.000000," ","integrate((f+g*x**(3*n))**2*ln(c*(d+e*x**n)**p)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,0,0,0,0.000000," ","integrate((f+g*x**(2*n))**2*ln(c*(d+e*x**n)**p)/x,x)","\int \frac{\left(f + g x^{2 n}\right)^{2} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral((f + g*x**(2*n))**2*log(c*(d + e*x**n)**p)/x, x)","F",0
367,0,0,0,0.000000," ","integrate((f+g*x**n)**2*ln(c*(d+e*x**n)**p)/x,x)","\int \frac{\left(f + g x^{n}\right)^{2} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral((f + g*x**n)**2*log(c*(d + e*x**n)**p)/x, x)","F",0
368,0,0,0,0.000000," ","integrate((f+g/(x**n))**2*ln(c*(d+e*x**n)**p)/x,x)","\int \frac{x^{- 2 n} \left(f x^{n} + g\right)^{2} \log{\left(c \left(d + e x^{n}\right)^{p} \right)}}{x}\, dx"," ",0,"Integral(x**(-2*n)*(f*x**n + g)**2*log(c*(d + e*x**n)**p)/x, x)","F",0
369,-1,0,0,0.000000," ","integrate((f+g/(x**(2*n)))**2*ln(c*(d+e*x**n)**p)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x/(f+g*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x/(f+g*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-2,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x/(f+g/(x**n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
373,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x/(f+g/(x**(2*n))),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x/(f+g*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x/(f+g*x**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x/(f+g/(x**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)/x/(f+g/(x**(2*n)))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-2,0,0,0.000000," ","integrate(ln(c*(d+e*x**n))/x/(c*e+(c*d-1)/(x**n)),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
379,-2,0,0,0.000000," ","integrate(x**(-1+n)*ln(c*(d+e*x**n))/(-1+c*d+c*e*x**n),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
380,-1,0,0,0.000000," ","integrate(ln(c*(d+e/(x**n)))/x/(c*e-(-c*d+1)*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((f+g*x**(2*n))**2*ln(c*(d+e*x**n)**p)**q/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate((f+g*x**n)**2*ln(c*(d+e*x**n)**p)**q/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate((f+g/(x**n))**2*ln(c*(d+e*x**n)**p)**q/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate((f+g/(x**(2*n)))**2*ln(c*(d+e*x**n)**p)**q/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)**q/x/(f+g*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,0,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)**q/x/(f+g*x**n),x)","\int \frac{\log{\left(c \left(d + e x^{n}\right)^{p} \right)}^{q}}{x \left(f + g x^{n}\right)}\, dx"," ",0,"Integral(log(c*(d + e*x**n)**p)**q/(x*(f + g*x**n)), x)","F",0
387,-2,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)**q/x/(f+g/(x**n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
388,-1,0,0,0.000000," ","integrate(ln(c*(d+e*x**n)**p)**q/x/(f+g/(x**(2*n))),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate(ln(x)*ln(d+e*x**m)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,0,0,0,0.000000," ","integrate(ln((a+x)/x)/x,x)","\int \frac{\log{\left(\frac{a}{x} + 1 \right)}}{x}\, dx"," ",0,"Integral(log(a/x + 1)/x, x)","F",0
391,0,0,0,0.000000," ","integrate(ln((x**2+a)/x**2)/x,x)","\int \frac{\log{\left(\frac{a}{x^{2}} + 1 \right)}}{x}\, dx"," ",0,"Integral(log(a/x**2 + 1)/x, x)","F",0
392,0,0,0,0.000000," ","integrate(ln((a+x**n)/(x**n))/x,x)","\int \frac{\log{\left(a x^{- n} + 1 \right)}}{x}\, dx"," ",0,"Integral(log(a*x**(-n) + 1)/x, x)","F",0
393,0,0,0,0.000000," ","integrate(ln((b*x+a)/x)/x,x)","\int \frac{\log{\left(\frac{a}{x} + b \right)}}{x}\, dx"," ",0,"Integral(log(a/x + b)/x, x)","F",0
394,0,0,0,0.000000," ","integrate(ln((b*x**2+a)/x**2)/x,x)","\int \frac{\log{\left(\frac{a}{x^{2}} + b \right)}}{x}\, dx"," ",0,"Integral(log(a/x**2 + b)/x, x)","F",0
395,0,0,0,0.000000," ","integrate(ln((a+b*x**n)/(x**n))/x,x)","\int \frac{\log{\left(a x^{- n} + b \right)}}{x}\, dx"," ",0,"Integral(log(a*x**(-n) + b)/x, x)","F",0
396,0,0,0,0.000000," ","integrate(ln((b*x+a)/x)/(d*x+c),x)","\int \frac{\log{\left(\frac{a}{x} + b \right)}}{c + d x}\, dx"," ",0,"Integral(log(a/x + b)/(c + d*x), x)","F",0
397,0,0,0,0.000000," ","integrate(ln((b*x**2+a)/x**2)/(d*x+c),x)","\int \frac{\log{\left(\frac{a}{x^{2}} + b \right)}}{c + d x}\, dx"," ",0,"Integral(log(a/x**2 + b)/(c + d*x), x)","F",0
398,0,0,0,0.000000," ","integrate(ln((a+b*x**n)/(x**n))/(d*x+c),x)","\int \frac{\log{\left(a x^{- n} + b \right)}}{c + d x}\, dx"," ",0,"Integral(log(a*x**(-n) + b)/(c + d*x), x)","F",0
399,0,0,0,0.000000," ","integrate((f*x)**q*(a+b*ln(c*(d+e*x**m)**n)),x)","\int \left(f x\right)^{q} \left(a + b \log{\left(c \left(d + e x^{m}\right)^{n} \right)}\right)\, dx"," ",0,"Integral((f*x)**q*(a + b*log(c*(d + e*x**m)**n)), x)","F",0
400,1,155,0,24.203699," ","integrate(x**3*(a+b*ln(c*(d+e*x**(1/2))**n)),x)","\frac{a x^{4}}{4} + b \left(- \frac{e n \left(\frac{2 d^{8} \left(\begin{cases} \frac{\sqrt{x}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e \sqrt{x} \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{8}} - \frac{2 d^{7} \sqrt{x}}{e^{8}} + \frac{d^{6} x}{e^{7}} - \frac{2 d^{5} x^{\frac{3}{2}}}{3 e^{6}} + \frac{d^{4} x^{2}}{2 e^{5}} - \frac{2 d^{3} x^{\frac{5}{2}}}{5 e^{4}} + \frac{d^{2} x^{3}}{3 e^{3}} - \frac{2 d x^{\frac{7}{2}}}{7 e^{2}} + \frac{x^{4}}{4 e}\right)}{8} + \frac{x^{4} \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}}{4}\right)"," ",0,"a*x**4/4 + b*(-e*n*(2*d**8*Piecewise((sqrt(x)/d, Eq(e, 0)), (log(d + e*sqrt(x))/e, True))/e**8 - 2*d**7*sqrt(x)/e**8 + d**6*x/e**7 - 2*d**5*x**(3/2)/(3*e**6) + d**4*x**2/(2*e**5) - 2*d**3*x**(5/2)/(5*e**4) + d**2*x**3/(3*e**3) - 2*d*x**(7/2)/(7*e**2) + x**4/(4*e))/8 + x**4*log(c*(d + e*sqrt(x))**n)/4)","A",0
401,1,128,0,9.657433," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/2))**n)),x)","\frac{a x^{3}}{3} + b \left(- \frac{e n \left(\frac{2 d^{6} \left(\begin{cases} \frac{\sqrt{x}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e \sqrt{x} \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{6}} - \frac{2 d^{5} \sqrt{x}}{e^{6}} + \frac{d^{4} x}{e^{5}} - \frac{2 d^{3} x^{\frac{3}{2}}}{3 e^{4}} + \frac{d^{2} x^{2}}{2 e^{3}} - \frac{2 d x^{\frac{5}{2}}}{5 e^{2}} + \frac{x^{3}}{3 e}\right)}{6} + \frac{x^{3} \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}}{3}\right)"," ",0,"a*x**3/3 + b*(-e*n*(2*d**6*Piecewise((sqrt(x)/d, Eq(e, 0)), (log(d + e*sqrt(x))/e, True))/e**6 - 2*d**5*sqrt(x)/e**6 + d**4*x/e**5 - 2*d**3*x**(3/2)/(3*e**4) + d**2*x**2/(2*e**3) - 2*d*x**(5/2)/(5*e**2) + x**3/(3*e))/6 + x**3*log(c*(d + e*sqrt(x))**n)/3)","A",0
402,1,100,0,4.682683," ","integrate(x*(a+b*ln(c*(d+e*x**(1/2))**n)),x)","\frac{a x^{2}}{2} + b \left(- \frac{e n \left(\frac{2 d^{4} \left(\begin{cases} \frac{\sqrt{x}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e \sqrt{x} \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{4}} - \frac{2 d^{3} \sqrt{x}}{e^{4}} + \frac{d^{2} x}{e^{3}} - \frac{2 d x^{\frac{3}{2}}}{3 e^{2}} + \frac{x^{2}}{2 e}\right)}{4} + \frac{x^{2} \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}}{2}\right)"," ",0,"a*x**2/2 + b*(-e*n*(2*d**4*Piecewise((sqrt(x)/d, Eq(e, 0)), (log(d + e*sqrt(x))/e, True))/e**4 - 2*d**3*sqrt(x)/e**4 + d**2*x/e**3 - 2*d*x**(3/2)/(3*e**2) + x**2/(2*e))/4 + x**2*log(c*(d + e*sqrt(x))**n)/2)","A",0
403,1,66,0,1.863713," ","integrate(a+b*ln(c*(d+e*x**(1/2))**n),x)","a x + b \left(- \frac{e n \left(\frac{2 d^{2} \left(\begin{cases} \frac{\sqrt{x}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e \sqrt{x} \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{2 d \sqrt{x}}{e^{2}} + \frac{x}{e}\right)}{2} + x \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)"," ",0,"a*x + b*(-e*n*(2*d**2*Piecewise((sqrt(x)/d, Eq(e, 0)), (log(d + e*sqrt(x))/e, True))/e**2 - 2*d*sqrt(x)/e**2 + x/e)/2 + x*log(c*(d + e*sqrt(x))**n))","A",0
404,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))/x,x)","\int \frac{a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))/x, x)","F",0
405,1,554,0,63.060798," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))/x**2,x)","\begin{cases} - \frac{2 a d^{3} \sqrt{x}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} - \frac{2 a d^{2} e x}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} - \frac{2 b d^{3} n \sqrt{x} \log{\left(d + e \sqrt{x} \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} - \frac{2 b d^{3} \sqrt{x} \log{\left(c \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} - \frac{2 b d^{2} e n x \log{\left(d + e \sqrt{x} \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} - \frac{2 b d^{2} e n x}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} - \frac{2 b d^{2} e x \log{\left(c \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} - \frac{b d e^{2} n x^{\frac{3}{2}} \log{\left(x \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} + \frac{2 b d e^{2} n x^{\frac{3}{2}} \log{\left(d + e \sqrt{x} \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} - \frac{2 b d e^{2} n x^{\frac{3}{2}}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} + \frac{2 b d e^{2} x^{\frac{3}{2}} \log{\left(c \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} - \frac{b e^{3} n x^{2} \log{\left(x \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} + \frac{2 b e^{3} n x^{2} \log{\left(d + e \sqrt{x} \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} + \frac{2 b e^{3} x^{2} \log{\left(c \right)}}{2 d^{3} x^{\frac{3}{2}} + 2 d^{2} e x^{2}} & \text{for}\: d \neq 0 \\- \frac{a}{x} - \frac{b n \log{\left(e \right)}}{x} - \frac{b n \log{\left(x \right)}}{2 x} - \frac{b n}{2 x} - \frac{b \log{\left(c \right)}}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*d**3*sqrt(x)/(2*d**3*x**(3/2) + 2*d**2*e*x**2) - 2*a*d**2*e*x/(2*d**3*x**(3/2) + 2*d**2*e*x**2) - 2*b*d**3*n*sqrt(x)*log(d + e*sqrt(x))/(2*d**3*x**(3/2) + 2*d**2*e*x**2) - 2*b*d**3*sqrt(x)*log(c)/(2*d**3*x**(3/2) + 2*d**2*e*x**2) - 2*b*d**2*e*n*x*log(d + e*sqrt(x))/(2*d**3*x**(3/2) + 2*d**2*e*x**2) - 2*b*d**2*e*n*x/(2*d**3*x**(3/2) + 2*d**2*e*x**2) - 2*b*d**2*e*x*log(c)/(2*d**3*x**(3/2) + 2*d**2*e*x**2) - b*d*e**2*n*x**(3/2)*log(x)/(2*d**3*x**(3/2) + 2*d**2*e*x**2) + 2*b*d*e**2*n*x**(3/2)*log(d + e*sqrt(x))/(2*d**3*x**(3/2) + 2*d**2*e*x**2) - 2*b*d*e**2*n*x**(3/2)/(2*d**3*x**(3/2) + 2*d**2*e*x**2) + 2*b*d*e**2*x**(3/2)*log(c)/(2*d**3*x**(3/2) + 2*d**2*e*x**2) - b*e**3*n*x**2*log(x)/(2*d**3*x**(3/2) + 2*d**2*e*x**2) + 2*b*e**3*n*x**2*log(d + e*sqrt(x))/(2*d**3*x**(3/2) + 2*d**2*e*x**2) + 2*b*e**3*x**2*log(c)/(2*d**3*x**(3/2) + 2*d**2*e*x**2), Ne(d, 0)), (-a/x - b*n*log(e)/x - b*n*log(x)/(2*x) - b*n/(2*x) - b*log(c)/x, True))","A",0
406,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
407,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
408,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/2))**n))**2,x)","\int x^{2} \left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*log(c*(d + e*sqrt(x))**n))**2, x)","F",0
409,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(1/2))**n))**2,x)","\int x \left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e*sqrt(x))**n))**2, x)","F",0
410,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))**2,x)","\int \left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))**2, x)","F",0
411,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))**2/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))**2/x, x)","F",0
412,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))**2/x**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))**2/x**2, x)","F",0
413,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))**2/x**3,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))**2/x**3, x)","F",0
414,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))**2/x**4,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{2}}{x^{4}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))**2/x**4, x)","F",0
415,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/2))**n))**3,x)","\int x^{2} \left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{3}\, dx"," ",0,"Integral(x**2*(a + b*log(c*(d + e*sqrt(x))**n))**3, x)","F",0
416,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(1/2))**n))**3,x)","\int x \left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e*sqrt(x))**n))**3, x)","F",0
417,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))**3,x)","\int \left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))**3, x)","F",0
418,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))**3/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))**3/x, x)","F",0
419,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))**3/x**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{3}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))**3/x**2, x)","F",0
420,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**n))**3/x**3,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt{x}\right)^{n} \right)}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*sqrt(x))**n))**3/x**3, x)","F",0
421,1,162,0,134.388650," ","integrate(x**3*(a+b*ln(c*(d+e/x**(1/2))**n)),x)","\frac{a x^{4}}{4} + b \left(\frac{e n \left(\frac{2 x^{\frac{7}{2}}}{7 d} - \frac{e x^{3}}{3 d^{2}} + \frac{2 e^{2} x^{\frac{5}{2}}}{5 d^{3}} - \frac{e^{3} x^{2}}{2 d^{4}} + \frac{2 e^{4} x^{\frac{3}{2}}}{3 d^{5}} - \frac{e^{5} x}{d^{6}} + \frac{2 e^{6} \sqrt{x}}{d^{7}} - \frac{2 e^{8} \left(\begin{cases} \frac{1}{d \sqrt{x}} & \text{for}\: e = 0 \\\frac{\log{\left(d + \frac{e}{\sqrt{x}} \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{8}} + \frac{2 e^{7} \log{\left(\frac{1}{\sqrt{x}} \right)}}{d^{8}}\right)}{8} + \frac{x^{4} \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}}{4}\right)"," ",0,"a*x**4/4 + b*(e*n*(2*x**(7/2)/(7*d) - e*x**3/(3*d**2) + 2*e**2*x**(5/2)/(5*d**3) - e**3*x**2/(2*d**4) + 2*e**4*x**(3/2)/(3*d**5) - e**5*x/d**6 + 2*e**6*sqrt(x)/d**7 - 2*e**8*Piecewise((1/(d*sqrt(x)), Eq(e, 0)), (log(d + e/sqrt(x))/e, True))/d**8 + 2*e**7*log(1/sqrt(x))/d**8)/8 + x**4*log(c*(d + e/sqrt(x))**n)/4)","A",0
422,1,134,0,49.019771," ","integrate(x**2*(a+b*ln(c*(d+e/x**(1/2))**n)),x)","\frac{a x^{3}}{3} + b \left(\frac{e n \left(\frac{2 x^{\frac{5}{2}}}{5 d} - \frac{e x^{2}}{2 d^{2}} + \frac{2 e^{2} x^{\frac{3}{2}}}{3 d^{3}} - \frac{e^{3} x}{d^{4}} + \frac{2 e^{4} \sqrt{x}}{d^{5}} - \frac{2 e^{6} \left(\begin{cases} \frac{1}{d \sqrt{x}} & \text{for}\: e = 0 \\\frac{\log{\left(d + \frac{e}{\sqrt{x}} \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{6}} + \frac{2 e^{5} \log{\left(\frac{1}{\sqrt{x}} \right)}}{d^{6}}\right)}{6} + \frac{x^{3} \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}}{3}\right)"," ",0,"a*x**3/3 + b*(e*n*(2*x**(5/2)/(5*d) - e*x**2/(2*d**2) + 2*e**2*x**(3/2)/(3*d**3) - e**3*x/d**4 + 2*e**4*sqrt(x)/d**5 - 2*e**6*Piecewise((1/(d*sqrt(x)), Eq(e, 0)), (log(d + e/sqrt(x))/e, True))/d**6 + 2*e**5*log(1/sqrt(x))/d**6)/6 + x**3*log(c*(d + e/sqrt(x))**n)/3)","A",0
423,1,88,0,17.257120," ","integrate(x*(a+b*ln(c*(d+e/x**(1/2))**n)),x)","\frac{a x^{2}}{2} + b \left(\frac{e n \left(\frac{2 x^{\frac{3}{2}}}{3 d} - \frac{e x}{d^{2}} - \frac{2 e^{3} \left(\begin{cases} \frac{\sqrt{x}}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d \sqrt{x} + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{2 e^{2} \sqrt{x}}{d^{3}}\right)}{4} + \frac{x^{2} \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}}{2}\right)"," ",0,"a*x**2/2 + b*(e*n*(2*x**(3/2)/(3*d) - e*x/d**2 - 2*e**3*Piecewise((sqrt(x)/e, Eq(d, 0)), (log(d*sqrt(x) + e)/d, True))/d**3 + 2*e**2*sqrt(x)/d**3)/4 + x**2*log(c*(d + e/sqrt(x))**n)/2)","A",0
424,1,76,0,8.420385," ","integrate(a+b*ln(c*(d+e/x**(1/2))**n),x)","a x + b \left(\frac{e n \left(\frac{2 \sqrt{x}}{d} - \frac{2 e^{2} \left(\begin{cases} \frac{1}{d \sqrt{x}} & \text{for}\: e = 0 \\\frac{\log{\left(d + \frac{e}{\sqrt{x}} \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{2 e \log{\left(\frac{1}{\sqrt{x}} \right)}}{d^{2}}\right)}{2} + x \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}\right)"," ",0,"a*x + b*(e*n*(2*sqrt(x)/d - 2*e**2*Piecewise((1/(d*sqrt(x)), Eq(e, 0)), (log(d + e/sqrt(x))/e, True))/d**2 + 2*e*log(1/sqrt(x))/d**2)/2 + x*log(c*(d + e/sqrt(x))**n))","A",0
425,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))/x,x)","\int \frac{a + b \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e/sqrt(x))**n))/x, x)","F",0
426,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e/x**(1/2))**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(1/2))**n))**2,x)","\int x \left(a + b \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e/sqrt(x))**n))**2, x)","F",0
431,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**2,x)","\int \left(a + b \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d + e/sqrt(x))**n))**2, x)","F",0
432,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**2/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e/sqrt(x))**n))**2/x, x)","F",0
433,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**2/x**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e/sqrt(x))**n))**2/x**2, x)","F",0
434,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**2/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(1/2))**n))**3,x)","\int x \left(a + b \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e/sqrt(x))**n))**3, x)","F",0
437,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**3,x)","\int \left(a + b \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*log(c*(d + e/sqrt(x))**n))**3, x)","F",0
438,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**3/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e/sqrt(x))**n))**3/x, x)","F",0
439,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**3/x**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + \frac{e}{\sqrt{x}}\right)^{n} \right)}\right)^{3}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e/sqrt(x))**n))**3/x**2, x)","F",0
440,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**3/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**n))**3/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,1,216,0,81.574000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(1/3))**n)),x)","\frac{a x^{4}}{4} + b \left(- \frac{e n \left(\frac{3 d^{12} \left(\begin{cases} \frac{\sqrt[3]{x}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e \sqrt[3]{x} \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{12}} - \frac{3 d^{11} \sqrt[3]{x}}{e^{12}} + \frac{3 d^{10} x^{\frac{2}{3}}}{2 e^{11}} - \frac{d^{9} x}{e^{10}} + \frac{3 d^{8} x^{\frac{4}{3}}}{4 e^{9}} - \frac{3 d^{7} x^{\frac{5}{3}}}{5 e^{8}} + \frac{d^{6} x^{2}}{2 e^{7}} - \frac{3 d^{5} x^{\frac{7}{3}}}{7 e^{6}} + \frac{3 d^{4} x^{\frac{8}{3}}}{8 e^{5}} - \frac{d^{3} x^{3}}{3 e^{4}} + \frac{3 d^{2} x^{\frac{10}{3}}}{10 e^{3}} - \frac{3 d x^{\frac{11}{3}}}{11 e^{2}} + \frac{x^{4}}{4 e}\right)}{12} + \frac{x^{4} \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}}{4}\right)"," ",0,"a*x**4/4 + b*(-e*n*(3*d**12*Piecewise((x**(1/3)/d, Eq(e, 0)), (log(d + e*x**(1/3))/e, True))/e**12 - 3*d**11*x**(1/3)/e**12 + 3*d**10*x**(2/3)/(2*e**11) - d**9*x/e**10 + 3*d**8*x**(4/3)/(4*e**9) - 3*d**7*x**(5/3)/(5*e**8) + d**6*x**2/(2*e**7) - 3*d**5*x**(7/3)/(7*e**6) + 3*d**4*x**(8/3)/(8*e**5) - d**3*x**3/(3*e**4) + 3*d**2*x**(10/3)/(10*e**3) - 3*d*x**(11/3)/(11*e**2) + x**4/(4*e))/12 + x**4*log(c*(d + e*x**(1/3))**n)/4)","A",0
443,1,173,0,19.484143," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/3))**n)),x)","\frac{a x^{3}}{3} + b \left(- \frac{e n \left(- \frac{3 d^{9} \left(\begin{cases} \frac{\sqrt[3]{x}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e \sqrt[3]{x} \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{9}} + \frac{3 d^{8} \sqrt[3]{x}}{e^{9}} - \frac{3 d^{7} x^{\frac{2}{3}}}{2 e^{8}} + \frac{d^{6} x}{e^{7}} - \frac{3 d^{5} x^{\frac{4}{3}}}{4 e^{6}} + \frac{3 d^{4} x^{\frac{5}{3}}}{5 e^{5}} - \frac{d^{3} x^{2}}{2 e^{4}} + \frac{3 d^{2} x^{\frac{7}{3}}}{7 e^{3}} - \frac{3 d x^{\frac{8}{3}}}{8 e^{2}} + \frac{x^{3}}{3 e}\right)}{9} + \frac{x^{3} \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}}{3}\right)"," ",0,"a*x**3/3 + b*(-e*n*(-3*d**9*Piecewise((x**(1/3)/d, Eq(e, 0)), (log(d + e*x**(1/3))/e, True))/e**9 + 3*d**8*x**(1/3)/e**9 - 3*d**7*x**(2/3)/(2*e**8) + d**6*x/e**7 - 3*d**5*x**(4/3)/(4*e**6) + 3*d**4*x**(5/3)/(5*e**5) - d**3*x**2/(2*e**4) + 3*d**2*x**(7/3)/(7*e**3) - 3*d*x**(8/3)/(8*e**2) + x**3/(3*e))/9 + x**3*log(c*(d + e*x**(1/3))**n)/3)","A",0
444,1,131,0,5.801173," ","integrate(x*(a+b*ln(c*(d+e*x**(1/3))**n)),x)","\frac{a x^{2}}{2} + b \left(- \frac{e n \left(\frac{3 d^{6} \left(\begin{cases} \frac{\sqrt[3]{x}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e \sqrt[3]{x} \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{6}} - \frac{3 d^{5} \sqrt[3]{x}}{e^{6}} + \frac{3 d^{4} x^{\frac{2}{3}}}{2 e^{5}} - \frac{d^{3} x}{e^{4}} + \frac{3 d^{2} x^{\frac{4}{3}}}{4 e^{3}} - \frac{3 d x^{\frac{5}{3}}}{5 e^{2}} + \frac{x^{2}}{2 e}\right)}{6} + \frac{x^{2} \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}}{2}\right)"," ",0,"a*x**2/2 + b*(-e*n*(3*d**6*Piecewise((x**(1/3)/d, Eq(e, 0)), (log(d + e*x**(1/3))/e, True))/e**6 - 3*d**5*x**(1/3)/e**6 + 3*d**4*x**(2/3)/(2*e**5) - d**3*x/e**4 + 3*d**2*x**(4/3)/(4*e**3) - 3*d*x**(5/3)/(5*e**2) + x**2/(2*e))/6 + x**2*log(c*(d + e*x**(1/3))**n)/2)","A",0
445,1,82,0,1.710144," ","integrate(a+b*ln(c*(d+e*x**(1/3))**n),x)","a x + b \left(- \frac{e n \left(- \frac{3 d^{3} \left(\begin{cases} \frac{\sqrt[3]{x}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e \sqrt[3]{x} \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{3 d^{2} \sqrt[3]{x}}{e^{3}} - \frac{3 d x^{\frac{2}{3}}}{2 e^{2}} + \frac{x}{e}\right)}{3} + x \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)"," ",0,"a*x + b*(-e*n*(-3*d**3*Piecewise((x**(1/3)/d, Eq(e, 0)), (log(d + e*x**(1/3))/e, True))/e**3 + 3*d**2*x**(1/3)/e**3 - 3*d*x**(2/3)/(2*e**2) + x/e)/3 + x*log(c*(d + e*x**(1/3))**n))","A",0
446,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))/x,x)","\int \frac{a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**(1/3))**n))/x, x)","F",0
447,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/3))**n))**2,x)","\int x^{2} \left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*log(c*(d + e*x**(1/3))**n))**2, x)","F",0
451,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(1/3))**n))**2,x)","\int x \left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e*x**(1/3))**n))**2, x)","F",0
452,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))**2,x)","\int \left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**(1/3))**n))**2, x)","F",0
453,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))**2/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**(1/3))**n))**2/x, x)","F",0
454,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))**2/x**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**(1/3))**n))**2/x**2, x)","F",0
455,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(1/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/3))**n))**3,x)","\int x^{2} \left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{3}\, dx"," ",0,"Integral(x**2*(a + b*log(c*(d + e*x**(1/3))**n))**3, x)","F",0
458,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(1/3))**n))**3,x)","\int x \left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e*x**(1/3))**n))**3, x)","F",0
459,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))**3,x)","\int \left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**(1/3))**n))**3, x)","F",0
460,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))**3/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**(1/3))**n))**3/x, x)","F",0
461,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))**3/x**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right)^{n} \right)}\right)^{3}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**(1/3))**n))**3/x**2, x)","F",0
462,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**n))**3/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(2/3))**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(2/3))**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
465,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(2/3))**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,1,133,0,7.611961," ","integrate(a+b*ln(c*(d+e*x**(2/3))**n),x)","a x + b \left(- \frac{2 e n \left(\begin{cases} - \frac{3 i d^{\frac{3}{2}} \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + \sqrt[3]{x} \right)}}{2 e^{3} \sqrt{\frac{1}{e}}} + \frac{3 i d^{\frac{3}{2}} \log{\left(i \sqrt{d} \sqrt{\frac{1}{e}} + \sqrt[3]{x} \right)}}{2 e^{3} \sqrt{\frac{1}{e}}} - \frac{3 d \sqrt[3]{x}}{e^{2}} + \frac{x}{e} & \text{for}\: e \neq 0 \\\frac{3 x^{\frac{5}{3}}}{5 d} & \text{otherwise} \end{cases}\right)}{3} + x \log{\left(c \left(d + e x^{\frac{2}{3}}\right)^{n} \right)}\right)"," ",0,"a*x + b*(-2*e*n*Piecewise((-3*I*d**(3/2)*log(-I*sqrt(d)*sqrt(1/e) + x**(1/3))/(2*e**3*sqrt(1/e)) + 3*I*d**(3/2)*log(I*sqrt(d)*sqrt(1/e) + x**(1/3))/(2*e**3*sqrt(1/e)) - 3*d*x**(1/3)/e**2 + x/e, Ne(e, 0)), (3*x**(5/3)/(5*d), True))/3 + x*log(c*(d + e*x**(2/3))**n))","A",0
467,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(2/3))**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(2/3))**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**2/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**2/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(2/3))**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**2,x)","\int \left(a + b \log{\left(c \left(d + e x^{\frac{2}{3}}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**(2/3))**n))**2, x)","F",0
478,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**2/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**2/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**2/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(2/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(2/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**3/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**3/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(2/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**3/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**n))**3/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e/x**(1/3))**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,1,180,0,102.005741," ","integrate(x**2*(a+b*ln(c*(d+e/x**(1/3))**n)),x)","\frac{a x^{3}}{3} + b \left(\frac{e n \left(\frac{3 x^{\frac{8}{3}}}{8 d} - \frac{3 e x^{\frac{7}{3}}}{7 d^{2}} + \frac{e^{2} x^{2}}{2 d^{3}} - \frac{3 e^{3} x^{\frac{5}{3}}}{5 d^{4}} + \frac{3 e^{4} x^{\frac{4}{3}}}{4 d^{5}} - \frac{e^{5} x}{d^{6}} + \frac{3 e^{6} x^{\frac{2}{3}}}{2 d^{7}} - \frac{3 e^{7} \sqrt[3]{x}}{d^{8}} + \frac{3 e^{9} \left(\begin{cases} \frac{1}{d \sqrt[3]{x}} & \text{for}\: e = 0 \\\frac{\log{\left(d + \frac{e}{\sqrt[3]{x}} \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{9}} - \frac{3 e^{8} \log{\left(\frac{1}{\sqrt[3]{x}} \right)}}{d^{9}}\right)}{9} + \frac{x^{3} \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}}{3}\right)"," ",0,"a*x**3/3 + b*(e*n*(3*x**(8/3)/(8*d) - 3*e*x**(7/3)/(7*d**2) + e**2*x**2/(2*d**3) - 3*e**3*x**(5/3)/(5*d**4) + 3*e**4*x**(4/3)/(4*d**5) - e**5*x/d**6 + 3*e**6*x**(2/3)/(2*d**7) - 3*e**7*x**(1/3)/d**8 + 3*e**9*Piecewise((1/(d*x**(1/3)), Eq(e, 0)), (log(d + e/x**(1/3))/e, True))/d**9 - 3*e**8*log(x**(-1/3))/d**9)/9 + x**3*log(c*(d + e/x**(1/3))**n)/3)","A",0
491,1,119,0,27.061812," ","integrate(x*(a+b*ln(c*(d+e/x**(1/3))**n)),x)","\frac{a x^{2}}{2} + b \left(\frac{e n \left(\frac{3 x^{\frac{5}{3}}}{5 d} - \frac{3 e x^{\frac{4}{3}}}{4 d^{2}} + \frac{e^{2} x}{d^{3}} - \frac{3 e^{3} x^{\frac{2}{3}}}{2 d^{4}} - \frac{3 e^{5} \left(\begin{cases} \frac{\sqrt[3]{x}}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d \sqrt[3]{x} + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{5}} + \frac{3 e^{4} \sqrt[3]{x}}{d^{5}}\right)}{6} + \frac{x^{2} \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}}{2}\right)"," ",0,"a*x**2/2 + b*(e*n*(3*x**(5/3)/(5*d) - 3*e*x**(4/3)/(4*d**2) + e**2*x/d**3 - 3*e**3*x**(2/3)/(2*d**4) - 3*e**5*Piecewise((x**(1/3)/e, Eq(d, 0)), (log(d*x**(1/3) + e)/d, True))/d**5 + 3*e**4*x**(1/3)/d**5)/6 + x**2*log(c*(d + e/x**(1/3))**n)/2)","A",0
492,1,92,0,7.104171," ","integrate(a+b*ln(c*(d+e/x**(1/3))**n),x)","a x + b \left(\frac{e n \left(\frac{3 x^{\frac{2}{3}}}{2 d} - \frac{3 e \sqrt[3]{x}}{d^{2}} + \frac{3 e^{3} \left(\begin{cases} \frac{1}{d \sqrt[3]{x}} & \text{for}\: e = 0 \\\frac{\log{\left(d + \frac{e}{\sqrt[3]{x}} \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{3 e^{2} \log{\left(\frac{1}{\sqrt[3]{x}} \right)}}{d^{3}}\right)}{3} + x \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}\right)"," ",0,"a*x + b*(e*n*(3*x**(2/3)/(2*d) - 3*e*x**(1/3)/d**2 + 3*e**3*Piecewise((1/(d*x**(1/3)), Eq(e, 0)), (log(d + e/x**(1/3))/e, True))/d**3 - 3*e**2*log(x**(-1/3))/d**3)/3 + x*log(c*(d + e/x**(1/3))**n))","A",0
493,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))/x,x)","\int \frac{a + b \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e/x**(1/3))**n))/x, x)","F",0
494,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e/x**(1/3))**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(1/3))**n))**2,x)","\int x \left(a + b \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*log(c*(d + e/x**(1/3))**n))**2, x)","F",0
499,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))**2,x)","\int \left(a + b \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d + e/x**(1/3))**n))**2, x)","F",0
500,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))**2/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e/x**(1/3))**n))**2/x, x)","F",0
501,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))**2/x**2,x)","\int \frac{\left(a + b \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e/x**(1/3))**n))**2/x**2, x)","F",0
502,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(1/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))**3,x)","\int \left(a + b \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*log(c*(d + e/x**(1/3))**n))**3, x)","F",0
505,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))**3/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + \frac{e}{\sqrt[3]{x}}\right)^{n} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e/x**(1/3))**n))**3/x, x)","F",0
506,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))**3/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**n))**3/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e/x**(2/3))**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e/x**(2/3))**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(2/3))**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,1,61,0,52.161961," ","integrate(a+b*ln(c*(d+e/x**(2/3))**n),x)","a x + b \left(\frac{2 e n \left(\frac{3 \sqrt[3]{x}}{d} - \frac{3 e \operatorname{atan}{\left(\frac{\sqrt[3]{x}}{\sqrt{\frac{e}{d}}} \right)}}{d^{2} \sqrt{\frac{e}{d}}}\right)}{3} + x \log{\left(c \left(d + \frac{e}{x^{\frac{2}{3}}}\right)^{n} \right)}\right)"," ",0,"a*x + b*(2*e*n*(3*x**(1/3)/d - 3*e*atan(x**(1/3)/sqrt(e/d))/(d**2*sqrt(e/d)))/3 + x*log(c*(d + e/x**(2/3))**n))","A",0
512,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
513,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
514,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e/x**(2/3))**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(2/3))**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**2/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**2/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e/x**(2/3))**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
523,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**2/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e/x**(2/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
525,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(2/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
526,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**3/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
527,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**3/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
528,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e/x**(2/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
529,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
530,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**3/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**n))**3/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(1/2))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
533,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/2))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(1/2))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(1/2))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/2))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(1/2))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**2))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/2))**2))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
544,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(1/2))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))))**p/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))))**p/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(1/2))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**2))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**2))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**2))**p/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/2))**2))**p/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(1/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(1/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))))**p,x)","\int \left(a + b \log{\left(c \left(d + e \sqrt[3]{x}\right) \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**(1/3))))**p, x)","F",0
560,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
561,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(1/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(1/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(1/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**2))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(1/3))**2))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(2/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(2/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))))**p/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(2/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e*x**(2/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e*x**(2/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**2))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**2))**p/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e*x**(2/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**(2/3))**2))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(1/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))))**p/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))))**p/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(1/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**2))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**2))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**2))**p/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(1/3))**2))**p/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e/x**(2/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e/x**(2/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(2/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*(d+e/x**(2/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*(d+e/x**(2/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*(d+e/x**(2/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**2))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**2))**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/x**(2/3))**2))**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
607,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
608,-1,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-2,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
612,-2,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
613,-1,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate((h*x)**(1/2)*(a+b*ln(c*(e*x**2+d)**p))/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x**2+d)**p))/(h*x)**(1/2)/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate((a+b*ln(c*(e*x**2+d)**p))/(h*x)**(3/2)/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate(ln(f*x**p)*ln(1+e*x**m)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,0,0,0,0.000000," ","integrate(x**(-1+m)*ln(f*x**p)**2/(d+e*x**m),x)","\int \frac{x^{m - 1} \log{\left(f x^{p} \right)}^{2}}{d + e x^{m}}\, dx"," ",0,"Integral(x**(m - 1)*log(f*x**p)**2/(d + e*x**m), x)","F",0
621,-1,0,0,0.000000," ","integrate(ln(f*x**p)**3*(a+b*ln(c*(d+e*x**m)**n))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,0,0,0,0.000000," ","integrate(ln(f*x**p)**2*(a+b*ln(c*(d+e*x**m)**n))/x,x)","\int \frac{\left(a + b \log{\left(c \left(d + e x^{m}\right)^{n} \right)}\right) \log{\left(f x^{p} \right)}^{2}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**m)**n))*log(f*x**p)**2/x, x)","F",0
623,-1,0,0,0.000000," ","integrate(ln(f*x**p)*(a+b*ln(c*(d+e*x**m)**n))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**m)**n))/x,x)","\int \frac{a + b \log{\left(c \left(d + e x^{m}\right)^{n} \right)}}{x}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**m)**n))/x, x)","F",0
625,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**m)**n))/x/ln(f*x**p),x)","\int \frac{a + b \log{\left(c \left(d + e x^{m}\right)^{n} \right)}}{x \log{\left(f x^{p} \right)}}\, dx"," ",0,"Integral((a + b*log(c*(d + e*x**m)**n))/(x*log(f*x**p)), x)","F",0
626,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**m)**n))/x/ln(f*x**p)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate((a+b*ln(c*(d+e*x**m)**n))/x/ln(f*x**p)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,0,0,0,0.000000," ","integrate(ln(c*(d+e*(g*x+f)**p)**q),x)","\int \log{\left(c \left(d + e \left(f + g x\right)^{p}\right)^{q} \right)}\, dx"," ",0,"Integral(log(c*(d + e*(f + g*x)**p)**q), x)","F",0
629,-1,0,0,0.000000," ","integrate(ln(c*(d+e*(g*x+f)**3)**q),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate(ln(c*(d+e*(g*x+f)**2)**q),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,1,80,0,1.520854," ","integrate(ln(c*(d+e*(g*x+f))**q),x)","\begin{cases} x \log{\left(c d^{q} \right)} & \text{for}\: e = 0 \wedge \left(e = 0 \vee g = 0\right) \\x \log{\left(c \left(d + e f\right)^{q} \right)} & \text{for}\: g = 0 \\\frac{d q \log{\left(d + e f + e g x \right)}}{e g} + \frac{f q \log{\left(d + e f + e g x \right)}}{g} + q x \log{\left(d + e f + e g x \right)} - q x + x \log{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*log(c*d**q), Eq(e, 0) & (Eq(e, 0) | Eq(g, 0))), (x*log(c*(d + e*f)**q), Eq(g, 0)), (d*q*log(d + e*f + e*g*x)/(e*g) + f*q*log(d + e*f + e*g*x)/g + q*x*log(d + e*f + e*g*x) - q*x + x*log(c), True))","A",0
632,1,109,0,2.078622," ","integrate(ln(c*(d+e/(g*x+f))**q),x)","\begin{cases} x \log{\left(c \left(\frac{e}{f}\right)^{q} \right)} & \text{for}\: d = 0 \wedge g = 0 \\x \log{\left(c \left(d + \frac{e}{f}\right)^{q} \right)} & \text{for}\: g = 0 \\- \frac{f q \log{\left(f + g x \right)}}{g} + q x \log{\left(e \right)} - q x \log{\left(f + g x \right)} + q x + x \log{\left(c \right)} & \text{for}\: d = 0 \\\frac{f q \log{\left(d + \frac{e}{f + g x} \right)}}{g} + q x \log{\left(d + \frac{e}{f + g x} \right)} + x \log{\left(c \right)} + \frac{e q \log{\left(d f + d g x + e \right)}}{d g} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*log(c*(e/f)**q), Eq(d, 0) & Eq(g, 0)), (x*log(c*(d + e/f)**q), Eq(g, 0)), (-f*q*log(f + g*x)/g + q*x*log(e) - q*x*log(f + g*x) + q*x + x*log(c), Eq(d, 0)), (f*q*log(d + e/(f + g*x))/g + q*x*log(d + e/(f + g*x)) + x*log(c) + e*q*log(d*f + d*g*x + e)/(d*g), True))","A",0
633,-1,0,0,0.000000," ","integrate(ln(c*(d+e/(g*x+f)**2)**q),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate(ln(c*(d+e/(g*x+f)**3)**q),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/(g*x+f))**p))**n,x)","\int \left(a + b \log{\left(c \left(d + \frac{e}{f + g x}\right)^{p} \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*log(c*(d + e/(f + g*x))**p))**n, x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/(g*x+f))**p))**4,x)","\int \left(a + b \log{\left(c \left(d + \frac{e}{f + g x}\right)^{p} \right)}\right)^{4}\, dx"," ",0,"Integral((a + b*log(c*(d + e/(f + g*x))**p))**4, x)","F",0
637,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/(g*x+f))**p))**3,x)","\int \left(a + b \log{\left(c \left(d + \frac{e}{f + g x}\right)^{p} \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*log(c*(d + e/(f + g*x))**p))**3, x)","F",0
638,0,0,0,0.000000," ","integrate((a+b*ln(c*(d+e/(g*x+f))**p))**2,x)","\int \left(a + b \log{\left(c \left(d + \frac{e}{f + g x}\right)^{p} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*log(c*(d + e/(f + g*x))**p))**2, x)","F",0
639,1,114,0,2.047141," ","integrate(a+b*ln(c*(d+e/(g*x+f))**p),x)","a x + b \left(\begin{cases} x \log{\left(c \left(\frac{e}{f}\right)^{p} \right)} & \text{for}\: d = 0 \wedge g = 0 \\x \log{\left(c \left(d + \frac{e}{f}\right)^{p} \right)} & \text{for}\: g = 0 \\- \frac{f p \log{\left(f + g x \right)}}{g} + p x \log{\left(e \right)} - p x \log{\left(f + g x \right)} + p x + x \log{\left(c \right)} & \text{for}\: d = 0 \\\frac{f p \log{\left(d + \frac{e}{f + g x} \right)}}{g} + p x \log{\left(d + \frac{e}{f + g x} \right)} + x \log{\left(c \right)} + \frac{e p \log{\left(d f + d g x + e \right)}}{d g} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((x*log(c*(e/f)**p), Eq(d, 0) & Eq(g, 0)), (x*log(c*(d + e/f)**p), Eq(g, 0)), (-f*p*log(f + g*x)/g + p*x*log(e) - p*x*log(f + g*x) + p*x + x*log(c), Eq(d, 0)), (f*p*log(d + e/(f + g*x))/g + p*x*log(d + e/(f + g*x)) + x*log(c) + e*p*log(d*f + d*g*x + e)/(d*g), True))","A",0
640,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d+e/(g*x+f))**p)),x)","\int \frac{1}{a + b \log{\left(c \left(d + \frac{e}{f + g x}\right)^{p} \right)}}\, dx"," ",0,"Integral(1/(a + b*log(c*(d + e/(f + g*x))**p)), x)","F",0
641,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*(d+e/(g*x+f))**p))**2,x)","\int \frac{1}{\left(a + b \log{\left(c \left(d + \frac{e}{f + g x}\right)^{p} \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*(d + e/(f + g*x))**p))**(-2), x)","F",0
