Optimal. Leaf size=38 \[ -\frac {3}{2} \left (e^x+x\right )^{2/3}+\text {Int}\left (\frac {1}{\sqrt [3]{e^x+x}},x\right )+\text {Int}\left (\left (e^x+x\right )^{2/3},x\right ) \]
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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 \frac {x}{\sqrt [3]{e^x+x}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x}{\sqrt [3]{e^x+x}} \, dx &=-\frac {3}{2} \left (e^x+x\right )^{2/3}+\int \frac {1}{\sqrt [3]{e^x+x}} \, dx+\int \left (e^x+x\right )^{2/3} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.04, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{\sqrt [3]{e^x+x}} \, 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 \[\int \frac {x}{\left ({\mathrm e}^{x}+x \right )^{\frac {1}{3}}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.00, 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 [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 [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{\sqrt [3]{x + e^{x}}}\, dx \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 = -0.03 \begin {gather*} \int \frac {x}{{\left (x+{\mathrm {e}}^x\right )}^{1/3}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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