Integrand size = 20, antiderivative size = 20 \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx=\frac {2}{5} x^2 \sqrt {5 e^x+x^3}-\frac {3}{5} \text {Int}\left (\frac {x^4}{\sqrt {5 e^x+x^3}},x\right )-\frac {4}{5} \text {Int}\left (x \sqrt {5 e^x+x^3},x\right ) \]
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Not integrable
Time = 0.11 (sec) , antiderivative size = 20, 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 = {} \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx=\int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {2}{5} x^2 \sqrt {5 e^x+x^3}-\frac {3}{5} \int \frac {x^4}{\sqrt {5 e^x+x^3}} \, dx-\frac {4}{5} \int x \sqrt {5 e^x+x^3} \, dx \\ \end{align*}
Not integrable
Time = 0.38 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx=\int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx \]
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Not integrable
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80
\[\int \frac {{\mathrm e}^{x} x^{2}}{\sqrt {5 \,{\mathrm e}^{x}+x^{3}}}d x\]
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Exception generated. \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 0.44 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx=\int \frac {x^{2} e^{x}}{\sqrt {x^{3} + 5 e^{x}}}\, dx \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx=\int { \frac {x^{2} e^{x}}{\sqrt {x^{3} + 5 \, e^{x}}} \,d x } \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx=\int { \frac {x^{2} e^{x}}{\sqrt {x^{3} + 5 \, e^{x}}} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx=\int \frac {x^2\,{\mathrm {e}}^x}{\sqrt {5\,{\mathrm {e}}^x+x^3}} \,d x \]
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