Optimal. Leaf size=22 \[ e^{-x+x^2+\frac {1}{2} \left (-3+x^2\right )}-x \]
________________________________________________________________________________________
Rubi [A] time = 0.07, antiderivative size = 20, normalized size of antiderivative = 0.91, number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {2244, 2236} \begin {gather*} e^{\frac {3 x^2}{2}-x-\frac {3}{2}}-x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2236
Rule 2244
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^{\frac {1}{2} \left (-3-2 x+3 x^2\right )} (-1+3 x) \, dx\\ &=-x+\int e^{-\frac {3}{2}-x+\frac {3 x^2}{2}} (-1+3 x) \, dx\\ &=e^{-\frac {3}{2}-x+\frac {3 x^2}{2}}-x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 20, normalized size = 0.91 \begin {gather*} e^{-\frac {3}{2}-x+\frac {3 x^2}{2}}-x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.96, size = 15, normalized size = 0.68 \begin {gather*} -x + e^{\left (\frac {3}{2} \, x^{2} - x - \frac {3}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.61, size = 15, normalized size = 0.68 \begin {gather*} -x + e^{\left (\frac {3}{2} \, x^{2} - x - \frac {3}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 16, normalized size = 0.73
method | result | size |
default | \({\mathrm e}^{\frac {3}{2} x^{2}-x -\frac {3}{2}}-x\) | \(16\) |
norman | \({\mathrm e}^{\frac {3}{2} x^{2}-x -\frac {3}{2}}-x\) | \(16\) |
risch | \({\mathrm e}^{\frac {3}{2} x^{2}-x -\frac {3}{2}}-x\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.55, size = 15, normalized size = 0.68 \begin {gather*} -x + e^{\left (\frac {3}{2} \, x^{2} - x - \frac {3}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.10, size = 15, normalized size = 0.68 \begin {gather*} {\mathrm {e}}^{\frac {3\,x^2}{2}-x-\frac {3}{2}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 14, normalized size = 0.64 \begin {gather*} - x + e^{\frac {3 x^{2}}{2} - x - \frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________