Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{1}{\left (f+g x^2\right ) \log ^2\left (c \left (d+e x^2\right )^p\right )},x\right ) \]
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Rubi [A] time = 0.0263288, 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 = {} \[ \int \frac{1}{\left (f+g x^2\right ) \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{\left (f+g x^2\right ) \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac{1}{\left (f+g x^2\right ) \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end{align*}
Mathematica [A] time = 4.56145, size = 0, normalized size = 0. \[ \int \frac{1}{\left (f+g x^2\right ) \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 4.606, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( g{x}^{2}+f \right ) \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 p x^{3} \log \left (c\right ) + e f p x \log \left (c\right ) +{\left (e g p x^{3} + e f p x\right )} \log \left ({\left (e x^{2} + d\right )}^{p}\right )\right )}} - \int \frac{e g x^{4} -{\left (e f - 3 \, d g\right )} x^{2} + d f}{2 \,{\left (e g^{2} p x^{6} \log \left (c\right ) + 2 \, e f g p x^{4} \log \left (c\right ) + e f^{2} p x^{2} \log \left (c\right ) +{\left (e g^{2} p x^{6} + 2 \, e f g p x^{4} + e f^{2} 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 x^{2} + f\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^{2} + f\right )} \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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