Optimal. Leaf size=13 \[ -\frac{3}{2} \left (x+e^x\right )^{2/3} \]
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Rubi [A] time = 0.024423, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {6686} \[ -\frac{3}{2} \left (x+e^x\right )^{2/3} \]
Antiderivative was successfully verified.
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Rule 6686
Rubi steps
\begin{align*} \int -\frac{1+e^x}{\sqrt [3]{e^x+x}} \, dx &=-\frac{3}{2} \left (e^x+x\right )^{2/3}\\ \end{align*}
Mathematica [A] time = 0.0086212, size = 13, normalized size = 1. \[ -\frac{3}{2} \left (x+e^x\right )^{2/3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.028, size = 9, normalized size = 0.7 \begin{align*} -{\frac{3}{2} \left ({{\rm e}^{x}}+x \right ) ^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.947088, size = 11, normalized size = 0.85 \begin{align*} -\frac{3}{2} \,{\left (x + e^{x}\right )}^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.220586, size = 12, normalized size = 0.92 \begin{align*} - \frac{3 \left (x + e^{x}\right )^{\frac{2}{3}}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23833, size = 11, normalized size = 0.85 \begin{align*} -\frac{3}{2} \,{\left (x + e^{x}\right )}^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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