Integrand size = 150, antiderivative size = 22 \[ \int \frac {e^{e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )} \left (18-18 x+\frac {e^x \left (-48+12 x+18 x^2\right )}{x}+\frac {e^{2 x} \left (48 x+18 x^2\right )}{x^2}\right )}{-\frac {2 e^{2 x}}{x}+\frac {e^{2 x+e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )}}{x}} \, dx=\log \left (-2+e^{-3+\left (-8-3 x+3 e^{-x} x\right )^2}\right ) \] Output:
ln(exp((3/exp(x-ln(x))-3*x-8)^2-3)-2)
Timed out. \[ \int \frac {e^{e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )} \left (18-18 x+\frac {e^x \left (-48+12 x+18 x^2\right )}{x}+\frac {e^{2 x} \left (48 x+18 x^2\right )}{x^2}\right )}{-\frac {2 e^{2 x}}{x}+\frac {e^{2 x+e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )}}{x}} \, dx=\text {\$Aborted} \] Input:
Integrate[(E^((x^2*(9 + (E^x*(-48 - 18*x))/x + (E^(2*x)*(61 + 48*x + 9*x^2 ))/x^2))/E^(2*x))*(18 - 18*x + (E^x*(-48 + 12*x + 18*x^2))/x + (E^(2*x)*(4 8*x + 18*x^2))/x^2))/((-2*E^(2*x))/x + E^(2*x + (x^2*(9 + (E^x*(-48 - 18*x ))/x + (E^(2*x)*(61 + 48*x + 9*x^2))/x^2))/E^(2*x))/x),x]
Output:
$Aborted
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (\frac {e^x \left (18 x^2+12 x-48\right )}{x}+\frac {e^{2 x} \left (18 x^2+48 x\right )}{x^2}-18 x+18\right ) \exp \left (e^{-2 x} x^2 \left (\frac {e^{2 x} \left (9 x^2+48 x+61\right )}{x^2}+\frac {e^x (-18 x-48)}{x}+9\right )\right )}{\frac {\exp \left (e^{-2 x} \left (\frac {e^{2 x} \left (9 x^2+48 x+61\right )}{x^2}+\frac {e^x (-18 x-48)}{x}+9\right ) x^2+2 x\right )}{x}-\frac {2 e^{2 x}}{x}} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 e^{-2 x} \left (e^x \left (3 x^2+2 x-8\right )-3 (x-1) x+e^{2 x} (3 x+8)\right )}{1-2 \exp \left (-9 e^{-2 x} \left (e^x-1\right )^2 x^2+48 \left (e^{-x}-1\right ) x-61\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 6 \int \frac {e^{-2 x} \left (3 (1-x) x+e^{2 x} (3 x+8)-e^x \left (-3 x^2-2 x+8\right )\right )}{1-2 \exp \left (-9 e^{-2 x} \left (1-e^x\right )^2 x^2-48 \left (1-e^{-x}\right ) x-61\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 6 \int \left (e^{-2 x} \left (x+e^x-1\right ) \left (3 e^x x-3 x+8 e^x\right )+\frac {2 e^{-2 x} \left (x+e^x-1\right ) \left (3 e^x x-3 x+8 e^x\right )}{-2+\exp \left (9 e^{-2 x} \left (-1+e^x\right )^2 x^2+\left (48-48 e^{-x}\right ) x+61\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 6 \left (16 \int \frac {1}{-2+\exp \left (9 e^{-2 x} \left (-1+e^x\right )^2 x^2+\left (48-48 e^{-x}\right ) x+61\right )}dx-16 \int \frac {e^{-x}}{-2+\exp \left (9 e^{-2 x} \left (-1+e^x\right )^2 x^2+\left (48-48 e^{-x}\right ) x+61\right )}dx+6 \int \frac {x}{-2+\exp \left (9 e^{-2 x} \left (-1+e^x\right )^2 x^2+\left (48-48 e^{-x}\right ) x+61\right )}dx+6 \int \frac {e^{-2 x} x}{-2+\exp \left (9 e^{-2 x} \left (-1+e^x\right )^2 x^2+\left (48-48 e^{-x}\right ) x+61\right )}dx+4 \int \frac {e^{-x} x}{-2+\exp \left (9 e^{-2 x} \left (-1+e^x\right )^2 x^2+\left (48-48 e^{-x}\right ) x+61\right )}dx-6 \int \frac {e^{-2 x} x^2}{-2+\exp \left (9 e^{-2 x} \left (-1+e^x\right )^2 x^2+\left (48-48 e^{-x}\right ) x+61\right )}dx+6 \int \frac {e^{-x} x^2}{-2+\exp \left (9 e^{-2 x} \left (-1+e^x\right )^2 x^2+\left (48-48 e^{-x}\right ) x+61\right )}dx+\frac {3}{2} e^{-2 x} x^2-3 e^{-x} x^2+\frac {3 x^2}{2}-8 e^{-x} x+8 x\right )\) |
Input:
Int[(E^((x^2*(9 + (E^x*(-48 - 18*x))/x + (E^(2*x)*(61 + 48*x + 9*x^2))/x^2 ))/E^(2*x))*(18 - 18*x + (E^x*(-48 + 12*x + 18*x^2))/x + (E^(2*x)*(48*x + 18*x^2))/x^2))/((-2*E^(2*x))/x + E^(2*x + (x^2*(9 + (E^x*(-48 - 18*x))/x + (E^(2*x)*(61 + 48*x + 9*x^2))/x^2))/E^(2*x))/x),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(49\) vs. \(2(24)=48\).
Time = 1.69 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.27
| method | result | size |
| parallelrisch | \(\ln \left ({\mathrm e}^{\left (\frac {\left (9 x^{2}+48 x +61\right ) {\mathrm e}^{2 x}}{x^{2}}+\left (-18 x -48\right ) {\mathrm e}^{x -\ln \left (x \right )}+9\right ) x^{2} {\mathrm e}^{-2 x}}-2\right )\) | \(50\) |
| risch | \(-61+\ln \left ({\mathrm e}^{-\left (18 \,{\mathrm e}^{x} x^{2}-9 \,{\mathrm e}^{2 x} x^{2}+48 \,{\mathrm e}^{x} x -48 x \,{\mathrm e}^{2 x}-9 x^{2}-61 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x}}-2\right )\) | \(53\) |
Input:
int(((18*x^2+48*x)*exp(x-ln(x))^2+(18*x^2+12*x-48)*exp(x-ln(x))-18*x+18)*e xp(((9*x^2+48*x+61)*exp(x-ln(x))^2+(-18*x-48)*exp(x-ln(x))+9)/exp(x-ln(x)) ^2)/(x*exp(x-ln(x))^2*exp(((9*x^2+48*x+61)*exp(x-ln(x))^2+(-18*x-48)*exp(x -ln(x))+9)/exp(x-ln(x))^2)-2*x*exp(x-ln(x))^2),x,method=_RETURNVERBOSE)
Output:
ln(exp(((9*x^2+48*x+61)*exp(x-ln(x))^2+(-18*x-48)*exp(x-ln(x))+9)/exp(x-ln (x))^2)-2)
Leaf count of result is larger than twice the leaf count of optimal. 50 vs. \(2 (22) = 44\).
Time = 0.07 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.27 \[ \int \frac {e^{e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )} \left (18-18 x+\frac {e^x \left (-48+12 x+18 x^2\right )}{x}+\frac {e^{2 x} \left (48 x+18 x^2\right )}{x^2}\right )}{-\frac {2 e^{2 x}}{x}+\frac {e^{2 x+e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )}}{x}} \, dx=\log \left (e^{\left ({\left ({\left (9 \, x^{2} + 48 \, x + 61\right )} e^{\left (2 \, x - 2 \, \log \left (x\right )\right )} - 6 \, {\left (3 \, x + 8\right )} e^{\left (x - \log \left (x\right )\right )} + 9\right )} e^{\left (-2 \, x + 2 \, \log \left (x\right )\right )}\right )} - 2\right ) \] Input:
integrate(((18*x^2+48*x)*exp(x-log(x))^2+(18*x^2+12*x-48)*exp(x-log(x))-18 *x+18)*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(-18*x-48)*exp(x-log(x))+9)/ex p(x-log(x))^2)/(x*exp(x-log(x))^2*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(-1 8*x-48)*exp(x-log(x))+9)/exp(x-log(x))^2)-2*x*exp(x-log(x))^2),x, algorith m="fricas")
Output:
log(e^(((9*x^2 + 48*x + 61)*e^(2*x - 2*log(x)) - 6*(3*x + 8)*e^(x - log(x) ) + 9)*e^(-2*x + 2*log(x))) - 2)
Leaf count of result is larger than twice the leaf count of optimal. 44 vs. \(2 (19) = 38\).
Time = 0.20 (sec) , antiderivative size = 44, normalized size of antiderivative = 2.00 \[ \int \frac {e^{e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )} \left (18-18 x+\frac {e^x \left (-48+12 x+18 x^2\right )}{x}+\frac {e^{2 x} \left (48 x+18 x^2\right )}{x^2}\right )}{-\frac {2 e^{2 x}}{x}+\frac {e^{2 x+e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )}}{x}} \, dx=\log {\left (e^{x^{2} \cdot \left (9 + \frac {\left (- 18 x - 48\right ) e^{x}}{x} + \frac {\left (9 x^{2} + 48 x + 61\right ) e^{2 x}}{x^{2}}\right ) e^{- 2 x}} - 2 \right )} \] Input:
integrate(((18*x**2+48*x)*exp(x-ln(x))**2+(18*x**2+12*x-48)*exp(x-ln(x))-1 8*x+18)*exp(((9*x**2+48*x+61)*exp(x-ln(x))**2+(-18*x-48)*exp(x-ln(x))+9)/e xp(x-ln(x))**2)/(x*exp(x-ln(x))**2*exp(((9*x**2+48*x+61)*exp(x-ln(x))**2+( -18*x-48)*exp(x-ln(x))+9)/exp(x-ln(x))**2)-2*x*exp(x-ln(x))**2),x)
Output:
log(exp(x**2*(9 + (-18*x - 48)*exp(x)/x + (9*x**2 + 48*x + 61)*exp(2*x)/x* *2)*exp(-2*x)) - 2)
Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (22) = 44\).
Time = 0.30 (sec) , antiderivative size = 81, normalized size of antiderivative = 3.68 \[ \int \frac {e^{e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )} \left (18-18 x+\frac {e^x \left (-48+12 x+18 x^2\right )}{x}+\frac {e^{2 x} \left (48 x+18 x^2\right )}{x^2}\right )}{-\frac {2 e^{2 x}}{x}+\frac {e^{2 x+e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )}}{x}} \, dx=9 \, x^{2} - 6 \, {\left (3 \, x^{2} + 8 \, x\right )} e^{\left (-x\right )} + 48 \, x + \log \left (-{\left (2 \, e^{\left (18 \, x^{2} e^{\left (-x\right )} + 48 \, x e^{\left (-x\right )}\right )} - e^{\left (9 \, x^{2} e^{\left (-2 \, x\right )} + 9 \, x^{2} + 48 \, x + 61\right )}\right )} e^{\left (-9 \, x^{2} - 48 \, x - 61\right )}\right ) \] Input:
integrate(((18*x^2+48*x)*exp(x-log(x))^2+(18*x^2+12*x-48)*exp(x-log(x))-18 *x+18)*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(-18*x-48)*exp(x-log(x))+9)/ex p(x-log(x))^2)/(x*exp(x-log(x))^2*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(-1 8*x-48)*exp(x-log(x))+9)/exp(x-log(x))^2)-2*x*exp(x-log(x))^2),x, algorith m="maxima")
Output:
9*x^2 - 6*(3*x^2 + 8*x)*e^(-x) + 48*x + log(-(2*e^(18*x^2*e^(-x) + 48*x*e^ (-x)) - e^(9*x^2*e^(-2*x) + 9*x^2 + 48*x + 61))*e^(-9*x^2 - 48*x - 61))
\[ \int \frac {e^{e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )} \left (18-18 x+\frac {e^x \left (-48+12 x+18 x^2\right )}{x}+\frac {e^{2 x} \left (48 x+18 x^2\right )}{x^2}\right )}{-\frac {2 e^{2 x}}{x}+\frac {e^{2 x+e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )}}{x}} \, dx=\int { \frac {6 \, {\left ({\left (3 \, x^{2} + 8 \, x\right )} e^{\left (2 \, x - 2 \, \log \left (x\right )\right )} + {\left (3 \, x^{2} + 2 \, x - 8\right )} e^{\left (x - \log \left (x\right )\right )} - 3 \, x + 3\right )} e^{\left ({\left ({\left (9 \, x^{2} + 48 \, x + 61\right )} e^{\left (2 \, x - 2 \, \log \left (x\right )\right )} - 6 \, {\left (3 \, x + 8\right )} e^{\left (x - \log \left (x\right )\right )} + 9\right )} e^{\left (-2 \, x + 2 \, \log \left (x\right )\right )}\right )}}{x e^{\left ({\left ({\left (9 \, x^{2} + 48 \, x + 61\right )} e^{\left (2 \, x - 2 \, \log \left (x\right )\right )} - 6 \, {\left (3 \, x + 8\right )} e^{\left (x - \log \left (x\right )\right )} + 9\right )} e^{\left (-2 \, x + 2 \, \log \left (x\right )\right )} + 2 \, x - 2 \, \log \left (x\right )\right )} - 2 \, x e^{\left (2 \, x - 2 \, \log \left (x\right )\right )}} \,d x } \] Input:
integrate(((18*x^2+48*x)*exp(x-log(x))^2+(18*x^2+12*x-48)*exp(x-log(x))-18 *x+18)*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(-18*x-48)*exp(x-log(x))+9)/ex p(x-log(x))^2)/(x*exp(x-log(x))^2*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(-1 8*x-48)*exp(x-log(x))+9)/exp(x-log(x))^2)-2*x*exp(x-log(x))^2),x, algorith m="giac")
Output:
integrate(6*((3*x^2 + 8*x)*e^(2*x - 2*log(x)) + (3*x^2 + 2*x - 8)*e^(x - l og(x)) - 3*x + 3)*e^(((9*x^2 + 48*x + 61)*e^(2*x - 2*log(x)) - 6*(3*x + 8) *e^(x - log(x)) + 9)*e^(-2*x + 2*log(x)))/(x*e^(((9*x^2 + 48*x + 61)*e^(2* x - 2*log(x)) - 6*(3*x + 8)*e^(x - log(x)) + 9)*e^(-2*x + 2*log(x)) + 2*x - 2*log(x)) - 2*x*e^(2*x - 2*log(x))), x)
Time = 2.23 (sec) , antiderivative size = 44, normalized size of antiderivative = 2.00 \[ \int \frac {e^{e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )} \left (18-18 x+\frac {e^x \left (-48+12 x+18 x^2\right )}{x}+\frac {e^{2 x} \left (48 x+18 x^2\right )}{x^2}\right )}{-\frac {2 e^{2 x}}{x}+\frac {e^{2 x+e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )}}{x}} \, dx=\ln \left ({\mathrm {e}}^{48\,x}\,{\mathrm {e}}^{61}\,{\mathrm {e}}^{-48\,x\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{9\,x^2}\,{\mathrm {e}}^{9\,x^2\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{-18\,x^2\,{\mathrm {e}}^{-x}}-2\right ) \] Input:
int(-(exp(exp(2*log(x) - 2*x)*(exp(2*x - 2*log(x))*(48*x + 9*x^2 + 61) - e xp(x - log(x))*(18*x + 48) + 9))*(exp(x - log(x))*(12*x + 18*x^2 - 48) - 1 8*x + exp(2*x - 2*log(x))*(48*x + 18*x^2) + 18))/(2*x*exp(2*x - 2*log(x)) - x*exp(exp(2*log(x) - 2*x)*(exp(2*x - 2*log(x))*(48*x + 9*x^2 + 61) - exp (x - log(x))*(18*x + 48) + 9))*exp(2*x - 2*log(x))),x)
Output:
log(exp(48*x)*exp(61)*exp(-48*x*exp(-x))*exp(9*x^2)*exp(9*x^2*exp(-2*x))*e xp(-18*x^2*exp(-x)) - 2)
\[ \int \frac {e^{e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )} \left (18-18 x+\frac {e^x \left (-48+12 x+18 x^2\right )}{x}+\frac {e^{2 x} \left (48 x+18 x^2\right )}{x^2}\right )}{-\frac {2 e^{2 x}}{x}+\frac {e^{2 x+e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )}}{x}} \, dx=6 e^{61} \left (8 \left (\int \frac {e^{\frac {9 e^{2 x} x^{2}+48 e^{2 x} x +9 x^{2}}{e^{2 x}}}}{e^{\frac {9 e^{2 x} x^{2}+48 e^{2 x} x +9 x^{2}}{e^{2 x}}} e^{61}-2 e^{\frac {18 x^{2}+48 x}{e^{x}}}}d x \right )-8 \left (\int \frac {e^{\frac {9 e^{2 x} x^{2}+47 e^{2 x} x +9 x^{2}}{e^{2 x}}}}{e^{\frac {9 e^{2 x} x^{2}+48 e^{2 x} x +9 x^{2}}{e^{2 x}}} e^{61}-2 e^{\frac {18 x^{2}+48 x}{e^{x}}}}d x \right )+3 \left (\int \frac {e^{\frac {9 e^{2 x} x^{2}+48 e^{2 x} x +9 x^{2}}{e^{2 x}}} x}{e^{\frac {9 e^{2 x} x^{2}+48 e^{2 x} x +9 x^{2}}{e^{2 x}}} e^{61}-2 e^{\frac {18 x^{2}+48 x}{e^{x}}}}d x \right )+3 \left (\int \frac {e^{\frac {9 e^{2 x} x^{2}+47 e^{2 x} x +9 x^{2}}{e^{2 x}}} x^{2}}{e^{\frac {9 e^{2 x} x^{2}+48 e^{2 x} x +9 x^{2}}{e^{2 x}}} e^{61}-2 e^{\frac {18 x^{2}+48 x}{e^{x}}}}d x \right )+2 \left (\int \frac {e^{\frac {9 e^{2 x} x^{2}+47 e^{2 x} x +9 x^{2}}{e^{2 x}}} x}{e^{\frac {9 e^{2 x} x^{2}+48 e^{2 x} x +9 x^{2}}{e^{2 x}}} e^{61}-2 e^{\frac {18 x^{2}+48 x}{e^{x}}}}d x \right )-3 \left (\int \frac {e^{\frac {9 e^{2 x} x^{2}+46 e^{2 x} x +9 x^{2}}{e^{2 x}}} x^{2}}{e^{\frac {9 e^{2 x} x^{2}+48 e^{2 x} x +9 x^{2}}{e^{2 x}}} e^{61}-2 e^{\frac {18 x^{2}+48 x}{e^{x}}}}d x \right )+3 \left (\int \frac {e^{\frac {9 e^{2 x} x^{2}+46 e^{2 x} x +9 x^{2}}{e^{2 x}}} x}{e^{\frac {9 e^{2 x} x^{2}+48 e^{2 x} x +9 x^{2}}{e^{2 x}}} e^{61}-2 e^{\frac {18 x^{2}+48 x}{e^{x}}}}d x \right )\right ) \] Input:
int(((18*x^2+48*x)*exp(x-log(x))^2+(18*x^2+12*x-48)*exp(x-log(x))-18*x+18) *exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(-18*x-48)*exp(x-log(x))+9)/exp(x-lo g(x))^2)/(x*exp(x-log(x))^2*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(-18*x-48 )*exp(x-log(x))+9)/exp(x-log(x))^2)-2*x*exp(x-log(x))^2),x)
Output:
6*e**61*(8*int(e**((9*e**(2*x)*x**2 + 48*e**(2*x)*x + 9*x**2)/e**(2*x))/(e **((9*e**(2*x)*x**2 + 48*e**(2*x)*x + 9*x**2)/e**(2*x))*e**61 - 2*e**((18* x**2 + 48*x)/e**x)),x) - 8*int(e**((9*e**(2*x)*x**2 + 47*e**(2*x)*x + 9*x* *2)/e**(2*x))/(e**((9*e**(2*x)*x**2 + 48*e**(2*x)*x + 9*x**2)/e**(2*x))*e* *61 - 2*e**((18*x**2 + 48*x)/e**x)),x) + 3*int((e**((9*e**(2*x)*x**2 + 48* e**(2*x)*x + 9*x**2)/e**(2*x))*x)/(e**((9*e**(2*x)*x**2 + 48*e**(2*x)*x + 9*x**2)/e**(2*x))*e**61 - 2*e**((18*x**2 + 48*x)/e**x)),x) + 3*int((e**((9 *e**(2*x)*x**2 + 47*e**(2*x)*x + 9*x**2)/e**(2*x))*x**2)/(e**((9*e**(2*x)* x**2 + 48*e**(2*x)*x + 9*x**2)/e**(2*x))*e**61 - 2*e**((18*x**2 + 48*x)/e* *x)),x) + 2*int((e**((9*e**(2*x)*x**2 + 47*e**(2*x)*x + 9*x**2)/e**(2*x))* x)/(e**((9*e**(2*x)*x**2 + 48*e**(2*x)*x + 9*x**2)/e**(2*x))*e**61 - 2*e** ((18*x**2 + 48*x)/e**x)),x) - 3*int((e**((9*e**(2*x)*x**2 + 46*e**(2*x)*x + 9*x**2)/e**(2*x))*x**2)/(e**((9*e**(2*x)*x**2 + 48*e**(2*x)*x + 9*x**2)/ e**(2*x))*e**61 - 2*e**((18*x**2 + 48*x)/e**x)),x) + 3*int((e**((9*e**(2*x )*x**2 + 46*e**(2*x)*x + 9*x**2)/e**(2*x))*x)/(e**((9*e**(2*x)*x**2 + 48*e **(2*x)*x + 9*x**2)/e**(2*x))*e**61 - 2*e**((18*x**2 + 48*x)/e**x)),x))