Integrand size = 22, antiderivative size = 22 \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx=\text {Int}\left (x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p,x\right ) \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx=\int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx \]
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Rubi steps \begin{align*} \text {integral}& = 3 \text {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*}
Not integrable
Time = 0.13 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx=\int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91
\[\int x^{2} {\left (a +b \ln \left (c \left (d +e \,x^{\frac {2}{3}}\right )\right )\right )}^{p}d x\]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx=\int { {\left (b \log \left ({\left (e x^{\frac {2}{3}} + d\right )} c\right ) + a\right )}^{p} x^{2} \,d x } \]
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Timed out. \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx=\text {Timed out} \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx=\int { {\left (b \log \left ({\left (e x^{\frac {2}{3}} + d\right )} c\right ) + a\right )}^{p} x^{2} \,d x } \]
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Not integrable
Time = 0.39 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx=\int { {\left (b \log \left ({\left (e x^{\frac {2}{3}} + d\right )} c\right ) + a\right )}^{p} x^{2} \,d x } \]
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Not integrable
Time = 1.64 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx=\int x^2\,{\left (a+b\,\ln \left (c\,\left (d+e\,x^{2/3}\right )\right )\right )}^p \,d x \]
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