Optimal. Leaf size=67 \[ -\frac {4}{5} \text {Int}\left (x \sqrt {x^3+5 e^x},x\right )-\frac {3}{5} \text {Int}\left (\frac {x^4}{\sqrt {x^3+5 e^x}},x\right )+\frac {2}{5} \sqrt {x^3+5 e^x} x^2 \]
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Rubi [A] time = 0.17, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \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} \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*}
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Mathematica [A] time = 0.19, size = 0, normalized size = 0.00 \[ \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx \]
Verification is Not applicable to the result.
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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 [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2} e^{x}}{\sqrt {x^{3} + 5 \, e^{x}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {x^{2} {\mathrm e}^{x}}{\sqrt {x^{3}+5 \,{\mathrm e}^{x}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2} e^{x}}{\sqrt {x^{3} + 5 \, e^{x}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.01 \[ \int \frac {x^2\,{\mathrm {e}}^x}{\sqrt {5\,{\mathrm {e}}^x+x^3}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2} e^{x}}{\sqrt {x^{3} + 5 e^{x}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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