Optimal. Leaf size=29 \[ e^{7+x+\frac {1}{3} x \left (x-\left (\frac {3}{5}+x\right ) \log \left (e^{-e^x} x\right )\right )} \]
________________________________________________________________________________________
Rubi [F] time = 2.83, 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}{15} \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) \left (12+5 x+e^x \left (3 x+5 x^2\right )+(-3-10 x) \log \left (e^{-e^x} x\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{15} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) \left (12+5 x+e^x \left (3 x+5 x^2\right )+(-3-10 x) \log \left (e^{-e^x} x\right )\right ) \, dx\\ &=\frac {1}{15} \int \left (12 \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right )+5 \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x+\exp \left (x+\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x (3+5 x)-\exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) (3+10 x) \log \left (e^{-e^x} x\right )\right ) \, dx\\ &=\frac {1}{15} \int \exp \left (x+\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x (3+5 x) \, dx-\frac {1}{15} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) (3+10 x) \log \left (e^{-e^x} x\right ) \, dx+\frac {1}{3} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x \, dx+\frac {4}{5} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) \, dx\\ &=\frac {1}{15} \int \left (3 \exp \left (x+\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x+5 \exp \left (x+\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x^2\right ) \, dx-\frac {1}{15} \int \left (3 \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) \log \left (e^{-e^x} x\right )+10 \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x \log \left (e^{-e^x} x\right )\right ) \, dx+\frac {1}{3} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x \, dx+\frac {4}{5} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) \, dx\\ &=\frac {1}{5} \int \exp \left (x+\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x \, dx-\frac {1}{5} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) \log \left (e^{-e^x} x\right ) \, dx+\frac {1}{3} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x \, dx+\frac {1}{3} \int \exp \left (x+\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x^2 \, dx-\frac {2}{3} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) x \log \left (e^{-e^x} x\right ) \, dx+\frac {4}{5} \int \exp \left (\frac {1}{15} \left (105+15 x+5 x^2+\left (-3 x-5 x^2\right ) \log \left (e^{-e^x} x\right )\right )\right ) \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.95, size = 33, normalized size = 1.14 \begin {gather*} e^{7+x+\frac {x^2}{3}} \left (e^{-e^x} x\right )^{-\frac {1}{15} x (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.57, size = 28, normalized size = 0.97 \begin {gather*} e^{\left (\frac {1}{3} \, x^{2} - \frac {1}{15} \, {\left (5 \, x^{2} + 3 \, x\right )} \log \left (x e^{\left (-e^{x}\right )}\right ) + x + 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.26, size = 33, normalized size = 1.14 \begin {gather*} e^{\left (-\frac {1}{3} \, x^{2} \log \left (x e^{\left (-e^{x}\right )}\right ) + \frac {1}{3} \, x^{2} - \frac {1}{5} \, x \log \left (x e^{\left (-e^{x}\right )}\right ) + x + 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.14, size = 235, normalized size = 8.10
method | result | size |
risch | \(x^{-\frac {x^{2}}{3}} x^{-\frac {x}{5}} \left ({\mathrm e}^{{\mathrm e}^{x}}\right )^{\frac {x^{2}}{3}} \left ({\mathrm e}^{{\mathrm e}^{x}}\right )^{\frac {x}{5}} {\mathrm e}^{7+\frac {i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-{\mathrm e}^{x}}\right )^{3} x^{2}}{6}+\frac {i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-{\mathrm e}^{x}}\right )^{3} x}{10}-\frac {i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-{\mathrm e}^{x}}\right )^{2} \mathrm {csgn}\left (i x \right ) x^{2}}{6}-\frac {i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-{\mathrm e}^{x}}\right )^{2} \mathrm {csgn}\left (i x \right ) x}{10}-\frac {i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-{\mathrm e}^{x}}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{x}}\right ) x^{2}}{6}-\frac {i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-{\mathrm e}^{x}}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{x}}\right ) x}{10}+\frac {i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-{\mathrm e}^{x}}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{x}}\right ) x^{2}}{6}+\frac {i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-{\mathrm e}^{x}}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{x}}\right ) x}{10}+\frac {x^{2}}{3}+x}\) | \(235\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.45, size = 33, normalized size = 1.14 \begin {gather*} e^{\left (\frac {1}{3} \, x^{2} e^{x} - \frac {1}{3} \, x^{2} \log \relax (x) + \frac {1}{3} \, x^{2} + \frac {1}{5} \, x e^{x} - \frac {1}{5} \, x \log \relax (x) + x + 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.24, size = 38, normalized size = 1.31 \begin {gather*} \frac {{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^x}{5}}\,{\mathrm {e}}^7\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^x}{3}}\,{\mathrm {e}}^{\frac {x^2}{3}}\,{\mathrm {e}}^x}{x^{\frac {x^2}{3}+\frac {x}{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________