Optimal. Leaf size=15 \[ -2 e^{-x} x-\log ^2(2) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.33, number of steps
used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {2207, 2225}
\begin {gather*} 2 e^{-x} (1-x)-2 e^{-x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 e^{-x} (1-x)+2 \int e^{-x} \, dx\\ &=-2 e^{-x}+2 e^{-x} (1-x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 8, normalized size = 0.53 \begin {gather*} -2 e^{-x} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.11, size = 8, normalized size = 0.53
method | result | size |
gosper | \(-2 x \,{\mathrm e}^{-x}\) | \(8\) |
default | \(-2 x \,{\mathrm e}^{-x}\) | \(8\) |
norman | \(-2 x \,{\mathrm e}^{-x}\) | \(8\) |
risch | \(-2 x \,{\mathrm e}^{-x}\) | \(8\) |
meijerg | \(-\left (2 x +2\right ) {\mathrm e}^{-x}+2 \,{\mathrm e}^{-x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 16, normalized size = 1.07 \begin {gather*} -2 \, {\left (x + 1\right )} e^{\left (-x\right )} + 2 \, e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.34, size = 7, normalized size = 0.47 \begin {gather*} -2 \, x e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 7, normalized size = 0.47 \begin {gather*} - 2 x e^{- x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 7, normalized size = 0.47 \begin {gather*} -2 \, x e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 7, normalized size = 0.47 \begin {gather*} -2\,x\,{\mathrm {e}}^{-x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________