Optimal. Leaf size=19 \[ 2 e^{x^2} x-\frac{e^{x^2}}{x} \]
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Rubi [A] time = 0.100237, 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, Rules used = {6742, 2214, 2204, 2212} \[ 2 e^{x^2} x-\frac{e^{x^2}}{x} \]
Antiderivative was successfully verified.
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Rule 6742
Rule 2214
Rule 2204
Rule 2212
Rubi steps
\begin{align*} \int \frac{e^{x^2} \left (1+4 x^4\right )}{x^2} \, dx &=\int \left (\frac{e^{x^2}}{x^2}+4 e^{x^2} x^2\right ) \, dx\\ &=4 \int e^{x^2} x^2 \, dx+\int \frac{e^{x^2}}{x^2} \, dx\\ &=-\frac{e^{x^2}}{x}+2 e^{x^2} x\\ \end{align*}
Mathematica [A] time = 0.0137588, size = 16, normalized size = 0.84 \[ \frac{e^{x^2} \left (2 x^2-1\right )}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.019, size = 16, normalized size = 0.8 \begin{align*}{\frac{{{\rm e}^{{x}^{2}}} \left ( 2\,{x}^{2}-1 \right ) }{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] time = 1.05857, size = 49, normalized size = 2.58 \begin{align*} 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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.854392, size = 31, normalized size = 1.63 \begin{align*} \frac{{\left (2 \, x^{2} - 1\right )} e^{\left (x^{2}\right )}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.08812, size = 12, normalized size = 0.63 \begin{align*} \frac{\left (2 x^{2} - 1\right ) e^{x^{2}}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.24531, size = 27, normalized size = 1.42 \begin{align*} \frac{2 \, x^{2} e^{\left (x^{2}\right )} - e^{\left (x^{2}\right )}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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