Integrand size = 14, antiderivative size = 14 \[ \int \frac {e^x x}{\sqrt {e^x+x}} \, dx=2 \sqrt {e^x+x}+2 x \sqrt {e^x+x}-\text {Int}\left (\frac {1}{\sqrt {e^x+x}},x\right )-3 \text {Int}\left (\sqrt {e^x+x},x\right ) \]
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Not integrable
Time = 0.07 (sec) , antiderivative size = 14, 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 = {} \[ \int \frac {e^x x}{\sqrt {e^x+x}} \, dx=\int \frac {e^x x}{\sqrt {e^x+x}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = 2 x \sqrt {e^x+x}-2 \int \sqrt {e^x+x} \, dx-\int \frac {x}{\sqrt {e^x+x}} \, dx \\ & = 2 \sqrt {e^x+x}+2 x \sqrt {e^x+x}-2 \int \sqrt {e^x+x} \, dx-\int \frac {1}{\sqrt {e^x+x}} \, dx-\int \sqrt {e^x+x} \, dx \\ \end{align*}
Not integrable
Time = 0.14 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {e^x x}{\sqrt {e^x+x}} \, dx=\int \frac {e^x x}{\sqrt {e^x+x}} \, dx \]
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Not integrable
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71
\[\int \frac {{\mathrm e}^{x} x}{\sqrt {{\mathrm e}^{x}+x}}d x\]
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Exception generated. \[ \int \frac {e^x x}{\sqrt {e^x+x}} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 0.34 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {e^x x}{\sqrt {e^x+x}} \, dx=\int \frac {x e^{x}}{\sqrt {x + e^{x}}}\, dx \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {e^x x}{\sqrt {e^x+x}} \, dx=\int { \frac {x e^{x}}{\sqrt {x + e^{x}}} \,d x } \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {e^x x}{\sqrt {e^x+x}} \, dx=\int { \frac {x e^{x}}{\sqrt {x + e^{x}}} \,d x } \]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {e^x x}{\sqrt {e^x+x}} \, dx=\int \frac {x\,{\mathrm {e}}^x}{\sqrt {x+{\mathrm {e}}^x}} \,d x \]
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