3.538 \(\int e^{x^2} x \left (1+x^2\right ) \, dx\)

Optimal. Leaf size=12 \[ \frac{1}{2} e^{x^2} x^2 \]

[Out]

(E^x^2*x^2)/2

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Rubi [A]  time = 0.0718183, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{1}{2} e^{x^2} x^2 \]

Antiderivative was successfully verified.

[In]  Int[E^x^2*x*(1 + x^2),x]

[Out]

(E^x^2*x^2)/2

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Rubi in Sympy [A]  time = 3.65258, size = 8, normalized size = 0.67 \[ \frac{x^{2} e^{x^{2}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**2*exp(x**2)/2

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Mathematica [A]  time = 0.00432201, size = 12, normalized size = 1. \[ \frac{1}{2} e^{x^2} x^2 \]

Antiderivative was successfully verified.

[In]  Integrate[E^x^2*x*(1 + x^2),x]

[Out]

(E^x^2*x^2)/2

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Maple [A]  time = 0.005, size = 10, normalized size = 0.8 \[{\frac{{{\rm e}^{{x}^{2}}}{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x^2)*x*(x^2+1),x)

[Out]

1/2*exp(x^2)*x^2

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Maxima [A]  time = 1.40663, size = 24, normalized size = 2. \[ \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} + \frac{1}{2} \, e^{\left (x^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(x^2 - 1)*e^(x^2) + 1/2*e^(x^2)

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Fricas [A]  time = 0.215933, size = 12, normalized size = 1. \[ \frac{1}{2} \, x^{2} e^{\left (x^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*x^2*e^(x^2)

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Sympy [A]  time = 0.072963, size = 8, normalized size = 0.67 \[ \frac{x^{2} e^{x^{2}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**2*exp(x**2)/2

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GIAC/XCAS [A]  time = 0.212216, size = 24, normalized size = 2. \[ \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} + \frac{1}{2} \, e^{\left (x^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(x^2 - 1)*e^(x^2) + 1/2*e^(x^2)