Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )},x\right ) \]
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Rubi [A] time = 0.0263193, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac{1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end{align*}
Mathematica [A] time = 14.5919, size = 0, normalized size = 0. \[ \int \frac{1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 4.97, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( g{x}^{3}+f \right ) ^{2} \left ( \ln \left ( c \left ( e{x}^{2}+d \right ) ^{p} \right ) \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{e x^{2} + d}{2 \,{\left (e g^{2} p x^{7} \log \left (c\right ) + 2 \, e f g p x^{4} \log \left (c\right ) + e f^{2} p x \log \left (c\right ) +{\left (e g^{2} p x^{7} + 2 \, e f g p x^{4} + e f^{2} p x\right )} \log \left ({\left (e x^{2} + d\right )}^{p}\right )\right )}} - \int \frac{5 \, e g x^{5} + 7 \, d g x^{3} - e f x^{2} + d f}{2 \,{\left (e g^{3} p x^{11} \log \left (c\right ) + 3 \, e f g^{2} p x^{8} \log \left (c\right ) + 3 \, e f^{2} g p x^{5} \log \left (c\right ) + e f^{3} p x^{2} \log \left (c\right ) +{\left (e g^{3} p x^{11} + 3 \, e f g^{2} p x^{8} + 3 \, e f^{2} g p x^{5} + e f^{3} p x^{2}\right )} \log \left ({\left (e x^{2} + d\right )}^{p}\right )\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{{\left (g^{2} x^{6} + 2 \, f g x^{3} + f^{2}\right )} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}, 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 [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (g x^{3} + f\right )}^{2} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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