Optimal. Leaf size=22 \[ -1-e^5+e^{2 \left (-3+\log \left (-1+e^2 x\right )\right )}+x \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.77, number of steps used = 2, number of rules used = 1, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {1586} \begin {gather*} \frac {x^2}{e^2}+\left (1-\frac {2}{e^4}\right ) x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 1586
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {2}{e^4}+\frac {2 x}{e^2}\right ) \, dx\\ &=\left (1-\frac {2}{e^4}\right ) x+\frac {x^2}{e^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 15, normalized size = 0.68 \begin {gather*} x-\frac {2 x}{e^4}+\frac {x^2}{e^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.82, size = 17, normalized size = 0.77 \begin {gather*} {\left (x^{2} e^{2} + x e^{4} - 2 \, x\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.41, size = 17, normalized size = 0.77 \begin {gather*} {\left (x^{2} e^{2} + x e^{4} - 2 \, x\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.30, size = 14, normalized size = 0.64
method | result | size |
risch | \(-2 x \,{\mathrm e}^{-4}+x^{2} {\mathrm e}^{-2}+x\) | \(14\) |
default | \(x +{\mathrm e}^{2 \ln \left ({\mathrm e}^{2} x -1\right )-6}\) | \(15\) |
norman | \({\mathrm e}^{4} {\mathrm e}^{-6} x^{2}-\left (2 \,{\mathrm e}^{2}-{\mathrm e}^{6}\right ) {\mathrm e}^{-6} x\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.39, size = 16, normalized size = 0.73 \begin {gather*} {\left (x^{2} e^{2} + x {\left (e^{4} - 2\right )}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.07, size = 12, normalized size = 0.55 \begin {gather*} x\,\left (x\,{\mathrm {e}}^{-2}-2\,{\mathrm {e}}^{-4}+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 15, normalized size = 0.68 \begin {gather*} \frac {x^{2}}{e^{2}} + \frac {x \left (-2 + e^{4}\right )}{e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________