Optimal. Leaf size=13 \[ 6+e^{-2 x} x+\log \left (\frac {5}{3}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.85, 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*} \frac {e^{-2 x}}{2}-\frac {1}{2} e^{-2 x} (1-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{2} e^{-2 x} (1-2 x)-\int e^{-2 x} \, dx\\ &=\frac {e^{-2 x}}{2}-\frac {1}{2} e^{-2 x} (1-2 x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 7, normalized size = 0.54 \begin {gather*} e^{-2 x} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.26, size = 7, normalized size = 0.54
method | result | size |
gosper | \(x \,{\mathrm e}^{-2 x}\) | \(7\) |
default | \(x \,{\mathrm e}^{-2 x}\) | \(7\) |
norman | \(x \,{\mathrm e}^{-2 x}\) | \(7\) |
risch | \(x \,{\mathrm e}^{-2 x}\) | \(7\) |
meijerg | \(-\frac {{\mathrm e}^{-2 x}}{2}+\frac {\left (4 x +2\right ) {\mathrm e}^{-2 x}}{4}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 18, normalized size = 1.38 \begin {gather*} \frac {1}{2} \, {\left (2 \, x + 1\right )} e^{\left (-2 \, x\right )} - \frac {1}{2} \, e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.42, size = 6, normalized size = 0.46 \begin {gather*} x e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 5, normalized size = 0.38 \begin {gather*} x e^{- 2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 6, normalized size = 0.46 \begin {gather*} x e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 6, normalized size = 0.46 \begin {gather*} x\,{\mathrm {e}}^{-2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________