Optimal. Leaf size=19 \[ 2 e^{x^2} x-\frac{e^{x^2}}{x} \]
[Out]
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Rubi [A] time = 0.153611, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ 2 e^{x^2} x-\frac{e^{x^2}}{x} \]
Antiderivative was successfully verified.
[In] Int[(E^x^2*(1 + 4*x^4))/x^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (4 x^{4} + 1\right ) e^{x^{2}}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x**2)*(4*x**4+1)/x**2,x)
[Out]
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Mathematica [A] time = 0.00785526, size = 15, normalized size = 0.79 \[ e^{x^2} \left (2 x-\frac{1}{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(E^x^2*(1 + 4*x^4))/x^2,x]
[Out]
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Maple [A] time = 0.007, size = 16, normalized size = 0.8 \[{\frac{{{\rm e}^{{x}^{2}}} \left ( 2\,{x}^{2}-1 \right ) }{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x^2)*(4*x^4+1)/x^2,x)
[Out]
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Maxima [A] time = 0.839024, size = 49, normalized size = 2.58 \[ 2 \, x e^{\left (x^{2}\right )} + i \, \sqrt{\pi } \operatorname{erf}\left (i \, x\right ) - \frac{\sqrt{-x^{2}} \Gamma \left (-\frac{1}{2}, -x^{2}\right )}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^4 + 1)*e^(x^2)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.246013, size = 20, normalized size = 1.05 \[ \frac{{\left (2 \, x^{2} - 1\right )} e^{\left (x^{2}\right )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^4 + 1)*e^(x^2)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.070949, size = 12, normalized size = 0.63 \[ \frac{\left (2 x^{2} - 1\right ) e^{x^{2}}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x**2)*(4*x**4+1)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.219867, size = 27, normalized size = 1.42 \[ \frac{2 \, x^{2} e^{\left (x^{2}\right )} - e^{\left (x^{2}\right )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^4 + 1)*e^(x^2)/x^2,x, algorithm="giac")
[Out]