Optimal. Leaf size=651 \[ \frac{i g^{3/2} p \text{PolyLog}\left (2,1+\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\left (\sqrt{f}-i \sqrt{g} x\right ) \left (-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right )}\right )}{2 f^{5/2}}+\frac{i g^{3/2} p \text{PolyLog}\left (2,1-\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\left (\sqrt{f}-i \sqrt{g} x\right ) \left (\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right )}\right )}{2 f^{5/2}}-\frac{i g^{3/2} p \text{PolyLog}\left (2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right )}{f^{5/2}}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}-\frac{2 e^{3/2} p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 d^{3/2} f}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (-\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\left (\sqrt{f}-i \sqrt{g} x\right ) \left (-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right )}\right )}{f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\left (\sqrt{f}-i \sqrt{g} x\right ) \left (\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right )}\right )}{f^{5/2}}-\frac{2 \sqrt{e} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} f^2}-\frac{2 e p}{3 d f x}+\frac{2 g^{3/2} p \log \left (\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right ) \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right )}{f^{5/2}} \]
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Rubi [A] time = 0.649823, antiderivative size = 651, normalized size of antiderivative = 1., number of steps used = 19, number of rules used = 11, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.44, Rules used = {2476, 2455, 325, 205, 2470, 12, 4928, 4856, 2402, 2315, 2447} \[ \frac{i g^{3/2} p \text{PolyLog}\left (2,1+\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\left (\sqrt{f}-i \sqrt{g} x\right ) \left (-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right )}\right )}{2 f^{5/2}}+\frac{i g^{3/2} p \text{PolyLog}\left (2,1-\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\left (\sqrt{f}-i \sqrt{g} x\right ) \left (\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right )}\right )}{2 f^{5/2}}-\frac{i g^{3/2} p \text{PolyLog}\left (2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right )}{f^{5/2}}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}-\frac{2 e^{3/2} p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 d^{3/2} f}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (-\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\left (\sqrt{f}-i \sqrt{g} x\right ) \left (-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right )}\right )}{f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\left (\sqrt{f}-i \sqrt{g} x\right ) \left (\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right )}\right )}{f^{5/2}}-\frac{2 \sqrt{e} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} f^2}-\frac{2 e p}{3 d f x}+\frac{2 g^{3/2} p \log \left (\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right ) \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right )}{f^{5/2}} \]
Antiderivative was successfully verified.
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Rule 2476
Rule 2455
Rule 325
Rule 205
Rule 2470
Rule 12
Rule 4928
Rule 4856
Rule 2402
Rule 2315
Rule 2447
Rubi steps
\begin{align*} \int \frac{\log \left (c \left (d+e x^2\right )^p\right )}{x^4 \left (f+g x^2\right )} \, dx &=\int \left (\frac{\log \left (c \left (d+e x^2\right )^p\right )}{f x^4}-\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x^2}+\frac{g^2 \log \left (c \left (d+e x^2\right )^p\right )}{f^2 \left (f+g x^2\right )}\right ) \, dx\\ &=\frac{\int \frac{\log \left (c \left (d+e x^2\right )^p\right )}{x^4} \, dx}{f}-\frac{g \int \frac{\log \left (c \left (d+e x^2\right )^p\right )}{x^2} \, dx}{f^2}+\frac{g^2 \int \frac{\log \left (c \left (d+e x^2\right )^p\right )}{f+g x^2} \, dx}{f^2}\\ &=-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}+\frac{(2 e p) \int \frac{1}{x^2 \left (d+e x^2\right )} \, dx}{3 f}-\frac{(2 e g p) \int \frac{1}{d+e x^2} \, dx}{f^2}-\frac{\left (2 e g^2 p\right ) \int \frac{x \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right )}{\sqrt{f} \sqrt{g} \left (d+e x^2\right )} \, dx}{f^2}\\ &=-\frac{2 e p}{3 d f x}-\frac{2 \sqrt{e} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} f^2}-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}-\frac{\left (2 e^2 p\right ) \int \frac{1}{d+e x^2} \, dx}{3 d f}-\frac{\left (2 e g^{3/2} p\right ) \int \frac{x \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right )}{d+e x^2} \, dx}{f^{5/2}}\\ &=-\frac{2 e p}{3 d f x}-\frac{2 e^{3/2} p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 d^{3/2} f}-\frac{2 \sqrt{e} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} f^2}-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}-\frac{\left (2 e g^{3/2} p\right ) \int \left (-\frac{\tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right )}{2 \sqrt{e} \left (\sqrt{-d}-\sqrt{e} x\right )}+\frac{\tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right )}{2 \sqrt{e} \left (\sqrt{-d}+\sqrt{e} x\right )}\right ) \, dx}{f^{5/2}}\\ &=-\frac{2 e p}{3 d f x}-\frac{2 e^{3/2} p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 d^{3/2} f}-\frac{2 \sqrt{e} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} f^2}-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}+\frac{\left (\sqrt{e} g^{3/2} p\right ) \int \frac{\tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right )}{\sqrt{-d}-\sqrt{e} x} \, dx}{f^{5/2}}-\frac{\left (\sqrt{e} g^{3/2} p\right ) \int \frac{\tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right )}{\sqrt{-d}+\sqrt{e} x} \, dx}{f^{5/2}}\\ &=-\frac{2 e p}{3 d f x}-\frac{2 e^{3/2} p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 d^{3/2} f}-\frac{2 \sqrt{e} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} f^2}+\frac{2 g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right )}{f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (-\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{f^{5/2}}-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}-2 \frac{\left (g^2 p\right ) \int \frac{\log \left (\frac{2}{1-\frac{i \sqrt{g} x}{\sqrt{f}}}\right )}{1+\frac{g x^2}{f}} \, dx}{f^3}+\frac{\left (g^2 p\right ) \int \frac{\log \left (\frac{2 \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\sqrt{f} \left (-i \sqrt{e}+\frac{\sqrt{-d} \sqrt{g}}{\sqrt{f}}\right ) \left (1-\frac{i \sqrt{g} x}{\sqrt{f}}\right )}\right )}{1+\frac{g x^2}{f}} \, dx}{f^3}+\frac{\left (g^2 p\right ) \int \frac{\log \left (\frac{2 \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\sqrt{f} \left (i \sqrt{e}+\frac{\sqrt{-d} \sqrt{g}}{\sqrt{f}}\right ) \left (1-\frac{i \sqrt{g} x}{\sqrt{f}}\right )}\right )}{1+\frac{g x^2}{f}} \, dx}{f^3}\\ &=-\frac{2 e p}{3 d f x}-\frac{2 e^{3/2} p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 d^{3/2} f}-\frac{2 \sqrt{e} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} f^2}+\frac{2 g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right )}{f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (-\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{f^{5/2}}-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}+\frac{i g^{3/2} p \text{Li}_2\left (1+\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{2 f^{5/2}}+\frac{i g^{3/2} p \text{Li}_2\left (1-\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{2 f^{5/2}}-2 \frac{\left (i g^{3/2} p\right ) \operatorname{Subst}\left (\int \frac{\log (2 x)}{1-2 x} \, dx,x,\frac{1}{1-\frac{i \sqrt{g} x}{\sqrt{f}}}\right )}{f^{5/2}}\\ &=-\frac{2 e p}{3 d f x}-\frac{2 e^{3/2} p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 d^{3/2} f}-\frac{2 \sqrt{e} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} f^2}+\frac{2 g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right )}{f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (-\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{f^{5/2}}-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}-\frac{i g^{3/2} p \text{Li}_2\left (1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right )}{f^{5/2}}+\frac{i g^{3/2} p \text{Li}_2\left (1+\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{2 f^{5/2}}+\frac{i g^{3/2} p \text{Li}_2\left (1-\frac{2 \sqrt{f} \sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\left (i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right ) \left (\sqrt{f}-i \sqrt{g} x\right )}\right )}{2 f^{5/2}}\\ \end{align*}
Mathematica [C] time = 0.26156, size = 754, normalized size = 1.16 \[ -\frac{2 e g^{3/2} p \left (\frac{i \left (\frac{\text{PolyLog}\left (2,\frac{\sqrt{e} \left (\sqrt{f}-i \sqrt{g} x\right )}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right )}{\sqrt{e}}+\frac{\log \left (1-\frac{i \sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{\sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right )}{\sqrt{e}}\right )}{4 \sqrt{e}}+\frac{i \left (\frac{\text{PolyLog}\left (2,\frac{\sqrt{e} \left (\sqrt{f}-i \sqrt{g} x\right )}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right )}{\sqrt{e}}+\frac{\log \left (1-\frac{i \sqrt{g} x}{\sqrt{f}}\right ) \log \left (-\frac{\sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right )}{\sqrt{e}}\right )}{4 \sqrt{e}}-\frac{i \left (\frac{\text{PolyLog}\left (2,\frac{\sqrt{e} \left (\sqrt{f}+i \sqrt{g} x\right )}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right )}{\sqrt{e}}+\frac{\log \left (1+\frac{i \sqrt{g} x}{\sqrt{f}}\right ) \log \left (\frac{\sqrt{g} \left (\sqrt{-d}+\sqrt{e} x\right )}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right )}{\sqrt{e}}\right )}{4 \sqrt{e}}-\frac{i \left (\frac{\text{PolyLog}\left (2,\frac{\sqrt{e} \left (\sqrt{f}+i \sqrt{g} x\right )}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right )}{\sqrt{e}}+\frac{\log \left (1+\frac{i \sqrt{g} x}{\sqrt{f}}\right ) \log \left (-\frac{\sqrt{g} \left (\sqrt{-d}-\sqrt{e} x\right )}{-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right )}{\sqrt{e}}\right )}{4 \sqrt{e}}\right )}{f^{5/2}}+\frac{g^{3/2} \tan ^{-1}\left (\frac{\sqrt{g} x}{\sqrt{f}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{f^{5/2}}+\frac{g \log \left (c \left (d+e x^2\right )^p\right )}{f^2 x}-\frac{\log \left (c \left (d+e x^2\right )^p\right )}{3 f x^3}-\frac{2 \sqrt{e} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} f^2}-\frac{2 e p \, _2F_1\left (-\frac{1}{2},1;\frac{1}{2};-\frac{e x^2}{d}\right )}{3 d f x} \]
Warning: Unable to verify antiderivative.
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Maple [C] time = 0.651, size = 1005, normalized size = 1.5 \begin{align*} \text{result too large to display} \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^{2} + d\right )}^{p} c\right )}{g x^{6} + f x^{4}}, 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^{2} + d\right )}^{p} c\right )}{{\left (g x^{2} + f\right )} x^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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