Optimal. Leaf size=23 \[ \sqrt {\pi } \text {erfi}(a+x)-\frac {e^{(a+x)^2}}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.05, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {2220, 2204} \[ \sqrt {\pi } \text {Erfi}(a+x)-\frac {e^{(a+x)^2}}{x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2204
Rule 2220
Rubi steps
\begin {align*} \int \left (\frac {e^{(a+x)^2}}{x^2}-\frac {2 a e^{(a+x)^2}}{x}\right ) \, dx &=-\left ((2 a) \int \frac {e^{(a+x)^2}}{x} \, dx\right )+\int \frac {e^{(a+x)^2}}{x^2} \, dx\\ &=-\frac {e^{(a+x)^2}}{x}+2 \int e^{(a+x)^2} \, dx\\ &=-\frac {e^{(a+x)^2}}{x}+\sqrt {\pi } \text {erfi}(a+x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.09, size = 23, normalized size = 1.00 \[ \sqrt {\pi } \text {erfi}(a+x)-\frac {e^{(a+x)^2}}{x} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 28, normalized size = 1.22 \[ \frac {\sqrt {\pi } x \operatorname {erfi}\left (a + x\right ) - e^{\left (a^{2} + 2 \, a x + x^{2}\right )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int -\frac {2 \, a e^{\left ({\left (a + x\right )}^{2}\right )}}{x} + \frac {e^{\left ({\left (a + x\right )}^{2}\right )}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [F] time = 0.17, size = 0, normalized size = 0.00 \[ \int -\frac {2 a \,{\mathrm e}^{\left (a +x \right )^{2}}}{x}+\frac {{\mathrm e}^{\left (a +x \right )^{2}}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int -\frac {2 \, a e^{\left ({\left (a + x\right )}^{2}\right )}}{x} + \frac {e^{\left ({\left (a + x\right )}^{2}\right )}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.41, size = 27, normalized size = 1.17 \[ \sqrt {\pi }\,\mathrm {erfi}\left (a+x\right )-\frac {{\mathrm {e}}^{a^2}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{2\,a\,x}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ - \left (\int \left (- \frac {e^{x^{2}} e^{2 a x}}{x^{2}}\right )\, dx + \int \frac {2 a e^{x^{2}} e^{2 a x}}{x}\, dx\right ) e^{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________