Optimal. Leaf size=20 \[ \frac {1}{9} e^{-\frac {2}{e^5}+6 x-2 x^2} \]
________________________________________________________________________________________
Rubi [A] time = 0.06, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {2244, 12, 2236} \begin {gather*} \frac {1}{9} e^{-2 x^2+6 x-\frac {2}{e^5}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2236
Rule 2244
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{9} e^{-\frac {2}{e^5}+6 x-2 x^2} (6-4 x) \, dx\\ &=\frac {1}{9} \int e^{-\frac {2}{e^5}+6 x-2 x^2} (6-4 x) \, dx\\ &=\frac {1}{9} e^{-\frac {2}{e^5}+6 x-2 x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.07, size = 20, normalized size = 1.00 \begin {gather*} \frac {1}{9} e^{-\frac {2}{e^5}+6 x-2 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.66, size = 22, normalized size = 1.10 \begin {gather*} e^{\left (-2 \, {\left ({\left (x^{2} - 3 \, x\right )} e^{5} + e^{5} \log \relax (3) + 1\right )} e^{\left (-5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.30, size = 18, normalized size = 0.90 \begin {gather*} e^{\left (-2 \, x^{2} + 6 \, x - 2 \, e^{\left (-5\right )} - 2 \, \log \relax (3)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 17, normalized size = 0.85
method | result | size |
risch | \(\frac {{\mathrm e}^{-2 x^{2}+6 x -2 \,{\mathrm e}^{-5}}}{9}\) | \(17\) |
gosper | \({\mathrm e}^{-2 \left (x^{2} {\mathrm e}^{5}+{\mathrm e}^{5} \ln \relax (3)-3 x \,{\mathrm e}^{5}+1\right ) {\mathrm e}^{-5}}\) | \(28\) |
default | \({\mathrm e}^{2 \left (-{\mathrm e}^{5} \ln \relax (3)+\left (-x^{2}+3 x \right ) {\mathrm e}^{5}-1\right ) {\mathrm e}^{-5}}\) | \(29\) |
norman | \({\mathrm e}^{2 \left (-{\mathrm e}^{5} \ln \relax (3)+\left (-x^{2}+3 x \right ) {\mathrm e}^{5}-1\right ) {\mathrm e}^{-5}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.48, size = 22, normalized size = 1.10 \begin {gather*} e^{\left (-2 \, {\left ({\left (x^{2} - 3 \, x\right )} e^{5} + e^{5} \log \relax (3) + 1\right )} e^{\left (-5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.14, size = 17, normalized size = 0.85 \begin {gather*} \frac {{\mathrm {e}}^{-2\,{\mathrm {e}}^{-5}}\,{\mathrm {e}}^{6\,x}\,{\mathrm {e}}^{-2\,x^2}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 26, normalized size = 1.30 \begin {gather*} e^{\frac {2 \left (\left (- x^{2} + 3 x\right ) e^{5} - e^{5} \log {\relax (3 )} - 1\right )}{e^{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________