Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{\left (f+g x^2\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )},x\right ) \]
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Rubi [A] time = 0.0240136, 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 = {} \[ \int \frac{\left (f+g x^2\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (f+g x^2\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac{\left (f+g x^2\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.864631, size = 0, normalized size = 0. \[ \int \frac{\left (f+g x^2\right )^2}{\log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 3.822, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( g{x}^{2}+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 g^{2} x^{6} +{\left (2 \, e f g + d g^{2}\right )} x^{4} + d f^{2} +{\left (e f^{2} + 2 \, d f g\right )} x^{2}}{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{5 \, e g^{2} x^{6} + 3 \,{\left (2 \, e f g + d g^{2}\right )} x^{4} - d f^{2} +{\left (e f^{2} + 2 \, d f g\right )} x^{2}}{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^{2} x^{4} + 2 \, f g x^{2} + f^{2}}{\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{\left (f + g x^{2}\right )^{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{{\left (g x^{2} + 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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