Optimal. Leaf size=24 \[ \text{Unintegrable}\left (x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p,x\right ) \]
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Rubi [A] time = 0.0547608, 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 = {} \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx \]
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 )\right )\right )^p \, dx &=3 \operatorname{Subst}\left (\int x^8 \left (a+b \log \left (c \left (d+e x^2\right )\right )\right )^p \, dx,x,\sqrt [3]{x}\right )\\ \end{align*}
Mathematica [A] time = 0.719293, size = 0, normalized size = 0. \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.086, size = 0, normalized size = 0. \begin{align*} \int{x}^{2} \left ( a+b\ln \left ( c \left ( d+e{x}^{{\frac{2}{3}}} \right ) \right ) \right ) ^{p}\, 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*} \int{\left (b \log \left ({\left (e x^{\frac{2}{3}} + d\right )} c\right ) + a\right )}^{p} x^{2}\,{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 ({\left (b \log \left (c e x^{\frac{2}{3}} + c d\right ) + a\right )}^{p} x^{2}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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{\left (b \log \left ({\left (e x^{\frac{2}{3}} + d\right )} c\right ) + a\right )}^{p} x^{2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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