Optimal. Leaf size=13 \[ -\frac {3}{2} \left (x+e^x\right )^{2/3} \]
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Rubi [A] time = 0.07, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {2273} \[ -\frac {3}{2} \left (x+e^x\right )^{2/3} \]
Antiderivative was successfully verified.
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Rule 2273
Rubi steps
\begin {align*} \int \left (-\frac {1}{\sqrt [3]{e^x+x}}+\frac {x}{\sqrt [3]{e^x+x}}-\left (e^x+x\right )^{2/3}\right ) \, dx &=-\int \frac {1}{\sqrt [3]{e^x+x}} \, dx+\int \frac {x}{\sqrt [3]{e^x+x}} \, dx-\int \left (e^x+x\right )^{2/3} \, dx\\ &=-\frac {3}{2} \left (e^x+x\right )^{2/3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ -\frac {3}{2} \left (x+e^x\right )^{2/3} \]
Antiderivative was successfully verified.
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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 [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int -{\left (x + e^{x}\right )}^{\frac {2}{3}} + \frac {x}{{\left (x + e^{x}\right )}^{\frac {1}{3}}} - \frac {1}{{\left (x + e^{x}\right )}^{\frac {1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 9, normalized size = 0.69 \[ -\frac {3 \left (x +{\mathrm e}^{x}\right )^{\frac {2}{3}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.20, size = 8, normalized size = 0.62 \[ -\frac {3}{2} \, {\left (x + e^{x}\right )}^{\frac {2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.38, size = 8, normalized size = 0.62 \[ -\frac {3\,{\left (x+{\mathrm {e}}^x\right )}^{2/3}}{2} \]
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 \[ - \int \frac {e^{x}}{\sqrt [3]{x + e^{x}}}\, dx - \int \frac {1}{\sqrt [3]{x + e^{x}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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