3.653 \(\int e^{1+x^3} x^2 \, dx\)

Optimal. Leaf size=11 \[ \frac{e^{x^3+1}}{3} \]

[Out]

E^(1 + x^3)/3

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Rubi [A]  time = 0.024096, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{e^{x^3+1}}{3} \]

Antiderivative was successfully verified.

[In]  Int[E^(1 + x^3)*x^2,x]

[Out]

E^(1 + x^3)/3

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Rubi in Sympy [A]  time = 2.85131, size = 7, normalized size = 0.64 \[ \frac{e^{x^{3} + 1}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x**3+1)*x**2,x)

[Out]

exp(x**3 + 1)/3

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Mathematica [A]  time = 0.00320751, size = 11, normalized size = 1. \[ \frac{e^{x^3+1}}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[E^(1 + x^3)*x^2,x]

[Out]

E^(1 + x^3)/3

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Maple [A]  time = 0.003, size = 9, normalized size = 0.8 \[{\frac{{{\rm e}^{{x}^{3}+1}}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x^3+1)*x^2,x)

[Out]

1/3*exp(x^3+1)

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Maxima [A]  time = 0.831565, size = 11, normalized size = 1. \[ \frac{1}{3} \, e^{\left (x^{3} + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2*e^(x^3 + 1),x, algorithm="maxima")

[Out]

1/3*e^(x^3 + 1)

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Fricas [A]  time = 0.262835, size = 11, normalized size = 1. \[ \frac{1}{3} \, e^{\left (x^{3} + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2*e^(x^3 + 1),x, algorithm="fricas")

[Out]

1/3*e^(x^3 + 1)

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Sympy [A]  time = 0.060588, size = 7, normalized size = 0.64 \[ \frac{e^{x^{3} + 1}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x**3+1)*x**2,x)

[Out]

exp(x**3 + 1)/3

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GIAC/XCAS [A]  time = 0.226586, size = 11, normalized size = 1. \[ \frac{1}{3} \, e^{\left (x^{3} + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2*e^(x^3 + 1),x, algorithm="giac")

[Out]

1/3*e^(x^3 + 1)