Optimal. Leaf size=26 \[ \log \left (\frac {60 e^{-e^2+2 x \left (-e^{x^2}+x\right )}}{x}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.05, antiderivative size = 18, normalized size of antiderivative = 0.69, number of steps used = 9, number of rules used = 4, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {14, 2226, 2204, 2212} \begin {gather*} 2 x^2-2 e^{x^2} x-\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 2204
Rule 2212
Rule 2226
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 e^{x^2} \left (1+2 x^2\right )+\frac {-1+4 x^2}{x}\right ) \, dx\\ &=-\left (2 \int e^{x^2} \left (1+2 x^2\right ) \, dx\right )+\int \frac {-1+4 x^2}{x} \, dx\\ &=-\left (2 \int \left (e^{x^2}+2 e^{x^2} x^2\right ) \, dx\right )+\int \left (-\frac {1}{x}+4 x\right ) \, dx\\ &=2 x^2-\log (x)-2 \int e^{x^2} \, dx-4 \int e^{x^2} x^2 \, dx\\ &=-2 e^{x^2} x+2 x^2-\sqrt {\pi } \text {erfi}(x)-\log (x)+2 \int e^{x^2} \, dx\\ &=-2 e^{x^2} x+2 x^2-\log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 18, normalized size = 0.69 \begin {gather*} -2 e^{x^2} x+2 x^2-\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.55, size = 17, normalized size = 0.65 \begin {gather*} 2 \, x^{2} - 2 \, x e^{\left (x^{2}\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.14, size = 17, normalized size = 0.65 \begin {gather*} 2 \, x^{2} - 2 \, x e^{\left (x^{2}\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 18, normalized size = 0.69
method | result | size |
default | \(2 x^{2}-\ln \relax (x )-2 \,{\mathrm e}^{x^{2}} x\) | \(18\) |
norman | \(2 x^{2}-\ln \relax (x )-2 \,{\mathrm e}^{x^{2}} x\) | \(18\) |
risch | \(2 x^{2}-\ln \relax (x )-2 \,{\mathrm e}^{x^{2}} x\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 17, normalized size = 0.65 \begin {gather*} 2 \, x^{2} - 2 \, x e^{\left (x^{2}\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 17, normalized size = 0.65 \begin {gather*} 2\,x^2-2\,x\,{\mathrm {e}}^{x^2}-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 15, normalized size = 0.58 \begin {gather*} 2 x^{2} - 2 x e^{x^{2}} - \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________