Optimal. Leaf size=25 \[ \text {Int}\left (\frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )},x\right ) \]
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Rubi [A] time = 0.01, 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 = {} \[ \int \frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.31, size = 0, normalized size = 0.00 \[ \int \frac {f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.96, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {g x^{2} + f}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}, x\right ) \]
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 \[ \int \frac {g x^{2} + f}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.57, size = 0, normalized size = 0.00 \[ \int \frac {g \,x^{2}+f}{\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )}\, dx \]
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 \[ \int \frac {g x^{2} + f}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}\,{d x} \]
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 \[ \int \frac {g\,x^2+f}{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )} \,d x \]
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 \[ \int \frac {f + g x^{2}}{\log {\left (c \left (d + e x^{2}\right )^{p} \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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