Optimal. Leaf size=19 \[ -\frac {e^{x^2}}{x}+\sqrt {\pi } \text {erfi}(x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, 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 = {2245, 2235}
\begin {gather*} \sqrt {\pi } \text {Erfi}(x)-\frac {e^{x^2}}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2235
Rule 2245
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*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 19, normalized size = 1.00 \begin {gather*} -\frac {e^{x^2}}{x}+\sqrt {\pi } \text {erfi}(x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 17, normalized size = 0.89
method | result | size |
default | \(-\frac {{\mathrm e}^{x^{2}}}{x}+\erfi \left (x \right ) \sqrt {\pi }\) | \(17\) |
risch | \(-\frac {{\mathrm e}^{x^{2}}}{x}+\erfi \left (x \right ) \sqrt {\pi }\) | \(17\) |
meijerg | \(\frac {i \left (\frac {2 i {\mathrm e}^{x^{2}}}{x}-2 i \erfi \left (x \right ) \sqrt {\pi }\right )}{2}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.31, size = 19, normalized size = 1.00 \begin {gather*} -\frac {\sqrt {-x^{2}} \Gamma \left (-\frac {1}{2}, -x^{2}\right )}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 18, normalized size = 0.95 \begin {gather*} \frac {\sqrt {\pi } x \operatorname {erfi}\left (x\right ) - e^{\left (x^{2}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.14, size = 14, normalized size = 0.74 \begin {gather*} \sqrt {\pi } \operatorname {erfi}{\left (x \right )} - \frac {e^{x^{2}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.60, size = 21, normalized size = 1.11 \begin {gather*} -\frac {{\mathrm {e}}^{x^2}}{x}+\sqrt {\pi }\,\mathrm {erfc}\left (x\,1{}\mathrm {i}\right )\,1{}\mathrm {i} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________