3.717 \(\int \frac{e^{x^2}}{x^2} \, dx\)

Optimal. Leaf size=19 \[ \sqrt{\pi } \text{Erfi}(x)-\frac{e^{x^2}}{x} \]

[Out]

-(E^x^2/x) + Sqrt[Pi]*Erfi[x]

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Rubi [A]  time = 0.0268408, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \sqrt{\pi } \text{Erfi}(x)-\frac{e^{x^2}}{x} \]

Antiderivative was successfully verified.

[In]  Int[E^x^2/x^2,x]

[Out]

-(E^x^2/x) + Sqrt[Pi]*Erfi[x]

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Rubi in Sympy [A]  time = 2.91421, size = 14, normalized size = 0.74 \[ \sqrt{\pi } \operatorname{erfi}{\left (x \right )} - \frac{e^{x^{2}}}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(pi)*erfi(x) - exp(x**2)/x

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Mathematica [A]  time = 0.00752248, size = 19, normalized size = 1. \[ \sqrt{\pi } \text{Erfi}(x)-\frac{e^{x^2}}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[E^x^2/x^2,x]

[Out]

-(E^x^2/x) + Sqrt[Pi]*Erfi[x]

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Maple [A]  time = 0.004, size = 17, normalized size = 0.9 \[ -{\frac{{{\rm e}^{{x}^{2}}}}{x}}+{\it erfi} \left ( x \right ) \sqrt{\pi } \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x^2)/x^2,x)

[Out]

-exp(x^2)/x+erfi(x)*Pi^(1/2)

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Maxima [A]  time = 0.808435, size = 26, normalized size = 1.37 \[ -\frac{\sqrt{-x^{2}} \Gamma \left (-\frac{1}{2}, -x^{2}\right )}{2 \, x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2*sqrt(-x^2)*gamma(-1/2, -x^2)/x

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Fricas [A]  time = 0.283472, size = 24, normalized size = 1.26 \[ \frac{\sqrt{\pi } x \operatorname{erfi}\left (x\right ) - e^{\left (x^{2}\right )}}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(sqrt(pi)*x*erfi(x) - e^(x^2))/x

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Sympy [A]  time = 1.08088, size = 14, normalized size = 0.74 \[ \sqrt{\pi } \operatorname{erfi}{\left (x \right )} - \frac{e^{x^{2}}}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x**2)/x**2,x)

[Out]

sqrt(pi)*erfi(x) - exp(x**2)/x

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left (x^{2}\right )}}{x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate(e^(x^2)/x^2, x)