Optimal. Leaf size=8 \[ \frac {x}{2 e^2} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \begin {gather*} \frac {x}{2 e^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 8
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {x}{2 e^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {x}{2 e^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.67, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{2} \, x e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{2} \, x e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 6, normalized size = 0.75
method | result | size |
risch | \(\frac {x \,{\mathrm e}^{-2}}{2}\) | \(6\) |
default | \(\frac {x \,{\mathrm e}^{-2}}{2}\) | \(8\) |
norman | \(\frac {x \,{\mathrm e}^{-2}}{2}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.34, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{2} \, x e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.00, size = 5, normalized size = 0.62 \begin {gather*} \frac {x\,{\mathrm {e}}^{-2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.01, size = 5, normalized size = 0.62 \begin {gather*} \frac {x}{2 e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________