Optimal. Leaf size=34 \[ e^x-e^{x \left (x+\frac {(-x+\log (3))^2}{x^2}\right )}-x+(1-2 x) x \]
________________________________________________________________________________________
Rubi [A] time = 0.27, antiderivative size = 28, normalized size of antiderivative = 0.82, number of steps used = 4, number of rules used = 3, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.055, Rules used = {14, 2194, 6706} \begin {gather*} -2 x^2-\frac {1}{9} e^{x^2+x+\frac {\log ^2(3)}{x}}+e^x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 2194
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^x-4 x-\frac {e^{x+x^2+\frac {\log ^2(3)}{x}} \left (x^2+2 x^3-\log ^2(3)\right )}{9 x^2}\right ) \, dx\\ &=-2 x^2-\frac {1}{9} \int \frac {e^{x+x^2+\frac {\log ^2(3)}{x}} \left (x^2+2 x^3-\log ^2(3)\right )}{x^2} \, dx+\int e^x \, dx\\ &=e^x-\frac {1}{9} e^{x+x^2+\frac {\log ^2(3)}{x}}-2 x^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.13, size = 28, normalized size = 0.82 \begin {gather*} e^x-\frac {1}{9} e^{x+x^2+\frac {\log ^2(3)}{x}}-2 x^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.67, size = 31, normalized size = 0.91 \begin {gather*} -2 \, x^{2} + e^{x} - e^{\left (\frac {x^{3} + x^{2} - 2 \, x \log \relax (3) + \log \relax (3)^{2}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.41, size = 26, normalized size = 0.76 \begin {gather*} -2 \, x^{2} + e^{x} - \frac {1}{9} \, e^{\left (\frac {x^{3} + x^{2} + \log \relax (3)^{2}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 27, normalized size = 0.79
method | result | size |
risch | \(-2 x^{2}+{\mathrm e}^{x}-\frac {{\mathrm e}^{\frac {x^{3}+\ln \relax (3)^{2}+x^{2}}{x}}}{9}\) | \(27\) |
norman | \(\frac {{\mathrm e}^{x} x -2 x^{3}-x \,{\mathrm e}^{\frac {\ln \relax (3)^{2}-2 x \ln \relax (3)+x^{3}+x^{2}}{x}}}{x}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.87, size = 24, normalized size = 0.71 \begin {gather*} -2 \, x^{2} - \frac {1}{9} \, e^{\left (x^{2} + x + \frac {\log \relax (3)^{2}}{x}\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.38, size = 25, normalized size = 0.74 \begin {gather*} {\mathrm {e}}^x-2\,x^2-\frac {{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{\frac {{\ln \relax (3)}^2}{x}}\,{\mathrm {e}}^x}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.21, size = 29, normalized size = 0.85 \begin {gather*} - 2 x^{2} + e^{x} - e^{\frac {x^{3} + x^{2} - 2 x \log {\relax (3 )} + \log {\relax (3 )}^{2}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________