3.17 \(\int e^x x^2 \, dx\)

Optimal. Leaf size=19 \[ e^x x^2-2 e^x x+2 e^x \]

[Out]

2*E^x - 2*E^x*x + E^x*x^2

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Rubi [A]  time = 0.0227575, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ e^x x^2-2 e^x x+2 e^x \]

Antiderivative was successfully verified.

[In]  Int[E^x*x^2,x]

[Out]

2*E^x - 2*E^x*x + E^x*x^2

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Rubi in Sympy [A]  time = 1.77955, size = 17, normalized size = 0.89 \[ x^{2} e^{x} - 2 x e^{x} + 2 e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x)*x**2,x)

[Out]

x**2*exp(x) - 2*x*exp(x) + 2*exp(x)

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Mathematica [A]  time = 0.00237395, size = 12, normalized size = 0.63 \[ e^x \left (x^2-2 x+2\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[E^x*x^2,x]

[Out]

E^x*(2 - 2*x + x^2)

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Maple [A]  time = 0., size = 12, normalized size = 0.6 \[ \left ({x}^{2}-2\,x+2 \right ){{\rm e}^{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x)*x^2,x)

[Out]

(x^2-2*x+2)*exp(x)

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Maxima [A]  time = 1.33839, size = 15, normalized size = 0.79 \[{\left (x^{2} - 2 \, x + 2\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(x^2 - 2*x + 2)*e^x

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Fricas [A]  time = 0.200032, size = 15, normalized size = 0.79 \[{\left (x^{2} - 2 \, x + 2\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(x^2 - 2*x + 2)*e^x

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Sympy [A]  time = 0.065619, size = 10, normalized size = 0.53 \[ \left (x^{2} - 2 x + 2\right ) e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x)*x**2,x)

[Out]

(x**2 - 2*x + 2)*exp(x)

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GIAC/XCAS [A]  time = 0.199207, size = 15, normalized size = 0.79 \[{\left (x^{2} - 2 \, x + 2\right )} e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(x^2 - 2*x + 2)*e^x