Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{f+g x^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )},x\right ) \]
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Rubi [A] time = 0.0133854, 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 = {} \[ \int \frac{f+g x^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{f+g x^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac{f+g x^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.625663, size = 0, normalized size = 0. \[ \int \frac{f+g x^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 3.711, size = 0, normalized size = 0. \begin{align*} \int{\frac{g{x}^{2}+f}{ \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 g x^{4} +{\left (e f + d g\right )} x^{2} + d f}{2 \,{\left (e p x \log \left ({\left (e x^{2} + d\right )}^{p}\right ) + e p x \log \left (c\right )\right )}} + \int \frac{3 \, e g x^{4} +{\left (e f + d g\right )} x^{2} - d f}{2 \,{\left (e p x^{2} \log \left ({\left (e x^{2} + d\right )}^{p}\right ) + e p x^{2} \log \left (c\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{g x^{2} + f}{\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 [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{f + g x^{2}}{\log{\left (c \left (d + e x^{2}\right )^{p} \right )}^{2}}\, dx \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{g x^{2} + f}{\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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