Optimal. Leaf size=27 \[ \text {Int}\left (x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )^2\right )\right )^p,x\right ) \]
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Rubi [A] time = 0.06, 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 = {} \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )^2\right )\right )^p \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )^2\right )\right )^p \, dx &=3 \operatorname {Subst}\left (\int x^8 \left (a+b \log \left (c \left (d+e x^2\right )^2\right )\right )^p \, dx,x,\sqrt [3]{x}\right )\\ \end {align*}
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Mathematica [A] time = 0.18, size = 0, normalized size = 0.00 \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )^2\right )\right )^p \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.53, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b \log \left (c e^{2} x^{\frac {4}{3}} + 2 \, c d e x^{\frac {2}{3}} + c d^{2}\right ) + a\right )}^{p} x^{2}, x\right ) \]
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 \[ \int {\left (b \log \left ({\left (e x^{\frac {2}{3}} + d\right )}^{2} c\right ) + a\right )}^{p} x^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 0, normalized size = 0.00 \[ \int x^{2} \left (b \ln \left (\left (e \,x^{\frac {2}{3}}+d \right )^{2} c \right )+a \right )^{p}\, dx \]
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 \[ \int {\left (b \log \left ({\left (e x^{\frac {2}{3}} + d\right )}^{2} c\right ) + a\right )}^{p} x^{2}\,{d x} \]
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 \[ \int x^2\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x^{2/3}\right )}^2\right )\right )}^p \,d x \]
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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