Optimal. Leaf size=22 \[ e^{e^{-\frac {4 e^{25+e^x+x} (-1+x)}{x}} x} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 15.99, 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 \exp \left (e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \left (1+\frac {e^{25+e^x+x} \left (-4+4 x-4 x^2+e^x \left (4 x-4 x^2\right )\right )}{x}\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\exp \left (e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right )-\frac {4 \exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \left (1-x-e^x x+x^2+e^x x^2\right )}{x}\right ) \, dx\\ &=-\left (4 \int \frac {\exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \left (1-x-e^x x+x^2+e^x x^2\right )}{x} \, dx\right )+\int \exp \left (e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \, dx\\ &=-\left (4 \int \left (\exp \left (25+e^x+2 x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) (-1+x)+\frac {\exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \left (1-x+x^2\right )}{x}\right ) \, dx\right )+\int \exp \left (e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \, dx\\ &=-\left (4 \int \exp \left (25+e^x+2 x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) (-1+x) \, dx\right )-4 \int \frac {\exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \left (1-x+x^2\right )}{x} \, dx+\int \exp \left (e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \, dx\\ &=-\left (4 \int \left (-\exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right )+\frac {\exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right )}{x}+\exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) x\right ) \, dx\right )-4 \int \left (-\exp \left (25+e^x+2 x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right )+\exp \left (25+e^x+2 x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) x\right ) \, dx+\int \exp \left (e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \, dx\\ &=4 \int \exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \, dx+4 \int \exp \left (25+e^x+2 x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \, dx-4 \int \frac {\exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right )}{x} \, dx-4 \int \exp \left (25+e^x+x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) x \, dx-4 \int \exp \left (25+e^x+2 x+e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) x \, dx+\int \exp \left (e^{-\frac {e^{25+e^x+x} (-4+4 x)}{x}} x-\frac {e^{25+e^x+x} (-4+4 x)}{x}\right ) \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 2.21, size = 22, normalized size = 1.00 \begin {gather*} e^{e^{-\frac {4 e^{25+e^x+x} (-1+x)}{x}} x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.40, size = 19, normalized size = 0.86
method | result | size |
risch | \({\mathrm e}^{x \,{\mathrm e}^{-\frac {4 \left (x -1\right ) {\mathrm e}^{25+{\mathrm e}^{x}+x}}{x}}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.54, size = 24, normalized size = 1.09 \begin {gather*} e^{\left (x e^{\left (\frac {4 \, e^{\left (x + e^{x} + 25\right )}}{x} - 4 \, e^{\left (x + e^{x} + 25\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.43, size = 21, normalized size = 0.95 \begin {gather*} e^{\left (x e^{\left (-4 \, {\left (x - 1\right )} e^{\left (x + e^{x} + \log \left (\frac {e^{25}}{x}\right )\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 25.54, size = 20, normalized size = 0.91 \begin {gather*} e^{x e^{- \frac {\left (4 x - 4\right ) e^{25} e^{x + e^{x}}}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 8.11, size = 26, normalized size = 1.18 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^x}{x}}\,{\mathrm {e}}^{-4\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________