Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\left (f+g x^2\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )},x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\left (f+g x^2\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]
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 \left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac {\left (f+g x^2\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.49, size = 0, normalized size = 0.00 \[ \int \frac {\left (f+g x^2\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.63, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (g x^{2} + f\right )}^{2}}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.84, size = 0, normalized size = 0.00 \[ \int \frac {\left (g \,x^{2}+f \right )^{2}}{\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (g x^{2} + f\right )}^{2}}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (g\,x^2+f\right )}^2}{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (f + g x^{2}\right )^{2}}{\log {\left (c \left (d + e x^{2}\right )^{p} \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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