Optimal. Leaf size=65 \[ -\frac{3}{5} \text{CannotIntegrate}\left (\frac{x^4}{\sqrt{x^3+5 e^x}},x\right )-\frac{4}{5} \text{CannotIntegrate}\left (x \sqrt{x^3+5 e^x},x\right )+\frac{2}{5} \sqrt{x^3+5 e^x} x^2 \]
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Rubi [A] time = 0.165871, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}
Mathematica [A] time = 0.187728, size = 0, normalized size = 0. \[ \int \frac{e^x x^2}{\sqrt{5 e^x+x^3}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.041, size = 0, normalized size = 0. \begin{align*} \int{{{\rm e}^{x}}{x}^{2}{\frac{1}{\sqrt{5\,{{\rm e}^{x}}+{x}^{3}}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{2} e^{x}}{\sqrt{x^{3} + 5 \, e^{x}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{2} e^{x}}{\sqrt{x^{3} + 5 e^{x}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{2} e^{x}}{\sqrt{x^{3} + 5 \, e^{x}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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