Optimal. Leaf size=28 \[ \frac{2}{3} e^{x^{3/2}} x^{3/2}-\frac{2 e^{x^{3/2}}}{3} \]
[Out]
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Rubi [A] time = 0.0630159, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ \frac{2}{3} e^{x^{3/2}} x^{3/2}-\frac{2 e^{x^{3/2}}}{3} \]
Antiderivative was successfully verified.
[In] Int[E^x^(3/2)*x^2,x]
[Out]
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Rubi in Sympy [A] time = 6.50796, size = 24, normalized size = 0.86 \[ \frac{2 x^{\frac{3}{2}} e^{x^{\frac{3}{2}}}}{3} - \frac{2 e^{x^{\frac{3}{2}}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x**(3/2))*x**2,x)
[Out]
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Mathematica [A] time = 0.0049831, size = 18, normalized size = 0.64 \[ \frac{2}{3} e^{x^{3/2}} \left (x^{3/2}-1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^x^(3/2)*x^2,x]
[Out]
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Maple [A] time = 0.001, size = 17, normalized size = 0.6 \[ -{\frac{2}{3}{{\rm e}^{{x}^{{\frac{3}{2}}}}}}+{\frac{2}{3}{{\rm e}^{{x}^{{\frac{3}{2}}}}}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x^(3/2))*x^2,x)
[Out]
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Maxima [A] time = 0.775684, size = 15, normalized size = 0.54 \[ \frac{2}{3} \,{\left (x^{\frac{3}{2}} - 1\right )} e^{\left (x^{\frac{3}{2}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(x^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.245369, size = 15, normalized size = 0.54 \[ \frac{2}{3} \,{\left (x^{\frac{3}{2}} - 1\right )} e^{\left (x^{\frac{3}{2}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(x^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.78464, size = 24, normalized size = 0.86 \[ \frac{2 x^{\frac{3}{2}} e^{x^{\frac{3}{2}}}}{3} - \frac{2 e^{x^{\frac{3}{2}}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x**(3/2))*x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.238286, size = 18, normalized size = 0.64 \[ \frac{2}{3} \,{\left (x^{\frac{3}{2}} - 1\right )} e^{\left (x^{\frac{3}{2}}\right )} + \frac{2}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(x^(3/2)),x, algorithm="giac")
[Out]