Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^2\right )^2},x\right ) \]
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Rubi [A] time = 0.03, 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 = {} \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^2\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^2\right )^2} \, dx &=\int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^2\right )^2} \, dx\\ \end {align*}
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Mathematica [A] time = 8.95, size = 0, normalized size = 0.00 \[ \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^2\right )^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.57, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right ) \]
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 \[ \int \frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{{\left (g x^{2} + f\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 41.74, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )^{2}}{\left (g \,x^{2}+f \right )^{2}}\, dx \]
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 \[ \int \frac {\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{{\left (g x^{2} + f\right )}^{2}}\,{d x} \]
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 \[ \int \frac {{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )}^2}{{\left (g\,x^2+f\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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