Optimal. Leaf size=24 \[ \text{Unintegrable}\left (x \left (a+b \log \left (c \left (d+\frac{e}{\sqrt [3]{x}}\right )^2\right )\right )^p,x\right ) \]
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Rubi [A] time = 0.0469373, 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 = {} \[ \int x \left (a+b \log \left (c \left (d+\frac{e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int x \left (a+b \log \left (c \left (d+\frac{e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx &=3 \operatorname{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*}
Mathematica [A] time = 0.228788, size = 0, normalized size = 0. \[ \int x \left (a+b \log \left (c \left (d+\frac{e}{\sqrt [3]{x}}\right )^2\right )\right )^p \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.574, size = 0, normalized size = 0. \begin{align*} \int x \left ( a+b\ln \left ( c \left ( d+{e{\frac{1}{\sqrt [3]{x}}}} \right ) ^{2} \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 (c{\left (d + \frac{e}{x^{\frac{1}{3}}}\right )}^{2}\right ) + a\right )}^{p} x\,{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 (\frac{c d^{2} x + 2 \, c d e x^{\frac{2}{3}} + c e^{2} x^{\frac{1}{3}}}{x}\right ) + a\right )}^{p} x, 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 (c{\left (d + \frac{e}{x^{\frac{1}{3}}}\right )}^{2}\right ) + a\right )}^{p} x\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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