3.68 \(\int e^{x^3} x^2 \, dx\)

Optimal. Leaf size=9 \[ \frac{e^{x^3}}{3} \]

[Out]

E^x^3/3

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Rubi [A]  time = 0.0200876, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{e^{x^3}}{3} \]

Antiderivative was successfully verified.

[In]  Int[E^x^3*x^2,x]

[Out]

E^x^3/3

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Rubi in Sympy [A]  time = 1.3841, size = 5, normalized size = 0.56 \[ \frac{e^{x^{3}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x**3)*x**2,x)

[Out]

exp(x**3)/3

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Mathematica [A]  time = 0.00274353, size = 9, normalized size = 1. \[ \frac{e^{x^3}}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[E^x^3*x^2,x]

[Out]

E^x^3/3

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Maple [A]  time = 0.004, size = 7, normalized size = 0.8 \[{\frac{{{\rm e}^{{x}^{3}}}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x^3)*x^2,x)

[Out]

1/3*exp(x^3)

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Maxima [A]  time = 1.54756, size = 8, normalized size = 0.89 \[ \frac{1}{3} \, e^{\left (x^{3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2*e^(x^3),x, algorithm="maxima")

[Out]

1/3*e^(x^3)

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Fricas [A]  time = 0.208143, size = 8, normalized size = 0.89 \[ \frac{1}{3} \, e^{\left (x^{3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2*e^(x^3),x, algorithm="fricas")

[Out]

1/3*e^(x^3)

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Sympy [A]  time = 0.062543, size = 5, normalized size = 0.56 \[ \frac{e^{x^{3}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x**3)*x**2,x)

[Out]

exp(x**3)/3

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GIAC/XCAS [A]  time = 0.221627, size = 8, normalized size = 0.89 \[ \frac{1}{3} \, e^{\left (x^{3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2*e^(x^3),x, algorithm="giac")

[Out]

1/3*e^(x^3)