Optimal. Leaf size=67 \[ \frac {2}{5} x^2 \sqrt {5 e^x+x^3}-\frac {3}{5} \text {Int}\left (\frac {x^4}{\sqrt {5 e^x+x^3}},x\right )-\frac {4}{5} \text {Int}\left (x \sqrt {5 e^x+x^3},x\right ) \]
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Rubi [A]
time = 0.11, 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 = {}
\begin {gather*} \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx \end {gather*}
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 = 0.36, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^x x^2}{\sqrt {5 e^x+x^3}} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.00, size = 0, normalized size = 0.00 \[\int \frac {{\mathrm e}^{x} x^{2}}{\sqrt {5 \,{\mathrm e}^{x}+x^{3}}}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
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 \begin {gather*} \int \frac {x^{2} e^{x}}{\sqrt {x^{3} + 5 e^{x}}}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {x^2\,{\mathrm {e}}^x}{\sqrt {5\,{\mathrm {e}}^x+x^3}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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