Integrand size = 22, antiderivative size = 22 \[ \int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx=\text {Int}\left (x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p,x\right ) \]
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Not integrable
Time = 0.03 (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 = {} \[ \int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx=\int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx \]
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Rubi steps \begin{align*} \text {integral}& = 3 \text {Subst}\left (\int x^5 \left (a+b \log \left (c \left (d+\frac {e}{x}\right )^2\right )\right )^p \, dx,x,\sqrt [3]{x}\right ) \\ \end{align*}
Not integrable
Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx=\int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx \]
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Not integrable
Time = 0.10 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91
\[\int x {\left (a +b \ln \left (c \left (d +\frac {e}{x^{\frac {1}{3}}}\right )^{2}\right )\right )}^{p}d x\]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.73 \[ \int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx=\int { {\left (b \log \left (c {\left (d + \frac {e}{x^{\frac {1}{3}}}\right )}^{2}\right ) + a\right )}^{p} x \,d x } \]
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Timed out. \[ \int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx=\text {Timed out} \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx=\int { {\left (b \log \left (c {\left (d + \frac {e}{x^{\frac {1}{3}}}\right )}^{2}\right ) + a\right )}^{p} x \,d x } \]
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Not integrable
Time = 1.51 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx=\int { {\left (b \log \left (c {\left (d + \frac {e}{x^{\frac {1}{3}}}\right )}^{2}\right ) + a\right )}^{p} x \,d x } \]
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Not integrable
Time = 1.74 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx=\int x\,{\left (a+b\,\ln \left (c\,{\left (d+\frac {e}{x^{1/3}}\right )}^2\right )\right )}^p \,d x \]
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