Optimal. Leaf size=25 \[ \text {Int}\left (x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^2\right )\right )^p,x\right ) \]
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Rubi [A]
time = 0.03, 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 = {}
\begin {gather*} \int x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^2\right )\right )^p \, dx \end {gather*}
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}{x^{2/3}}\right )^2\right )\right )^p \, dx &=3 \text {Subst}\left (\int x^5 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^2\right )\right )^p \, dx,x,\sqrt [3]{x}\right )\\ \end {align*}
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Mathematica [A]
time = 0.19, size = 0, normalized size = 0.00 \begin {gather*} \int x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^2\right )\right )^p \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.00, size = 0, normalized size = 0.00 \[\int x \left (a +b \ln \left (c \left (d +\frac {e}{x^{\frac {2}{3}}}\right )^{2}\right )\right )^{p}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int x\,{\left (a+b\,\ln \left (c\,{\left (d+\frac {e}{x^{2/3}}\right )}^2\right )\right )}^p \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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