Optimal. Leaf size=19 \[ e^{3+3^{\frac {1}{25+x}}-e^x-2 x} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.85, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 65, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {27, 6838}
\begin {gather*} e^{-2 x-e^x+3^{\frac {1}{x+25}}+3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{3+3^{\frac {1}{25+x}}-e^x-2 x} \left (-1250-100 x-2 x^2+e^x \left (-625-50 x-x^2\right )-3^{\frac {1}{25+x}} \log (3)\right )}{(25+x)^2} \, dx\\ &=e^{3+3^{\frac {1}{25+x}}-e^x-2 x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.71, size = 19, normalized size = 1.00 \begin {gather*} e^{3+3^{\frac {1}{25+x}}-e^x-2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.44, size = 18, normalized size = 0.95
method | result | size |
risch | \({\mathrm e}^{3^{\frac {1}{x +25}}-{\mathrm e}^{x}+3-2 x}\) | \(18\) |
norman | \(\frac {x \,{\mathrm e}^{{\mathrm e}^{\frac {\ln \left (3\right )}{x +25}}-{\mathrm e}^{x}+3-2 x}+25 \,{\mathrm e}^{{\mathrm e}^{\frac {\ln \left (3\right )}{x +25}}-{\mathrm e}^{x}+3-2 x}}{x +25}\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.54, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (3^{\left (\frac {1}{x + 25}\right )} - 2 \, x - e^{x} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (3^{\left (\frac {1}{x + 25}\right )} - 2 \, x - e^{x} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.38, size = 17, normalized size = 0.89 \begin {gather*} e^{- 2 x - e^{x} + e^{\frac {\log {\left (3 \right )}}{x + 25}} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (3^{\left (\frac {1}{x + 25}\right )} - 2 \, x - e^{x} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.22, size = 20, normalized size = 1.05 \begin {gather*} {\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\mathrm {e}}^{3^{\frac {1}{x+25}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________