Optimal. Leaf size=26 \[ \frac {17}{2} e^{e^{x^2}-x}+5 e^{-2-x} x \]
________________________________________________________________________________________
Rubi [F] time = 0.34, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{2} e^{-2+e^{x^2}-2 x} \left (-17 e^{2+x}+e^{-e^{x^2}+x} (10-10 x)+34 e^{2+x+x^2} x\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int e^{-2+e^{x^2}-2 x} \left (-17 e^{2+x}+e^{-e^{x^2}+x} (10-10 x)+34 e^{2+x+x^2} x\right ) \, dx\\ &=\frac {1}{2} \int \left (-17 e^{e^{x^2}-x}-10 e^{-2-x} (-1+x)+34 e^{e^{x^2}-x+x^2} x\right ) \, dx\\ &=-\left (5 \int e^{-2-x} (-1+x) \, dx\right )-\frac {17}{2} \int e^{e^{x^2}-x} \, dx+17 \int e^{e^{x^2}-x+x^2} x \, dx\\ &=-5 e^{-2-x} (1-x)-5 \int e^{-2-x} \, dx-\frac {17}{2} \int e^{e^{x^2}-x} \, dx+17 \int e^{e^{x^2}-x+x^2} x \, dx\\ &=5 e^{-2-x}-5 e^{-2-x} (1-x)-\frac {17}{2} \int e^{e^{x^2}-x} \, dx+17 \int e^{e^{x^2}-x+x^2} x \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 26, normalized size = 1.00 \begin {gather*} \frac {1}{2} e^{-2-x} \left (17 e^{2+e^{x^2}}+10 x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.89, size = 37, normalized size = 1.42 \begin {gather*} \frac {1}{2} \, {\left (10 \, x e^{\left (2 \, x^{2}\right )} + 17 \, e^{\left (2 \, x^{2} + e^{\left (x^{2}\right )} + 2\right )}\right )} e^{\left (-2 \, x^{2} - x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 24, normalized size = 0.92 \begin {gather*} \frac {1}{2} \, {\left (10 \, x e^{\left (-x\right )} + 17 \, e^{\left (-x + e^{\left (x^{2}\right )} + 2\right )}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 22, normalized size = 0.85
method | result | size |
risch | \(5 x \,{\mathrm e}^{-x -2}+\frac {17 \,{\mathrm e}^{{\mathrm e}^{x^{2}}-x}}{2}\) | \(22\) |
norman | \(\left (5 \,{\mathrm e}^{-{\mathrm e}^{x^{2}}+x} x +\frac {17 \,{\mathrm e}^{2+x}}{2}\right ) {\mathrm e}^{-x -2} {\mathrm e}^{{\mathrm e}^{x^{2}}-x}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.40, size = 31, normalized size = 1.19 \begin {gather*} 5 \, {\left (x + 1\right )} e^{\left (-x - 2\right )} + \frac {17}{2} \, e^{\left (-x + e^{\left (x^{2}\right )}\right )} - 5 \, e^{\left (-x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.17, size = 21, normalized size = 0.81 \begin {gather*} \frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-2}\,\left (10\,x+17\,{\mathrm {e}}^2\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.41, size = 20, normalized size = 0.77 \begin {gather*} 5 x e^{- x - 2} + \frac {17 e^{- x + e^{x^{2}}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________