Optimal. Leaf size=19 \[ \sqrt {\pi } \text {erfi}(x)-\frac {e^{x^2}}{x} \]
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Rubi [A] time = 0.02, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2214, 2204} \[ \sqrt {\pi } \text {Erfi}(x)-\frac {e^{x^2}}{x} \]
Antiderivative was successfully verified.
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Rule 2204
Rule 2214
Rubi steps
\begin {align*} \int \frac {e^{x^2}}{x^2} \, dx &=-\frac {e^{x^2}}{x}+2 \int e^{x^2} \, dx\\ &=-\frac {e^{x^2}}{x}+\sqrt {\pi } \text {erfi}(x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ \sqrt {\pi } \text {erfi}(x)-\frac {e^{x^2}}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 18, normalized size = 0.95 \[ \frac {\sqrt {\pi } x \operatorname {erfi}\relax (x) - e^{\left (x^{2}\right )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{\left (x^{2}\right )}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 0.89 \[ \sqrt {\pi }\, \erfi \relax (x )-\frac {{\mathrm e}^{x^{2}}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.15, size = 19, normalized size = 1.00 \[ -\frac {\sqrt {-x^{2}} \Gamma \left (-\frac {1}{2}, -x^{2}\right )}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.60, size = 21, normalized size = 1.11 \[ -\frac {{\mathrm {e}}^{x^2}}{x}+\sqrt {\pi }\,\mathrm {erfc}\left (x\,1{}\mathrm {i}\right )\,1{}\mathrm {i} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.47, size = 14, normalized size = 0.74 \[ \sqrt {\pi } \operatorname {erfi}{\relax (x )} - \frac {e^{x^{2}}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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