Integrand size = 26, antiderivative size = 26 \[ \int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx=2 x \sqrt {e^x+x}-2 \text {Int}\left (\sqrt {e^x+x},x\right ) \]
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Not integrable
Time = 0.09 (sec) , antiderivative size = 26, 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 = {} \[ \int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx=\int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x}{\sqrt {e^x+x}} \, dx+\int \frac {e^x 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 \frac {x}{\sqrt {e^x+x}} \, dx+\int \sqrt {e^x+x} \, dx \\ & = 2 x \sqrt {e^x+x}-2 \int \sqrt {e^x+x} \, dx \\ \end{align*}
Not integrable
Time = 0.01 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx=\int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx \]
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Not integrable
Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.73
\[\int \left (\frac {x}{\sqrt {{\mathrm e}^{x}+x}}+\frac {{\mathrm e}^{x} x}{\sqrt {{\mathrm e}^{x}+x}}\right )d x\]
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Exception generated. \[ \int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 0.22 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.58 \[ \int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx=\int \frac {x \left (e^{x} + 1\right )}{\sqrt {x + e^{x}}}\, dx \]
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Not integrable
Time = 0.22 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx=\int { \frac {x e^{x}}{\sqrt {x + e^{x}}} + \frac {x}{\sqrt {x + e^{x}}} \,d x } \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx=\int { \frac {x e^{x}}{\sqrt {x + e^{x}}} + \frac {x}{\sqrt {x + e^{x}}} \,d x } \]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \left (\frac {x}{\sqrt {e^x+x}}+\frac {e^x x}{\sqrt {e^x+x}}\right ) \, dx=\int \frac {x}{\sqrt {x+{\mathrm {e}}^x}}+\frac {x\,{\mathrm {e}}^x}{\sqrt {x+{\mathrm {e}}^x}} \,d x \]
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