Optimal. Leaf size=17 \[ 3 x \left (e^x+x\right )^{2/3}+3 \log (x) \]
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Rubi [A]
time = 0.43, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 8, number of rules used = 4, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.093, Rules used = {6874, 2293,
2305, 2294} \begin {gather*} 3 \left (x+e^x\right )^{2/3} x+3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2293
Rule 2294
Rule 2305
Rule 6874
Rubi steps
\begin {align*} \int f^{x^n} x^m \, dx &=-\frac {x^{1+m} \Gamma \left (\frac {1+m}{n},-x^n \log (f)\right ) \left (-x^n \log (f)\right )^{-\frac {1+m}{n}}}{n}\\ \end {align*}
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Mathematica [A]
time = 0.54, size = 17, normalized size = 1.00 \begin {gather*} 3 x \left (e^x+x\right )^{2/3}+3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.00, size = 0, normalized size = 0.00 \[\int \frac {5 x^{2}+3 \left ({\mathrm e}^{x}+x \right )^{\frac {1}{3}}+{\mathrm e}^{x} \left (2 x^{2}+3 x \right )}{x \left ({\mathrm e}^{x}+x \right )^{\frac {1}{3}}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 21, normalized size = 1.24 \begin {gather*} \frac {3 \, {\left (x^{2} + x e^{x}\right )}}{{\left (x + e^{x}\right )}^{\frac {1}{3}}} + 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 x^{2} e^{x} + 5 x^{2} + 3 x e^{x} + 3 \sqrt [3]{x + e^{x}}}{x \sqrt [3]{x + e^{x}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
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 [B]
time = 3.67, size = 14, normalized size = 0.82 \begin {gather*} 3\,\ln \left (x\right )+3\,x\,{\left (x+{\mathrm {e}}^x\right )}^{2/3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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