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

Optimal. Leaf size=7 \[ e^{x^2} x \]

[Out]

E^x^2*x

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Rubi [A]  time = 0.0459435, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ e^{x^2} x \]

Antiderivative was successfully verified.

[In]  Int[E^x^2*(1 + 2*x^2),x]

[Out]

E^x^2*x

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Rubi in Sympy [A]  time = 2.78317, size = 5, normalized size = 0.71 \[ x e^{x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x*exp(x**2)

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Mathematica [A]  time = 0.00405578, size = 7, normalized size = 1. \[ e^{x^2} x \]

Antiderivative was successfully verified.

[In]  Integrate[E^x^2*(1 + 2*x^2),x]

[Out]

E^x^2*x

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Maple [A]  time = 0., size = 7, normalized size = 1. \[{{\rm e}^{{x}^{2}}}x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x^2)*(2*x^2+1),x)

[Out]

exp(x^2)*x

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Maxima [A]  time = 1.33247, size = 8, normalized size = 1.14 \[ x e^{\left (x^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x*e^(x^2)

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Fricas [A]  time = 0.209038, size = 8, normalized size = 1.14 \[ x e^{\left (x^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x*e^(x^2)

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Sympy [A]  time = 0.068189, size = 5, normalized size = 0.71 \[ x e^{x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x*exp(x**2)

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GIAC/XCAS [A]  time = 0.204917, size = 8, normalized size = 1.14 \[ x e^{\left (x^{2}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x*e^(x^2)