Optimal. Leaf size=38 \[ \text {Int}\left (\frac {1}{\sqrt [3]{x+e^x}},x\right )+\text {Int}\left (\left (x+e^x\right )^{2/3},x\right )-\frac {3}{2} \left (x+e^x\right )^{2/3} \]
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Rubi [A] time = 0.04, 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 = {} \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx \]
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 = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx \]
Verification is Not applicable to the result.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
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 \[ \int \frac {x}{{\left (x + e^{x}\right )}^{\frac {1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {x}{\left (x +{\mathrm e}^{x}\right )^{\frac {1}{3}}}\, dx \]
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 \[ \int \frac {x}{{\left (x + e^{x}\right )}^{\frac {1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {x}{{\left (x+{\mathrm {e}}^x\right )}^{1/3}} \,d x \]
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 \[ \int \frac {x}{\sqrt [3]{x + e^{x}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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