Optimal. Leaf size=21 \[ \frac {-4+\frac {3}{e^5}+x}{2-11 e^{-x}+x} \]
________________________________________________________________________________________
Rubi [F] time = 1.55, 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 {e^{2 x} \left (-3+6 e^5+e^{-x} \left (3+e^5 (-3+x)\right )\right )+e^x \left (-36+e^5 (36-12 x)\right )}{144 e^5+e^x \left (-24 e^{5-x}+e^5 (-48-24 x)\right )+e^{2 x} \left (e^{5-2 x}+e^{5-x} (4+2 x)+e^5 \left (4+4 x+x^2\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-5+x} \left (-33-3 e^x \left (1-2 e^5\right )-11 e^5 (-3+x)\right )}{\left (11-e^x (2+x)\right )^2} \, dx\\ &=\int \left (\frac {3 e^{-5+x} \left (-1+2 e^5\right )}{(2+x) \left (-11+2 e^x+e^x x\right )}+\frac {11 e^{-5+x} \left (-3 \left (3-4 e^5\right )-\left (3-e^5\right ) x-e^5 x^2\right )}{(2+x) \left (11-2 e^x-e^x x\right )^2}\right ) \, dx\\ &=11 \int \frac {e^{-5+x} \left (-3 \left (3-4 e^5\right )-\left (3-e^5\right ) x-e^5 x^2\right )}{(2+x) \left (11-2 e^x-e^x x\right )^2} \, dx-\left (3 \left (1-2 e^5\right )\right ) \int \frac {e^{-5+x}}{(2+x) \left (-11+2 e^x+e^x x\right )} \, dx\\ &=11 \int \left (\frac {3 e^{-5+x} \left (-1+e^5\right )}{\left (-11+2 e^x+e^x x\right )^2}-\frac {e^x x}{\left (-11+2 e^x+e^x x\right )^2}+\frac {3 e^{-5+x} \left (-1+2 e^5\right )}{(2+x) \left (-11+2 e^x+e^x x\right )^2}\right ) \, dx-\left (3 \left (1-2 e^5\right )\right ) \int \frac {e^{-5+x}}{(2+x) \left (-11+2 e^x+e^x x\right )} \, dx\\ &=-\left (11 \int \frac {e^x x}{\left (-11+2 e^x+e^x x\right )^2} \, dx\right )-\left (3 \left (1-2 e^5\right )\right ) \int \frac {e^{-5+x}}{(2+x) \left (-11+2 e^x+e^x x\right )} \, dx-\left (33 \left (1-2 e^5\right )\right ) \int \frac {e^{-5+x}}{(2+x) \left (-11+2 e^x+e^x x\right )^2} \, dx-\left (33 \left (1-e^5\right )\right ) \int \frac {e^{-5+x}}{\left (-11+2 e^x+e^x x\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 1.03, size = 33, normalized size = 1.57 \begin {gather*} \frac {11 e^5+3 e^x-6 e^{5+x}}{e^5 \left (-11+e^x (2+x)\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.63, size = 32, normalized size = 1.52 \begin {gather*} -\frac {3 \, {\left (2 \, e^{5} - 1\right )} e^{x} - 11 \, e^{5}}{{\left (x + 2\right )} e^{\left (x + 5\right )} - 11 \, e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.23, size = 35, normalized size = 1.67 \begin {gather*} \frac {11 \, e^{5} - 6 \, e^{\left (x + 5\right )} + 3 \, e^{x}}{x e^{\left (x + 5\right )} - 11 \, e^{5} + 2 \, e^{\left (x + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.18, size = 41, normalized size = 1.95
method | result | size |
norman | \(\frac {\left (11 \,{\mathrm e}^{3 x}-3 \left (2 \,{\mathrm e}^{5}-1\right ) {\mathrm e}^{-5} {\mathrm e}^{4 x}\right ) {\mathrm e}^{-3 x}}{{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}-11}\) | \(41\) |
risch | \(-\frac {6 \,{\mathrm e}^{-5} {\mathrm e}^{5}}{2+x}+\frac {3 \,{\mathrm e}^{-5}}{2+x}+\frac {11 \left (x \,{\mathrm e}^{5}-4 \,{\mathrm e}^{5}+3\right ) {\mathrm e}^{-5}}{\left (2+x \right ) \left ({\mathrm e}^{x} x +2 \,{\mathrm e}^{x}-11\right )}\) | \(53\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.42, size = 36, normalized size = 1.71 \begin {gather*} -\frac {3 \, {\left (2 \, e^{5} - 1\right )} e^{x} - 11 \, e^{5}}{{\left (x e^{5} + 2 \, e^{5}\right )} e^{x} - 11 \, e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.59, size = 27, normalized size = 1.29 \begin {gather*} \frac {{\mathrm {e}}^{x-5}\,\left (x\,{\mathrm {e}}^5-4\,{\mathrm {e}}^5+3\right )}{2\,{\mathrm {e}}^x+x\,{\mathrm {e}}^x-11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 29, normalized size = 1.38 \begin {gather*} \frac {- x e^{5} - 3 + 4 e^{5}}{- x e^{5} - 2 e^{5} + 11 e^{5} e^{- x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________