Optimal. Leaf size=24 \[ e^{\frac {x+\log (4)}{5-e^{\frac {1}{e^{26}}-e^2}}} \]
________________________________________________________________________________________
Rubi [B] time = 0.07, antiderivative size = 50, normalized size of antiderivative = 2.08, number of steps used = 2, number of rules used = 2, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {12, 2203} \begin {gather*} 4^{-\frac {e^{e^2}}{e^{\frac {1}{e^{26}}}-5 e^{e^2}}} e^{-\frac {e^{e^2} x}{e^{\frac {1}{e^{26}}}-5 e^{e^2}}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2203
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {\int \exp \left (e^2+\frac {e^{e^2} (x+\log (4))}{-e^{\frac {1}{e^{26}}}+5 e^{e^2}}\right ) \, dx}{e^{\frac {1}{e^{26}}}-5 e^{e^2}}\\ &=4^{-\frac {e^{e^2}}{e^{\frac {1}{e^{26}}}-5 e^{e^2}}} e^{-\frac {e^{e^2} x}{e^{\frac {1}{e^{26}}}-5 e^{e^2}}}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] time = 0.09, size = 82, normalized size = 3.42 \begin {gather*} -\frac {e^{-\frac {e^{e^2} x}{e^{\frac {1}{e^{26}}}-5 e^{e^2}}-\frac {e^{e^2} \log (4)}{e^{\frac {1}{e^{26}}}-5 e^{e^2}}} \left (e^{\frac {1}{e^{26}}}-5 e^{e^2}\right )}{-e^{\frac {1}{e^{26}}}+5 e^{e^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.55, size = 42, normalized size = 1.75 \begin {gather*} e^{\left (\frac {{\left (x + 5 \, e^{2} + 2 \, \log \relax (2)\right )} e^{\left (e^{2}\right )} - e^{\left (e^{\left (-26\right )} + 2\right )}}{5 \, e^{\left (e^{2}\right )} - e^{\left (e^{\left (-26\right )}\right )}} - e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.23, size = 24, normalized size = 1.00 \begin {gather*} e^{\left (\frac {{\left (x + 2 \, \log \relax (2)\right )} e^{\left (e^{2}\right )}}{5 \, e^{\left (e^{2}\right )} - e^{\left (e^{\left (-26\right )}\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 24, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{-\frac {\left (x +2 \ln \relax (2)\right ) {\mathrm e}^{{\mathrm e}^{2}}}{-5 \,{\mathrm e}^{{\mathrm e}^{2}}+{\mathrm e}^{{\mathrm e}^{-26}}}}\) | \(24\) |
gosper | \({\mathrm e}^{\frac {\left (x +2 \ln \relax (2)\right ) {\mathrm e}^{{\mathrm e}^{2}}}{5 \,{\mathrm e}^{{\mathrm e}^{2}}-{\mathrm e}^{{\mathrm e}^{-26}}}}\) | \(27\) |
derivativedivides | \({\mathrm e}^{\frac {\left (x +2 \ln \relax (2)\right ) {\mathrm e}^{{\mathrm e}^{2}}}{5 \,{\mathrm e}^{{\mathrm e}^{2}}-{\mathrm e}^{{\mathrm e}^{-26}}}}\) | \(27\) |
default | \({\mathrm e}^{\frac {\left (x +2 \ln \relax (2)\right ) {\mathrm e}^{{\mathrm e}^{2}}}{5 \,{\mathrm e}^{{\mathrm e}^{2}}-{\mathrm e}^{{\mathrm e}^{-26}}}}\) | \(27\) |
norman | \({\mathrm e}^{\frac {\left (x +2 \ln \relax (2)\right ) {\mathrm e}^{{\mathrm e}^{2}}}{5 \,{\mathrm e}^{{\mathrm e}^{2}}-{\mathrm e}^{{\mathrm e}^{-26}}}}\) | \(27\) |
meijerg | \(-{\mathrm e}^{\frac {2 \,{\mathrm e}^{{\mathrm e}^{2}} \ln \relax (2)}{5 \,{\mathrm e}^{{\mathrm e}^{2}}-{\mathrm e}^{{\mathrm e}^{-26}}}} \left (1-{\mathrm e}^{\frac {x \,{\mathrm e}^{{\mathrm e}^{2}}}{5 \,{\mathrm e}^{{\mathrm e}^{2}}-{\mathrm e}^{{\mathrm e}^{-26}}}}\right )\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 24, normalized size = 1.00 \begin {gather*} e^{\left (\frac {{\left (x + 2 \, \log \relax (2)\right )} e^{\left (e^{2}\right )}}{5 \, e^{\left (e^{2}\right )} - e^{\left (e^{\left (-26\right )}\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 24, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (x+2\,\ln \relax (2)\right )}{5\,{\mathrm {e}}^{{\mathrm {e}}^2}-{\mathrm {e}}^{{\mathrm {e}}^{-26}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 26, normalized size = 1.08 \begin {gather*} e^{\frac {\left (x + 2 \log {\relax (2 )}\right ) e^{e^{2}}}{- e^{e^{-26}} + 5 e^{e^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________