Optimal. Leaf size=25 \[ e^{e^{-1-x} x}-x-\log \left (3 e^{8 x}\right ) \]
________________________________________________________________________________________
Rubi [F] time = 0.33, 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 e^{-1-x} \left (-9 e^{1+x}+e^{e^{-1-x} x} (1-x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-9-e^{-1+\left (-1+e^{-1-x}\right ) x} (-1+x)\right ) \, dx\\ &=-9 x-\int e^{-1+\left (-1+e^{-1-x}\right ) x} (-1+x) \, dx\\ &=-9 x-\int \left (-e^{-1+\left (-1+e^{-1-x}\right ) x}+e^{-1+\left (-1+e^{-1-x}\right ) x} x\right ) \, dx\\ &=-9 x+\int e^{-1+\left (-1+e^{-1-x}\right ) x} \, dx-\int e^{-1+\left (-1+e^{-1-x}\right ) x} x \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.14, size = 15, normalized size = 0.60 \begin {gather*} e^{e^{-1-x} x}-9 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 13, normalized size = 0.52 \begin {gather*} -9 \, x + e^{\left (x e^{\left (-x - 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 27, normalized size = 1.08 \begin {gather*} -{\left (9 \, x e^{\left (-x\right )} - e^{\left (x e^{\left (-x - 1\right )} - x\right )}\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 14, normalized size = 0.56
method | result | size |
risch | \(-9 x +{\mathrm e}^{x \,{\mathrm e}^{-x -1}}\) | \(14\) |
norman | \(\left ({\mathrm e}^{x +1} {\mathrm e}^{x \,{\mathrm e}^{-x -1}}-9 x \,{\mathrm e}^{x +1}\right ) {\mathrm e}^{-x -1}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 13, normalized size = 0.52 \begin {gather*} -9 \, x + e^{\left (x e^{\left (-x - 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.45, size = 13, normalized size = 0.52 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-1}}-9\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 12, normalized size = 0.48 \begin {gather*} - 9 x + e^{x e^{- x - 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________