Optimal. Leaf size=1278 \[ \frac {568 a b^2 e^4 n^2 \sqrt [3]{x}}{105 d^4}-\frac {16 b^3 e^4 n^3 \sqrt [3]{x}}{7 d^4}+\frac {16 b^3 e^3 n^3 x}{105 d^3}+\frac {1376 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )}{105 d^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )^2}{105 d^{9/2}}-\frac {1136 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \log \left (2-\frac {2 \sqrt {e}}{\sqrt {e}-i \sqrt {d} \sqrt [3]{x}}\right )}{105 d^{9/2}}+\frac {568 b^3 e^4 n^2 \sqrt [3]{x} \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )}{105 d^4}-\frac {32 b^2 e^3 n^2 x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^3}+\frac {8 b^2 e^2 n^2 x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^2}-\frac {568 b^2 e^{9/2} n^2 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{105 d^{9/2}}-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {2 b^3 e^{9/2} n^3 \log ^2\left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {2 b^3 e^{9/2} n^3 \log ^2\left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {4 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {1}{2}-\frac {\sqrt {-d} \sqrt [3]{x}}{2 \sqrt {e}}\right )}{(-d)^{9/2}}-\frac {4 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {1}{2} \left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \text {Li}_2\left (-1+\frac {2 \sqrt {e}}{\sqrt {e}-i \sqrt {d} \sqrt [3]{x}}\right )}{105 d^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}-\frac {4 b^3 e^{9/2} n^3 \text {Li}_2\left (\frac {1}{2}-\frac {\sqrt {-d} \sqrt [3]{x}}{2 \sqrt {e}}\right )}{(-d)^{9/2}}+\frac {4 b^3 e^{9/2} n^3 \text {Li}_2\left (\frac {1}{2} \left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {2 b e^5 n \text {Int}\left (\frac {\left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{\left (e+d x^{2/3}\right ) x^{2/3}},x\right )}{3 d^4} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 1.99, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3 \, dx &=3 \text {Subst}\left (\int x^8 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^3 \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+(2 b e n) \text {Subst}\left (\int \frac {x^6 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{d+\frac {e}{x^2}} \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+(2 b e n) \text {Subst}\left (\int \left (-\frac {e^3 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{d^4}+\frac {e^2 x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{d^3}-\frac {e x^4 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{d^2}+\frac {x^6 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{d}+\frac {e^4 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{d^4 \left (e+d x^2\right )}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {(2 b e n) \text {Subst}\left (\int x^6 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2 \, dx,x,\sqrt [3]{x}\right )}{d}-\frac {\left (2 b e^2 n\right ) \text {Subst}\left (\int x^4 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2 \, dx,x,\sqrt [3]{x}\right )}{d^2}+\frac {\left (2 b e^3 n\right ) \text {Subst}\left (\int x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2 \, dx,x,\sqrt [3]{x}\right )}{d^3}-\frac {\left (2 b e^4 n\right ) \text {Subst}\left (\int \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2 \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}\\ &=-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (8 b^2 e^2 n^2\right ) \text {Subst}\left (\int \frac {x^4 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d+\frac {e}{x^2}} \, dx,x,\sqrt [3]{x}\right )}{7 d}-\frac {\left (8 b^2 e^3 n^2\right ) \text {Subst}\left (\int \frac {x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d+\frac {e}{x^2}} \, dx,x,\sqrt [3]{x}\right )}{5 d^2}+\frac {\left (8 b^2 e^4 n^2\right ) \text {Subst}\left (\int \frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{d+\frac {e}{x^2}} \, dx,x,\sqrt [3]{x}\right )}{3 d^3}-\frac {\left (8 b^2 e^5 n^2\right ) \text {Subst}\left (\int \frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{\left (d+\frac {e}{x^2}\right ) x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}\\ &=-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (8 b^2 e^2 n^2\right ) \text {Subst}\left (\int \left (\frac {e^2 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d^3}-\frac {e x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d^2}+\frac {x^4 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d}-\frac {e^3 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d^3 \left (e+d x^2\right )}\right ) \, dx,x,\sqrt [3]{x}\right )}{7 d}-\frac {\left (8 b^2 e^3 n^2\right ) \text {Subst}\left (\int \left (-\frac {e \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d^2}+\frac {x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d}+\frac {e^2 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d^2 \left (e+d x^2\right )}\right ) \, dx,x,\sqrt [3]{x}\right )}{5 d^2}+\frac {\left (8 b^2 e^4 n^2\right ) \text {Subst}\left (\int \left (\frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{d}-\frac {e \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )}{d \left (e+d x^2\right )}\right ) \, dx,x,\sqrt [3]{x}\right )}{3 d^3}-\frac {\left (8 b^2 e^5 n^2\right ) \text {Subst}\left (\int \left (\frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{2 \sqrt {e} \left (\sqrt {e}-\sqrt {-d} x\right )}+\frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{2 \sqrt {e} \left (\sqrt {e}+\sqrt {-d} x\right )}\right ) \, dx,x,\sqrt [3]{x}\right )}{d^4}\\ &=-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (8 b^2 e^2 n^2\right ) \text {Subst}\left (\int x^4 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right ) \, dx,x,\sqrt [3]{x}\right )}{7 d^2}-\frac {\left (8 b^2 e^3 n^2\right ) \text {Subst}\left (\int x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right ) \, dx,x,\sqrt [3]{x}\right )}{7 d^3}-\frac {\left (8 b^2 e^3 n^2\right ) \text {Subst}\left (\int x^2 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right ) \, dx,x,\sqrt [3]{x}\right )}{5 d^3}+\frac {\left (8 b^2 e^4 n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right ) \, dx,x,\sqrt [3]{x}\right )}{7 d^4}+\frac {\left (8 b^2 e^4 n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right ) \, dx,x,\sqrt [3]{x}\right )}{5 d^4}+\frac {\left (8 b^2 e^4 n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right ) \, dx,x,\sqrt [3]{x}\right )}{3 d^4}-\frac {\left (4 b^2 e^{9/2} n^2\right ) \text {Subst}\left (\int \frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{\sqrt {e}-\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}-\frac {\left (4 b^2 e^{9/2} n^2\right ) \text {Subst}\left (\int \frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{\sqrt {e}+\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}-\frac {\left (8 b^2 e^5 n^2\right ) \text {Subst}\left (\int \frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{7 d^4}-\frac {\left (8 b^2 e^5 n^2\right ) \text {Subst}\left (\int \frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{5 d^4}-\frac {\left (8 b^2 e^5 n^2\right ) \text {Subst}\left (\int \frac {a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{3 d^4}\\ &=\frac {568 a b^2 e^4 n^2 \sqrt [3]{x}}{105 d^4}-\frac {32 b^2 e^3 n^2 x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^3}+\frac {8 b^2 e^2 n^2 x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^2}-\frac {568 b^2 e^{9/2} n^2 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{105 d^{9/2}}-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (8 b^3 e^4 n^2\right ) \text {Subst}\left (\int \log \left (c \left (d+\frac {e}{x^2}\right )^n\right ) \, dx,x,\sqrt [3]{x}\right )}{7 d^4}+\frac {\left (8 b^3 e^4 n^2\right ) \text {Subst}\left (\int \log \left (c \left (d+\frac {e}{x^2}\right )^n\right ) \, dx,x,\sqrt [3]{x}\right )}{5 d^4}+\frac {\left (8 b^3 e^4 n^2\right ) \text {Subst}\left (\int \log \left (c \left (d+\frac {e}{x^2}\right )^n\right ) \, dx,x,\sqrt [3]{x}\right )}{3 d^4}+\frac {\left (16 b^3 e^3 n^3\right ) \text {Subst}\left (\int \frac {x^2}{d+\frac {e}{x^2}} \, dx,x,\sqrt [3]{x}\right )}{35 d^2}-\frac {\left (16 b^3 e^4 n^3\right ) \text {Subst}\left (\int \frac {1}{d+\frac {e}{x^2}} \, dx,x,\sqrt [3]{x}\right )}{21 d^3}-\frac {\left (16 b^3 e^4 n^3\right ) \text {Subst}\left (\int \frac {1}{d+\frac {e}{x^2}} \, dx,x,\sqrt [3]{x}\right )}{15 d^3}+\frac {\left (8 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\sqrt {e}-\sqrt {-d} x\right )}{\left (d+\frac {e}{x^2}\right ) x^3} \, dx,x,\sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {\left (8 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\sqrt {e}+\sqrt {-d} x\right )}{\left (d+\frac {e}{x^2}\right ) x^3} \, dx,x,\sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {\left (16 b^3 e^6 n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{\sqrt {d} \sqrt {e} \left (d+\frac {e}{x^2}\right ) x^3} \, dx,x,\sqrt [3]{x}\right )}{7 d^4}-\frac {\left (16 b^3 e^6 n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{\sqrt {d} \sqrt {e} \left (d+\frac {e}{x^2}\right ) x^3} \, dx,x,\sqrt [3]{x}\right )}{5 d^4}-\frac {\left (16 b^3 e^6 n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{\sqrt {d} \sqrt {e} \left (d+\frac {e}{x^2}\right ) x^3} \, dx,x,\sqrt [3]{x}\right )}{3 d^4}\\ &=\frac {568 a b^2 e^4 n^2 \sqrt [3]{x}}{105 d^4}+\frac {568 b^3 e^4 n^2 \sqrt [3]{x} \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )}{105 d^4}-\frac {32 b^2 e^3 n^2 x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^3}+\frac {8 b^2 e^2 n^2 x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^2}-\frac {568 b^2 e^{9/2} n^2 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{105 d^{9/2}}-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (16 b^3 e^3 n^3\right ) \text {Subst}\left (\int \frac {x^4}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{35 d^2}-\frac {\left (16 b^3 e^4 n^3\right ) \text {Subst}\left (\int \frac {x^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{21 d^3}-\frac {\left (16 b^3 e^4 n^3\right ) \text {Subst}\left (\int \frac {x^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{15 d^3}+\frac {\left (16 b^3 e^5 n^3\right ) \text {Subst}\left (\int \frac {1}{\left (d+\frac {e}{x^2}\right ) x^2} \, dx,x,\sqrt [3]{x}\right )}{7 d^4}+\frac {\left (16 b^3 e^5 n^3\right ) \text {Subst}\left (\int \frac {1}{\left (d+\frac {e}{x^2}\right ) x^2} \, dx,x,\sqrt [3]{x}\right )}{5 d^4}+\frac {\left (16 b^3 e^5 n^3\right ) \text {Subst}\left (\int \frac {1}{\left (d+\frac {e}{x^2}\right ) x^2} \, dx,x,\sqrt [3]{x}\right )}{3 d^4}+\frac {\left (8 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \left (\frac {\log \left (\sqrt {e}-\sqrt {-d} x\right )}{e x}-\frac {d x \log \left (\sqrt {e}-\sqrt {-d} x\right )}{e \left (e+d x^2\right )}\right ) \, dx,x,\sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {\left (8 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \left (\frac {\log \left (\sqrt {e}+\sqrt {-d} x\right )}{e x}-\frac {d x \log \left (\sqrt {e}+\sqrt {-d} x\right )}{e \left (e+d x^2\right )}\right ) \, dx,x,\sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {\left (16 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{\left (d+\frac {e}{x^2}\right ) x^3} \, dx,x,\sqrt [3]{x}\right )}{7 d^{9/2}}-\frac {\left (16 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{\left (d+\frac {e}{x^2}\right ) x^3} \, dx,x,\sqrt [3]{x}\right )}{5 d^{9/2}}-\frac {\left (16 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{\left (d+\frac {e}{x^2}\right ) x^3} \, dx,x,\sqrt [3]{x}\right )}{3 d^{9/2}}\\ &=\frac {568 a b^2 e^4 n^2 \sqrt [3]{x}}{105 d^4}-\frac {64 b^3 e^4 n^3 \sqrt [3]{x}}{35 d^4}+\frac {568 b^3 e^4 n^2 \sqrt [3]{x} \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )}{105 d^4}-\frac {32 b^2 e^3 n^2 x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^3}+\frac {8 b^2 e^2 n^2 x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^2}-\frac {568 b^2 e^{9/2} n^2 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{105 d^{9/2}}-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (16 b^3 e^3 n^3\right ) \text {Subst}\left (\int \left (-\frac {e}{d^2}+\frac {x^2}{d}+\frac {e^2}{d^2 \left (e+d x^2\right )}\right ) \, dx,x,\sqrt [3]{x}\right )}{35 d^2}+\frac {\left (8 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\sqrt {e}-\sqrt {-d} x\right )}{x} \, dx,x,\sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {\left (8 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\sqrt {e}+\sqrt {-d} x\right )}{x} \, dx,x,\sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {\left (8 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {x \log \left (\sqrt {e}-\sqrt {-d} x\right )}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{(-d)^{7/2}}-\frac {\left (8 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {x \log \left (\sqrt {e}+\sqrt {-d} x\right )}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{(-d)^{7/2}}+\frac {\left (16 b^3 e^5 n^3\right ) \text {Subst}\left (\int \frac {1}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{21 d^4}+\frac {\left (16 b^3 e^5 n^3\right ) \text {Subst}\left (\int \frac {1}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{15 d^4}+\frac {\left (16 b^3 e^5 n^3\right ) \text {Subst}\left (\int \frac {1}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{7 d^4}+\frac {\left (16 b^3 e^5 n^3\right ) \text {Subst}\left (\int \frac {1}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{5 d^4}+\frac {\left (16 b^3 e^5 n^3\right ) \text {Subst}\left (\int \frac {1}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{3 d^4}-\frac {\left (16 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{x \left (e+d x^2\right )} \, dx,x,\sqrt [3]{x}\right )}{7 d^{9/2}}-\frac {\left (16 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{x \left (e+d x^2\right )} \, dx,x,\sqrt [3]{x}\right )}{5 d^{9/2}}-\frac {\left (16 b^3 e^{11/2} n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{x \left (e+d x^2\right )} \, dx,x,\sqrt [3]{x}\right )}{3 d^{9/2}}\\ &=\frac {568 a b^2 e^4 n^2 \sqrt [3]{x}}{105 d^4}-\frac {16 b^3 e^4 n^3 \sqrt [3]{x}}{7 d^4}+\frac {16 b^3 e^3 n^3 x}{105 d^3}+\frac {1328 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )}{105 d^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )^2}{105 d^{9/2}}+\frac {568 b^3 e^4 n^2 \sqrt [3]{x} \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )}{105 d^4}-\frac {32 b^2 e^3 n^2 x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^3}+\frac {8 b^2 e^2 n^2 x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^2}-\frac {568 b^2 e^{9/2} n^2 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{105 d^{9/2}}-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (8 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \left (-\frac {\sqrt {-d} \log \left (\sqrt {e}-\sqrt {-d} x\right )}{2 d \left (\sqrt {e}-\sqrt {-d} x\right )}+\frac {\sqrt {-d} \log \left (\sqrt {e}-\sqrt {-d} x\right )}{2 d \left (\sqrt {e}+\sqrt {-d} x\right )}\right ) \, dx,x,\sqrt [3]{x}\right )}{(-d)^{7/2}}-\frac {\left (8 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \left (-\frac {\sqrt {-d} \log \left (\sqrt {e}+\sqrt {-d} x\right )}{2 d \left (\sqrt {e}-\sqrt {-d} x\right )}+\frac {\sqrt {-d} \log \left (\sqrt {e}+\sqrt {-d} x\right )}{2 d \left (\sqrt {e}+\sqrt {-d} x\right )}\right ) \, dx,x,\sqrt [3]{x}\right )}{(-d)^{7/2}}-\frac {\left (16 i b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{x \left (i+\frac {\sqrt {d} x}{\sqrt {e}}\right )} \, dx,x,\sqrt [3]{x}\right )}{7 d^{9/2}}-\frac {\left (16 i b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{x \left (i+\frac {\sqrt {d} x}{\sqrt {e}}\right )} \, dx,x,\sqrt [3]{x}\right )}{5 d^{9/2}}-\frac {\left (16 i b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\tan ^{-1}\left (\frac {\sqrt {d} x}{\sqrt {e}}\right )}{x \left (i+\frac {\sqrt {d} x}{\sqrt {e}}\right )} \, dx,x,\sqrt [3]{x}\right )}{3 d^{9/2}}+\frac {\left (8 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (-\frac {\sqrt {-d} x}{\sqrt {e}}\right )}{\sqrt {e}+\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (8 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\frac {\sqrt {-d} x}{\sqrt {e}}\right )}{\sqrt {e}-\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (16 b^3 e^5 n^3\right ) \text {Subst}\left (\int \frac {1}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{35 d^4}\\ &=\frac {568 a b^2 e^4 n^2 \sqrt [3]{x}}{105 d^4}-\frac {16 b^3 e^4 n^3 \sqrt [3]{x}}{7 d^4}+\frac {16 b^3 e^3 n^3 x}{105 d^3}+\frac {1376 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )}{105 d^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )^2}{105 d^{9/2}}-\frac {1136 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \log \left (2-\frac {2 \sqrt {e}}{\sqrt {e}-i \sqrt {d} \sqrt [3]{x}}\right )}{105 d^{9/2}}+\frac {568 b^3 e^4 n^2 \sqrt [3]{x} \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )}{105 d^4}-\frac {32 b^2 e^3 n^2 x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^3}+\frac {8 b^2 e^2 n^2 x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^2}-\frac {568 b^2 e^{9/2} n^2 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{105 d^{9/2}}-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (16 b^3 e^4 n^3\right ) \text {Subst}\left (\int \frac {\log \left (2-\frac {2}{1-\frac {i \sqrt {d} x}{\sqrt {e}}}\right )}{1+\frac {d x^2}{e}} \, dx,x,\sqrt [3]{x}\right )}{7 d^4}+\frac {\left (16 b^3 e^4 n^3\right ) \text {Subst}\left (\int \frac {\log \left (2-\frac {2}{1-\frac {i \sqrt {d} x}{\sqrt {e}}}\right )}{1+\frac {d x^2}{e}} \, dx,x,\sqrt [3]{x}\right )}{5 d^4}+\frac {\left (16 b^3 e^4 n^3\right ) \text {Subst}\left (\int \frac {\log \left (2-\frac {2}{1-\frac {i \sqrt {d} x}{\sqrt {e}}}\right )}{1+\frac {d x^2}{e}} \, dx,x,\sqrt [3]{x}\right )}{3 d^4}+\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\sqrt {e}-\sqrt {-d} x\right )}{\sqrt {e}-\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}-\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\sqrt {e}-\sqrt {-d} x\right )}{\sqrt {e}+\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}-\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\sqrt {e}+\sqrt {-d} x\right )}{\sqrt {e}-\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\sqrt {e}+\sqrt {-d} x\right )}{\sqrt {e}+\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}\\ &=\frac {568 a b^2 e^4 n^2 \sqrt [3]{x}}{105 d^4}-\frac {16 b^3 e^4 n^3 \sqrt [3]{x}}{7 d^4}+\frac {16 b^3 e^3 n^3 x}{105 d^3}+\frac {1376 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )}{105 d^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )^2}{105 d^{9/2}}-\frac {1136 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \log \left (2-\frac {2 \sqrt {e}}{\sqrt {e}-i \sqrt {d} \sqrt [3]{x}}\right )}{105 d^{9/2}}+\frac {568 b^3 e^4 n^2 \sqrt [3]{x} \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )}{105 d^4}-\frac {32 b^2 e^3 n^2 x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^3}+\frac {8 b^2 e^2 n^2 x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^2}-\frac {568 b^2 e^{9/2} n^2 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{105 d^{9/2}}-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {4 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {1}{2}-\frac {\sqrt {-d} \sqrt [3]{x}}{2 \sqrt {e}}\right )}{(-d)^{9/2}}-\frac {4 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {1}{2} \left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \text {Li}_2\left (-1+\frac {2 \sqrt {e}}{\sqrt {e}-i \sqrt {d} \sqrt [3]{x}}\right )}{105 d^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}-\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\frac {\sqrt {e}-\sqrt {-d} x}{2 \sqrt {e}}\right )}{\sqrt {e}+\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}-\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (\frac {\sqrt {e}+\sqrt {-d} x}{2 \sqrt {e}}\right )}{\sqrt {e}-\sqrt {-d} x} \, dx,x,\sqrt [3]{x}\right )}{d^4}\\ &=\frac {568 a b^2 e^4 n^2 \sqrt [3]{x}}{105 d^4}-\frac {16 b^3 e^4 n^3 \sqrt [3]{x}}{7 d^4}+\frac {16 b^3 e^3 n^3 x}{105 d^3}+\frac {1376 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )}{105 d^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )^2}{105 d^{9/2}}-\frac {1136 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \log \left (2-\frac {2 \sqrt {e}}{\sqrt {e}-i \sqrt {d} \sqrt [3]{x}}\right )}{105 d^{9/2}}+\frac {568 b^3 e^4 n^2 \sqrt [3]{x} \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )}{105 d^4}-\frac {32 b^2 e^3 n^2 x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^3}+\frac {8 b^2 e^2 n^2 x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^2}-\frac {568 b^2 e^{9/2} n^2 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{105 d^{9/2}}-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {2 b^3 e^{9/2} n^3 \log ^2\left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {2 b^3 e^{9/2} n^3 \log ^2\left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {4 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {1}{2}-\frac {\sqrt {-d} \sqrt [3]{x}}{2 \sqrt {e}}\right )}{(-d)^{9/2}}-\frac {4 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {1}{2} \left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \text {Li}_2\left (-1+\frac {2 \sqrt {e}}{\sqrt {e}-i \sqrt {d} \sqrt [3]{x}}\right )}{105 d^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}+\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (1-\frac {x}{2 \sqrt {e}}\right )}{x} \, dx,x,\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {\left (4 b^3 e^{9/2} n^3\right ) \text {Subst}\left (\int \frac {\log \left (1-\frac {x}{2 \sqrt {e}}\right )}{x} \, dx,x,\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}\\ &=\frac {568 a b^2 e^4 n^2 \sqrt [3]{x}}{105 d^4}-\frac {16 b^3 e^4 n^3 \sqrt [3]{x}}{7 d^4}+\frac {16 b^3 e^3 n^3 x}{105 d^3}+\frac {1376 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )}{105 d^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right )^2}{105 d^{9/2}}-\frac {1136 b^3 e^{9/2} n^3 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \log \left (2-\frac {2 \sqrt {e}}{\sqrt {e}-i \sqrt {d} \sqrt [3]{x}}\right )}{105 d^{9/2}}+\frac {568 b^3 e^4 n^2 \sqrt [3]{x} \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )}{105 d^4}-\frac {32 b^2 e^3 n^2 x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^3}+\frac {8 b^2 e^2 n^2 x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{35 d^2}-\frac {568 b^2 e^{9/2} n^2 \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{105 d^{9/2}}-\frac {2 b e^4 n \sqrt [3]{x} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3+\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {2 b^3 e^{9/2} n^3 \log ^2\left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}-\frac {4 b^2 e^{9/2} n^2 \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right ) \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {2 b^3 e^{9/2} n^3 \log ^2\left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right )}{(-d)^{9/2}}+\frac {4 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {1}{2}-\frac {\sqrt {-d} \sqrt [3]{x}}{2 \sqrt {e}}\right )}{(-d)^{9/2}}-\frac {4 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {1}{2} \left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}+\sqrt {-d} \sqrt [3]{x}\right ) \log \left (-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \log \left (\sqrt {e}-\sqrt {-d} \sqrt [3]{x}\right ) \log \left (\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {568 i b^3 e^{9/2} n^3 \text {Li}_2\left (-1+\frac {2 \sqrt {e}}{\sqrt {e}-i \sqrt {d} \sqrt [3]{x}}\right )}{105 d^{9/2}}+\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1-\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}-\frac {4 b^3 e^{9/2} n^3 \text {Li}_2\left (\frac {1}{2}-\frac {\sqrt {-d} \sqrt [3]{x}}{2 \sqrt {e}}\right )}{(-d)^{9/2}}+\frac {4 b^3 e^{9/2} n^3 \text {Li}_2\left (\frac {1}{2} \left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )\right )}{(-d)^{9/2}}-\frac {8 b^3 e^{9/2} n^3 \text {Li}_2\left (1+\frac {\sqrt {-d} \sqrt [3]{x}}{\sqrt {e}}\right )}{(-d)^{9/2}}+\frac {\left (2 b e^5 n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^n\right )\right )^2}{e+d x^2} \, dx,x,\sqrt [3]{x}\right )}{d^4}\\ \end {align*}
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Mathematica [A]
time = 2.94, size = 764, normalized size = 0.60 \begin {gather*} \frac {b^3 n^3 \left (54 e^5 \left (e+d x^{2/3}\right ) \, _5F_4\left (1,1,1,1,\frac {11}{2};2,2,2,2;1+\frac {e}{d x^{2/3}}\right )+\log \left (d+\frac {e}{x^{2/3}}\right ) \left (-54 e^5 \left (e+d x^{2/3}\right ) \, _4F_3\left (1,1,1,\frac {11}{2};2,2,2;1+\frac {e}{d x^{2/3}}\right )+\log \left (d+\frac {e}{x^{2/3}}\right ) \left (27 e^5 \left (e+d x^{2/3}\right ) \, _3F_2\left (1,1,\frac {11}{2};2,2;1+\frac {e}{d x^{2/3}}\right )+2 d x^{2/3} \left (e^5+d^5 \sqrt {-\frac {e}{d x^{2/3}}} x^{10/3}\right ) \log \left (d+\frac {e}{x^{2/3}}\right )\right )\right )\right )}{6 d^6 \sqrt {-\frac {e}{d x^{2/3}}} x}-\frac {b^2 n^2 \left (-9 e^5 \left (e+d x^{2/3}\right ) \, _4F_3\left (1,1,1,\frac {11}{2};2,2,2;1+\frac {e}{d x^{2/3}}\right )+\log \left (d+\frac {e}{x^{2/3}}\right ) \left (9 e^5 \left (e+d x^{2/3}\right ) \, _3F_2\left (1,1,\frac {11}{2};2,2;1+\frac {e}{d x^{2/3}}\right )+d x^{2/3} \left (e^5+d^5 \sqrt {-\frac {e}{d x^{2/3}}} x^{10/3}\right ) \log \left (d+\frac {e}{x^{2/3}}\right )\right )\right ) \left (-a+b n \log \left (d+\frac {e}{x^{2/3}}\right )-b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )}{d^6 \sqrt {-\frac {e}{d x^{2/3}}} x}-\frac {2 b e^4 n \sqrt [3]{x} \left (a-b n \log \left (d+\frac {e}{x^{2/3}}\right )+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^4}+\frac {2 b e^3 n x \left (a-b n \log \left (d+\frac {e}{x^{2/3}}\right )+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{3 d^3}-\frac {2 b e^2 n x^{5/3} \left (a-b n \log \left (d+\frac {e}{x^{2/3}}\right )+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{5 d^2}+\frac {2 b e n x^{7/3} \left (a-b n \log \left (d+\frac {e}{x^{2/3}}\right )+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{7 d}+\frac {2 b e^{9/2} n \tan ^{-1}\left (\frac {\sqrt {d} \sqrt [3]{x}}{\sqrt {e}}\right ) \left (a-b n \log \left (d+\frac {e}{x^{2/3}}\right )+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2}{d^{9/2}}+b n x^3 \log \left (d+\frac {e}{x^{2/3}}\right ) \left (a-b n \log \left (d+\frac {e}{x^{2/3}}\right )+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^2+\frac {1}{3} x^3 \left (a-b n \log \left (d+\frac {e}{x^{2/3}}\right )+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^n\right )\right )^3 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 0, normalized size = 0.00 \[\int x^{2} \left (a +b \ln \left (c \left (d +\frac {e}{x^{\frac {2}{3}}}\right )^{n}\right )\right )^{3}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int x^2\,{\left (a+b\,\ln \left (c\,{\left (d+\frac {e}{x^{2/3}}\right )}^n\right )\right )}^3 \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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