Optimal. Leaf size=25 \[ 10 e^{-2-x^2+\frac {x}{4+\frac {3 x}{\log (3)}}} x \]
________________________________________________________________________________________
Rubi [F] time = 1.91, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\exp \left (\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right ) \left (90 x^2-180 x^4+\left (240 x-480 x^3\right ) \log (3)+\left (160+40 x-320 x^2\right ) \log ^2(3)\right )}{9 e^2 x^2+24 e^2 x \log (3)+16 e^2 \log ^2(3)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right ) \left (90 x^2-180 x^4+\left (240 x-480 x^3\right ) \log (3)+\left (160+40 x-320 x^2\right ) \log ^2(3)\right )}{(3 x+4 \log (3))^2} \, dx\\ &=\int \frac {\exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right ) \left (-180 x^4-480 x^3 \log (3)+160 \log ^2(3)+40 x \log (3) (6+\log (3))+10 x^2 \left (9-32 \log ^2(3)\right )\right )}{(3 x+4 \log (3))^2} \, dx\\ &=\int \left (10 \exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right )-20 \exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right ) x^2+\frac {40 \exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right ) \log ^2(3)}{3 (3 x+4 \log (3))}-\frac {160 \exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right ) \log ^3(3)}{3 (3 x+\log (81))^2}\right ) \, dx\\ &=10 \int \exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right ) \, dx-20 \int \exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right ) x^2 \, dx+\frac {1}{3} \left (40 \log ^2(3)\right ) \int \frac {\exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right )}{3 x+4 \log (3)} \, dx-\frac {1}{3} \left (160 \log ^3(3)\right ) \int \frac {\exp \left (-2+\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}\right )}{(3 x+\log (81))^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [F] time = 1.68, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {-3 x^3+\left (x-4 x^2\right ) \log (3)}{3 x+4 \log (3)}} \left (90 x^2-180 x^4+\left (240 x-480 x^3\right ) \log (3)+\left (160+40 x-320 x^2\right ) \log ^2(3)\right )}{9 e^2 x^2+24 e^2 x \log (3)+16 e^2 \log ^2(3)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 36, normalized size = 1.44 \begin {gather*} 10 \, x e^{\left (-\frac {3 \, x^{3} + {\left (4 \, x^{2} - x\right )} \log \relax (3)}{3 \, x + 4 \, \log \relax (3)} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.28, size = 40, normalized size = 1.60 \begin {gather*} 10 \cdot 3^{\frac {1}{3}} x e^{\left (-\frac {9 \, x^{3} + 12 \, x^{2} \log \relax (3) + 4 \, \log \relax (3)^{2}}{3 \, {\left (3 \, x + 4 \, \log \relax (3)\right )}} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.42, size = 37, normalized size = 1.48
method | result | size |
gosper | \(10 \,{\mathrm e}^{-2} x \,{\mathrm e}^{-\frac {x \left (4 x \ln \relax (3)+3 x^{2}-\ln \relax (3)\right )}{4 \ln \relax (3)+3 x}}\) | \(37\) |
risch | \(10 x \,{\mathrm e}^{-\frac {4 x^{2} \ln \relax (3)+3 x^{3}-x \ln \relax (3)+8 \ln \relax (3)+6 x}{4 \ln \relax (3)+3 x}}\) | \(42\) |
norman | \(\frac {30 x^{2} {\mathrm e}^{-2} {\mathrm e}^{\frac {\left (-4 x^{2}+x \right ) \ln \relax (3)-3 x^{3}}{4 \ln \relax (3)+3 x}}+40 \,{\mathrm e}^{-2} \ln \relax (3) x \,{\mathrm e}^{\frac {\left (-4 x^{2}+x \right ) \ln \relax (3)-3 x^{3}}{4 \ln \relax (3)+3 x}}}{4 \ln \relax (3)+3 x}\) | \(87\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.61, size = 30, normalized size = 1.20 \begin {gather*} 10 \cdot 3^{\frac {1}{3}} x e^{\left (-x^{2} - \frac {4 \, \log \relax (3)^{2}}{3 \, {\left (3 \, x + 4 \, \log \relax (3)\right )}} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.63, size = 37, normalized size = 1.48 \begin {gather*} 10\,3^{\frac {x-4\,x^2}{3\,x+\ln \left (81\right )}}\,x\,{\mathrm {e}}^{-\frac {3\,x^3}{3\,x+\ln \left (81\right )}-2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.44, size = 31, normalized size = 1.24 \begin {gather*} \frac {10 x e^{\frac {- 3 x^{3} + \left (- 4 x^{2} + x\right ) \log {\relax (3 )}}{3 x + 4 \log {\relax (3 )}}}}{e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________