Optimal. Leaf size=25 \[ \text {Int}\left (\frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )\right )\right )^p}{x^2},x\right ) \]
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Rubi [A] time = 0.05, 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 = {} \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )\right )\right )^p}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )\right )\right )^p}{x^2} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b \log (c (d+e x)))^p}{x^4} \, dx,x,\sqrt [3]{x}\right )\\ \end {align*}
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Mathematica [A] time = 0.62, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )\right )\right )^p}{x^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.87, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b \log \left (c e x^{\frac {1}{3}} + c d\right ) + a\right )}^{p}}{x^{2}}, x\right ) \]
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 \[ \int \frac {{\left (b \log \left ({\left (e x^{\frac {1}{3}} + d\right )} c\right ) + a\right )}^{p}}{x^{2}}\,{d x} \]
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 \[ \int \frac {\left (b \ln \left (\left (e \,x^{\frac {1}{3}}+d \right ) c \right )+a \right )^{p}}{x^{2}}\, dx \]
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 \[ \int \frac {{\left (b \log \left ({\left (e x^{\frac {1}{3}} + d\right )} c\right ) + a\right )}^{p}}{x^{2}}\,{d x} \]
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 \[ \int \frac {{\left (a+b\,\ln \left (c\,\left (d+e\,x^{1/3}\right )\right )\right )}^p}{x^2} \,d x \]
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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