Optimal. Leaf size=1328 \[ \text{result too large to display} \]
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Rubi [A] time = 1.72346, antiderivative size = 1334, normalized size of antiderivative = 1., number of steps used = 48, number of rules used = 18, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 1., Rules used = {2457, 2476, 2455, 292, 31, 634, 617, 204, 628, 2462, 260, 2416, 2390, 2301, 2394, 2393, 2391, 12} \[ \text{result too large to display} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2457
Rule 2476
Rule 2455
Rule 292
Rule 31
Rule 634
Rule 617
Rule 204
Rule 628
Rule 2462
Rule 260
Rule 2416
Rule 2390
Rule 2301
Rule 2394
Rule 2393
Rule 2391
Rule 12
Rubi steps
\begin{align*} \int \frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{x^5} \, dx &=-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}+\frac{1}{2} (3 e p) \int \frac{\log \left (c \left (d+e x^3\right )^p\right )}{x^2 \left (d+e x^3\right )} \, dx\\ &=-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}+\frac{1}{2} (3 e p) \int \left (\frac{\log \left (c \left (d+e x^3\right )^p\right )}{d x^2}-\frac{e x \log \left (c \left (d+e x^3\right )^p\right )}{d \left (d+e x^3\right )}\right ) \, dx\\ &=-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}+\frac{(3 e p) \int \frac{\log \left (c \left (d+e x^3\right )^p\right )}{x^2} \, dx}{2 d}-\frac{\left (3 e^2 p\right ) \int \frac{x \log \left (c \left (d+e x^3\right )^p\right )}{d+e x^3} \, dx}{2 d}\\ &=-\frac{3 e p \log \left (c \left (d+e x^3\right )^p\right )}{2 d x}-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}-\frac{\left (3 e^2 p\right ) \int \left (-\frac{\log \left (c \left (d+e x^3\right )^p\right )}{3 \sqrt [3]{d} \sqrt [3]{e} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}-\frac{(-1)^{2/3} \log \left (c \left (d+e x^3\right )^p\right )}{3 \sqrt [3]{d} \sqrt [3]{e} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}+\frac{\sqrt [3]{-1} \log \left (c \left (d+e x^3\right )^p\right )}{3 \sqrt [3]{d} \sqrt [3]{e} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}\right ) \, dx}{2 d}+\frac{\left (9 e^2 p^2\right ) \int \frac{x}{d+e x^3} \, dx}{2 d}\\ &=-\frac{3 e p \log \left (c \left (d+e x^3\right )^p\right )}{2 d x}-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}+\frac{\left (e^{5/3} p\right ) \int \frac{\log \left (c \left (d+e x^3\right )^p\right )}{\sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}-\frac{\left (\sqrt [3]{-1} e^{5/3} p\right ) \int \frac{\log \left (c \left (d+e x^3\right )^p\right )}{\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x} \, dx}{2 d^{4/3}}+\frac{\left ((-1)^{2/3} e^{5/3} p\right ) \int \frac{\log \left (c \left (d+e x^3\right )^p\right )}{\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x} \, dx}{2 d^{4/3}}-\frac{\left (3 e^{5/3} p^2\right ) \int \frac{1}{\sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}+\frac{\left (3 e^{5/3} p^2\right ) \int \frac{\sqrt [3]{d}+\sqrt [3]{e} x}{d^{2/3}-\sqrt [3]{d} \sqrt [3]{e} x+e^{2/3} x^2} \, dx}{2 d^{4/3}}\\ &=-\frac{3 e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{3 e p \log \left (c \left (d+e x^3\right )^p\right )}{2 d x}+\frac{e^{4/3} p \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\sqrt [3]{-1} e^{4/3} p \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}+\frac{\left (3 e^{4/3} p^2\right ) \int \frac{-\sqrt [3]{d} \sqrt [3]{e}+2 e^{2/3} x}{d^{2/3}-\sqrt [3]{d} \sqrt [3]{e} x+e^{2/3} x^2} \, dx}{4 d^{4/3}}+\frac{\left (9 e^{5/3} p^2\right ) \int \frac{1}{d^{2/3}-\sqrt [3]{d} \sqrt [3]{e} x+e^{2/3} x^2} \, dx}{4 d}-\frac{\left (3 e^{7/3} p^2\right ) \int \frac{x^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{d+e x^3} \, dx}{2 d^{4/3}}+\frac{\left (3 \sqrt [3]{-1} e^{7/3} p^2\right ) \int \frac{x^2 \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{d+e x^3} \, dx}{2 d^{4/3}}-\frac{\left (3 (-1)^{2/3} e^{7/3} p^2\right ) \int \frac{x^2 \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{d+e x^3} \, dx}{2 d^{4/3}}\\ &=-\frac{3 e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{3 e^{4/3} p^2 \log \left (d^{2/3}-\sqrt [3]{d} \sqrt [3]{e} x+e^{2/3} x^2\right )}{4 d^{4/3}}-\frac{3 e p \log \left (c \left (d+e x^3\right )^p\right )}{2 d x}+\frac{e^{4/3} p \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\sqrt [3]{-1} e^{4/3} p \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}+\frac{\left (9 e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{1}{-3-x^2} \, dx,x,1-\frac{2 \sqrt [3]{e} x}{\sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{\left (3 e^{7/3} p^2\right ) \int \left (\frac{\log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{3 e^{2/3} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}+\frac{\log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{3 e^{2/3} \left (-\sqrt [3]{-1} \sqrt [3]{d}+\sqrt [3]{e} x\right )}+\frac{\log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{3 e^{2/3} \left ((-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x\right )}\right ) \, dx}{2 d^{4/3}}+\frac{\left (3 \sqrt [3]{-1} e^{7/3} p^2\right ) \int \left (\frac{\log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{3 e^{2/3} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}+\frac{\log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{3 e^{2/3} \left (-\sqrt [3]{-1} \sqrt [3]{d}+\sqrt [3]{e} x\right )}+\frac{\log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{3 e^{2/3} \left ((-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x\right )}\right ) \, dx}{2 d^{4/3}}-\frac{\left (3 (-1)^{2/3} e^{7/3} p^2\right ) \int \left (\frac{\log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{3 e^{2/3} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}+\frac{\log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{3 e^{2/3} \left (-\sqrt [3]{-1} \sqrt [3]{d}+\sqrt [3]{e} x\right )}+\frac{\log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{3 e^{2/3} \left ((-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x\right )}\right ) \, dx}{2 d^{4/3}}\\ &=-\frac{3 \sqrt{3} e^{4/3} p^2 \tan ^{-1}\left (\frac{\sqrt [3]{d}-2 \sqrt [3]{e} x}{\sqrt{3} \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{3 e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{3 e^{4/3} p^2 \log \left (d^{2/3}-\sqrt [3]{d} \sqrt [3]{e} x+e^{2/3} x^2\right )}{4 d^{4/3}}-\frac{3 e p \log \left (c \left (d+e x^3\right )^p\right )}{2 d x}+\frac{e^{4/3} p \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\sqrt [3]{-1} e^{4/3} p \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}-\frac{\left (e^{5/3} p^2\right ) \int \frac{\log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}-\frac{\left (e^{5/3} p^2\right ) \int \frac{\log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{-\sqrt [3]{-1} \sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}-\frac{\left (e^{5/3} p^2\right ) \int \frac{\log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{(-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}+\frac{\left (\sqrt [3]{-1} e^{5/3} p^2\right ) \int \frac{\log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}+\frac{\left (\sqrt [3]{-1} e^{5/3} p^2\right ) \int \frac{\log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{-\sqrt [3]{-1} \sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}+\frac{\left (\sqrt [3]{-1} e^{5/3} p^2\right ) \int \frac{\log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{(-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}-\frac{\left ((-1)^{2/3} e^{5/3} p^2\right ) \int \frac{\log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}-\frac{\left ((-1)^{2/3} e^{5/3} p^2\right ) \int \frac{\log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{-\sqrt [3]{-1} \sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}-\frac{\left ((-1)^{2/3} e^{5/3} p^2\right ) \int \frac{\log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{(-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}\\ &=-\frac{3 \sqrt{3} e^{4/3} p^2 \tan ^{-1}\left (\frac{\sqrt [3]{d}-2 \sqrt [3]{e} x}{\sqrt{3} \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{3 e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (-\frac{(-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (-\frac{(-1)^{2/3} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (-\frac{(-1)^{2/3} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{3 e^{4/3} p^2 \log \left (d^{2/3}-\sqrt [3]{d} \sqrt [3]{e} x+e^{2/3} x^2\right )}{4 d^{4/3}}-\frac{3 e p \log \left (c \left (d+e x^3\right )^p\right )}{2 d x}+\frac{e^{4/3} p \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\sqrt [3]{-1} e^{4/3} p \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}-\frac{\left (e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{\left (e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\sqrt [3]{-1} \log (x)}{x} \, dx,x,\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{\left (e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{(-1)^{2/3} \log (x)}{x} \, dx,x,\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{\left (e^{5/3} p^2\right ) \int \frac{\log \left (\frac{\sqrt [3]{e} \left (-\sqrt [3]{-1} \sqrt [3]{d}+\sqrt [3]{e} x\right )}{-\sqrt [3]{d} \sqrt [3]{e}-\sqrt [3]{-1} \sqrt [3]{d} \sqrt [3]{e}}\right )}{\sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}+\frac{\left (e^{5/3} p^2\right ) \int \frac{\log \left (\frac{\sqrt [3]{e} \left ((-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x\right )}{-\sqrt [3]{d} \sqrt [3]{e}+(-1)^{2/3} \sqrt [3]{d} \sqrt [3]{e}}\right )}{\sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}-\frac{\left (\sqrt [3]{-1} e^{5/3} p^2\right ) \int \frac{\log \left (\frac{(-1)^{2/3} \sqrt [3]{e} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{-\sqrt [3]{d} \sqrt [3]{e}+(-1)^{2/3} \sqrt [3]{d} \sqrt [3]{e}}\right )}{\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x} \, dx}{2 d^{4/3}}-\frac{\left (\sqrt [3]{-1} e^{5/3} p^2\right ) \int \frac{\log \left (\frac{(-1)^{2/3} \sqrt [3]{e} \left ((-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x\right )}{-\sqrt [3]{d} \sqrt [3]{e}-\sqrt [3]{-1} \sqrt [3]{d} \sqrt [3]{e}}\right )}{\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x} \, dx}{2 d^{4/3}}+\frac{\left ((-1)^{2/3} e^{5/3} p^2\right ) \int \frac{\log \left (-\frac{\sqrt [3]{-1} \sqrt [3]{e} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{-\sqrt [3]{d} \sqrt [3]{e}-\sqrt [3]{-1} \sqrt [3]{d} \sqrt [3]{e}}\right )}{\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x} \, dx}{2 d^{4/3}}+\frac{\left ((-1)^{2/3} e^{5/3} p^2\right ) \int \frac{\log \left (-\frac{\sqrt [3]{-1} \sqrt [3]{e} \left (-\sqrt [3]{-1} \sqrt [3]{d}+\sqrt [3]{e} x\right )}{-\sqrt [3]{d} \sqrt [3]{e}+(-1)^{2/3} \sqrt [3]{d} \sqrt [3]{e}}\right )}{\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x} \, dx}{2 d^{4/3}}\\ &=-\frac{3 \sqrt{3} e^{4/3} p^2 \tan ^{-1}\left (\frac{\sqrt [3]{d}-2 \sqrt [3]{e} x}{\sqrt{3} \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{3 e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \log ^2\left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{4 d^{4/3}}-\frac{e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (-\frac{(-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (-\frac{(-1)^{2/3} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\frac{\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (-\frac{(-1)^{2/3} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{3 e^{4/3} p^2 \log \left (d^{2/3}-\sqrt [3]{d} \sqrt [3]{e} x+e^{2/3} x^2\right )}{4 d^{4/3}}-\frac{3 e p \log \left (c \left (d+e x^3\right )^p\right )}{2 d x}+\frac{e^{4/3} p \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\sqrt [3]{-1} e^{4/3} p \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}+\frac{\left (e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{\sqrt [3]{e} x}{-\sqrt [3]{d} \sqrt [3]{e}-\sqrt [3]{-1} \sqrt [3]{d} \sqrt [3]{e}}\right )}{x} \, dx,x,\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{\left (e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{\sqrt [3]{e} x}{-\sqrt [3]{d} \sqrt [3]{e}+(-1)^{2/3} \sqrt [3]{d} \sqrt [3]{e}}\right )}{x} \, dx,x,\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{\left (\sqrt [3]{-1} e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{\left (\sqrt [3]{-1} e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{\sqrt [3]{e} x}{-\sqrt [3]{d} \sqrt [3]{e}-\sqrt [3]{-1} \sqrt [3]{d} \sqrt [3]{e}}\right )}{x} \, dx,x,\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{\left (\sqrt [3]{-1} e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{\sqrt [3]{e} x}{-\sqrt [3]{d} \sqrt [3]{e}+(-1)^{2/3} \sqrt [3]{d} \sqrt [3]{e}}\right )}{x} \, dx,x,\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{\left ((-1)^{2/3} e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{\left ((-1)^{2/3} e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{\sqrt [3]{e} x}{-\sqrt [3]{d} \sqrt [3]{e}+(-1)^{2/3} \sqrt [3]{d} \sqrt [3]{e}}\right )}{x} \, dx,x,\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{\left ((-1)^{2/3} e^{5/3} p^2\right ) \int \frac{\log \left (\frac{\sqrt [3]{e} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\sqrt [3]{d} \sqrt [3]{e}+\sqrt [3]{-1} \sqrt [3]{d} \sqrt [3]{e}}\right )}{(-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x} \, dx}{2 d^{4/3}}\\ &=-\frac{3 \sqrt{3} e^{4/3} p^2 \tan ^{-1}\left (\frac{\sqrt [3]{d}-2 \sqrt [3]{e} x}{\sqrt{3} \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{3 e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \log ^2\left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{4 d^{4/3}}-\frac{e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (-\frac{(-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log ^2\left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{4 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (-\frac{(-1)^{2/3} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log ^2\left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{4 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\frac{\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (-\frac{(-1)^{2/3} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{3 e^{4/3} p^2 \log \left (d^{2/3}-\sqrt [3]{d} \sqrt [3]{e} x+e^{2/3} x^2\right )}{4 d^{4/3}}-\frac{3 e p \log \left (c \left (d+e x^3\right )^p\right )}{2 d x}+\frac{e^{4/3} p \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\sqrt [3]{-1} e^{4/3} p \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}-\frac{e^{4/3} p^2 \text{Li}_2\left (\frac{\sqrt [3]{d}+\sqrt [3]{e} x}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \text{Li}_2\left (\frac{2 \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (3-i \sqrt{3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \text{Li}_2\left (-\frac{\sqrt [3]{-1} \left ((-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \text{Li}_2\left (\frac{\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \text{Li}_2\left (\frac{\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{\left ((-1)^{2/3} e^{4/3} p^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{(-1)^{2/3} \sqrt [3]{e} x}{\sqrt [3]{d} \sqrt [3]{e}+\sqrt [3]{-1} \sqrt [3]{d} \sqrt [3]{e}}\right )}{x} \, dx,x,(-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}\\ &=-\frac{3 \sqrt{3} e^{4/3} p^2 \tan ^{-1}\left (\frac{\sqrt [3]{d}-2 \sqrt [3]{e} x}{\sqrt{3} \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{3 e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \log ^2\left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{4 d^{4/3}}-\frac{e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (-\frac{(-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log ^2\left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{4 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (-\frac{(-1)^{2/3} \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \log ^2\left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{4 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p^2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right ) \log \left (\frac{\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (-\frac{(-1)^{2/3} \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{3 e^{4/3} p^2 \log \left (d^{2/3}-\sqrt [3]{d} \sqrt [3]{e} x+e^{2/3} x^2\right )}{4 d^{4/3}}-\frac{3 e p \log \left (c \left (d+e x^3\right )^p\right )}{2 d x}+\frac{e^{4/3} p \log \left (\sqrt [3]{d}+\sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\sqrt [3]{-1} e^{4/3} p \log \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p \log \left (\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x\right ) \log \left (c \left (d+e x^3\right )^p\right )}{2 d^{4/3}}-\frac{\log ^2\left (c \left (d+e x^3\right )^p\right )}{4 x^4}-\frac{e^{4/3} p^2 \text{Li}_2\left (\frac{\sqrt [3]{d}+\sqrt [3]{e} x}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{e^{4/3} p^2 \text{Li}_2\left (\frac{2 \left (\sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (3-i \sqrt{3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \text{Li}_2\left (-\frac{\sqrt [3]{-1} \left ((-1)^{2/3} \sqrt [3]{d}+\sqrt [3]{e} x\right )}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{\sqrt [3]{-1} e^{4/3} p^2 \text{Li}_2\left (\frac{\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} p^2 \text{Li}_2\left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} p^2 \text{Li}_2\left (\frac{\sqrt [3]{d}+(-1)^{2/3} \sqrt [3]{e} x}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )}{2 d^{4/3}}\\ \end{align*}
Mathematica [C] time = 1.60044, size = 847, normalized size = 0.64 \[ \frac{\frac{e p x^3 \left (9 e p \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};-\frac{e x^3}{d}\right ) x^3+2 d^{2/3} \sqrt [3]{e} \log \left (-\sqrt [3]{e} x-\sqrt [3]{d}\right ) \log \left (c \left (e x^3+d\right )^p\right ) x-2 \sqrt [3]{-1} d^{2/3} \sqrt [3]{e} \log \left (\sqrt [3]{-1} \sqrt [3]{e} x-\sqrt [3]{d}\right ) \log \left (c \left (e x^3+d\right )^p\right ) x+2 (-1)^{2/3} d^{2/3} \sqrt [3]{e} \log \left (-(-1)^{2/3} \sqrt [3]{e} x-\sqrt [3]{d}\right ) \log \left (c \left (e x^3+d\right )^p\right ) x+\sqrt [3]{-1} d^{2/3} \sqrt [3]{e} p \left (\log \left (\sqrt [3]{-1} \sqrt [3]{e} x-\sqrt [3]{d}\right ) \left (2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{e} x+\sqrt [3]{d}\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )+\log \left (\sqrt [3]{-1} \sqrt [3]{e} x-\sqrt [3]{d}\right )+2 \log \left (\frac{(-1)^{2/3} \left ((-1)^{2/3} \sqrt [3]{e} x+\sqrt [3]{d}\right )}{\left (-1+(-1)^{2/3}\right ) \sqrt [3]{d}}\right )\right )+2 \text{PolyLog}\left (2,\frac{\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )+2 \text{PolyLog}\left (2,\frac{\sqrt [3]{-1} \sqrt [3]{e} x-\sqrt [3]{d}}{\left (-1+(-1)^{2/3}\right ) \sqrt [3]{d}}\right )\right ) x-(-1)^{2/3} d^{2/3} \sqrt [3]{e} p \left (\log \left (-(-1)^{2/3} \sqrt [3]{e} x-\sqrt [3]{d}\right ) \left (2 \log \left (\frac{(-1)^{2/3} \left (\sqrt [3]{e} x+\sqrt [3]{d}\right )}{\left (-1+(-1)^{2/3}\right ) \sqrt [3]{d}}\right )+2 \log \left (\frac{\sqrt [3]{-1} \left (\sqrt [3]{d}-\sqrt [3]{-1} \sqrt [3]{e} x\right )}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )+\log \left (-(-1)^{2/3} \sqrt [3]{e} x-\sqrt [3]{d}\right )\right )+2 \text{PolyLog}\left (2,\frac{(-1)^{2/3} \sqrt [3]{e} x+\sqrt [3]{d}}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )+2 \text{PolyLog}\left (2,\frac{(-1)^{2/3} \sqrt [3]{e} x+\sqrt [3]{d}}{\left (1-(-1)^{2/3}\right ) \sqrt [3]{d}}\right )\right ) x-d^{2/3} \sqrt [3]{e} p \left (\log \left (-\sqrt [3]{e} x-\sqrt [3]{d}\right ) \left (\log \left (-\sqrt [3]{e} x-\sqrt [3]{d}\right )+2 \left (\log \left (\frac{\sqrt [3]{-1} \sqrt [3]{d}-\sqrt [3]{e} x}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )+\log \left (\frac{-\frac{2 i \sqrt [3]{e} x}{\sqrt [3]{d}}+\sqrt{3}+i}{3 i+\sqrt{3}}\right )\right )\right )+2 \text{PolyLog}\left (2,\frac{\sqrt [3]{e} x+\sqrt [3]{d}}{\left (1+\sqrt [3]{-1}\right ) \sqrt [3]{d}}\right )+2 \text{PolyLog}\left (2,\frac{2 i \left (\frac{\sqrt [3]{e} x}{\sqrt [3]{d}}+1\right )}{3 i+\sqrt{3}}\right )\right ) x-6 d \log \left (c \left (e x^3+d\right )^p\right )\right )}{d^2}-\log ^2\left (c \left (e x^3+d\right )^p\right )}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [F] time = 1.063, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \ln \left ( c \left ( e{x}^{3}+d \right ) ^{p} \right ) \right ) ^{2}}{{x}^{5}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}}{x^{5}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}}{x^{5}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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