Optimal. Leaf size=67 \[ -\frac{4}{5} \text{Int}\left (x \sqrt{x^3+5 e^x},x\right )-\frac{3}{5} \text{Int}\left (\frac{x^4}{\sqrt{x^3+5 e^x}},x\right )+\frac{2}{5} \sqrt{x^3+5 e^x} x^2 \]
[Out]
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Rubi [A] time = 0.2604, 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. \[ \text{Int}\left (\frac{e^x x^2}{\sqrt{5 e^x+x^3}},x\right ) \]
Verification is Not applicable to the result.
[In] Int[(E^x*x^2)/Sqrt[5*E^x + x^3],x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \frac{2 x^{2} \sqrt{x^{3} + 5 e^{x}}}{5} - \frac{4 \int x \sqrt{x^{3} + 5 e^{x}}\, dx}{5} - \frac{3 \int \frac{x^{4}}{\sqrt{x^{3} + 5 e^{x}}}\, dx}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x)*x**2/(5*exp(x)+x**3)**(1/2),x)
[Out]
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Mathematica [A] time = 0.20717, 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.
[In] Integrate[(E^x*x^2)/Sqrt[5*E^x + x^3],x]
[Out]
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Maple [A] time = 0.029, size = 0, normalized size = 0. \[ \int{{{\rm e}^{x}}{x}^{2}{\frac{1}{\sqrt{5\,{{\rm e}^{x}}+{x}^{3}}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x)*x^2/(5*exp(x)+x^3)^(1/2),x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2} e^{x}}{\sqrt{x^{3} + 5 \, e^{x}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^x/sqrt(x^3 + 5*e^x),x, algorithm="maxima")
[Out]
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^x/sqrt(x^3 + 5*e^x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2} e^{x}}{\sqrt{x^{3} + 5 e^{x}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x)*x**2/(5*exp(x)+x**3)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2} e^{x}}{\sqrt{x^{3} + 5 \, e^{x}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^x/sqrt(x^3 + 5*e^x),x, algorithm="giac")
[Out]