Integrand size = 11, antiderivative size = 11 \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx=-\frac {3}{2} \left (e^x+x\right )^{2/3}+\text {Int}\left (\frac {1}{\sqrt [3]{e^x+x}},x\right )+\text {Int}\left (\left (e^x+x\right )^{2/3},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx=\int \frac {x}{\sqrt [3]{e^x+x}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = -\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*}
Not integrable
Time = 0.05 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.18 \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx=\int \frac {x}{\sqrt [3]{e^x+x}} \, dx \]
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Not integrable
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73
\[\int \frac {x}{\left ({\mathrm e}^{x}+x \right )^{\frac {1}{3}}}d x\]
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Exception generated. \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx=\int \frac {x}{\sqrt [3]{x + e^{x}}}\, dx \]
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Not integrable
Time = 0.21 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx=\int { \frac {x}{{\left (x + e^{x}\right )}^{\frac {1}{3}}} \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx=\int { \frac {x}{{\left (x + e^{x}\right )}^{\frac {1}{3}}} \,d x } \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \frac {x}{\sqrt [3]{e^x+x}} \, dx=\int \frac {x}{{\left (x+{\mathrm {e}}^x\right )}^{1/3}} \,d x \]
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