Integrand size = 240, antiderivative size = 27 \[ \int \frac {-10+12 x-6 x^2+e^{20+x} \left (-6+12 x-6 x^2\right )+\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )}{\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )} \, dx=x+\log \left (\log \left (\frac {4}{\left (-3+e^{20+x}+\frac {2}{-3+\frac {3}{x}}+x\right )^2}\right )\right ) \]
Time = 0.18 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.22 \[ \int \frac {-10+12 x-6 x^2+e^{20+x} \left (-6+12 x-6 x^2\right )+\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )}{\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )} \, dx=x+\log \left (\log \left (\frac {36 (-1+x)^2}{\left (9+3 e^{20+x} (-1+x)-14 x+3 x^2\right )^2}\right )\right ) \]
Integrate[(-10 + 12*x - 6*x^2 + E^(20 + x)*(-6 + 12*x - 6*x^2) + (-9 + 23* x - 17*x^2 + 3*x^3 + E^(20 + x)*(3 - 6*x + 3*x^2))*Log[(36 - 72*x + 36*x^2 )/(81 - 252*x + 250*x^2 - 84*x^3 + 9*x^4 + E^(40 + 2*x)*(9 - 18*x + 9*x^2) + E^(20 + x)*(-54 + 138*x - 102*x^2 + 18*x^3))])/((-9 + 23*x - 17*x^2 + 3 *x^3 + E^(20 + x)*(3 - 6*x + 3*x^2))*Log[(36 - 72*x + 36*x^2)/(81 - 252*x + 250*x^2 - 84*x^3 + 9*x^4 + E^(40 + 2*x)*(9 - 18*x + 9*x^2) + E^(20 + x)* (-54 + 138*x - 102*x^2 + 18*x^3))]),x]
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.
| \(\displaystyle \int \frac {-6 x^2+e^{x+20} \left (-6 x^2+12 x-6\right )+\left (3 x^3-17 x^2+e^{x+20} \left (3 x^2-6 x+3\right )+23 x-9\right ) \log \left (\frac {36 x^2-72 x+36}{9 x^4-84 x^3+250 x^2+e^{2 x+40} \left (9 x^2-18 x+9\right )+e^{x+20} \left (18 x^3-102 x^2+138 x-54\right )-252 x+81}\right )+12 x-10}{\left (3 x^3-17 x^2+e^{x+20} \left (3 x^2-6 x+3\right )+23 x-9\right ) \log \left (\frac {36 x^2-72 x+36}{9 x^4-84 x^3+250 x^2+e^{2 x+40} \left (9 x^2-18 x+9\right )+e^{x+20} \left (18 x^3-102 x^2+138 x-54\right )-252 x+81}\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^2-\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right ) (x-1) \log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )+6 e^{x+20} (x-1)^2-12 x+10}{(1-x) \left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right ) \log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )-2}{\log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )}+\frac {2 \left (3 x^3-20 x^2+29 x-14\right )}{(x-1) \left (3 x^2+3 e^{x+20} x-14 x-3 e^{x+20}+9\right ) \log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \int \frac {1}{\log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )}dx+24 \int \frac {1}{\left (3 x^2+3 e^{x+20} x-14 x-3 e^{x+20}+9\right ) \log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )}dx-4 \int \frac {1}{(x-1) \left (3 x^2+3 e^{x+20} x-14 x-3 e^{x+20}+9\right ) \log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )}dx-34 \int \frac {x}{\left (3 x^2+3 e^{x+20} x-14 x-3 e^{x+20}+9\right ) \log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )}dx+6 \int \frac {x^2}{\left (3 x^2+3 e^{x+20} x-14 x-3 e^{x+20}+9\right ) \log \left (\frac {36 (x-1)^2}{\left (3 x^2-14 x+3 e^{x+20} (x-1)+9\right )^2}\right )}dx+x\) |
Int[(-10 + 12*x - 6*x^2 + E^(20 + x)*(-6 + 12*x - 6*x^2) + (-9 + 23*x - 17 *x^2 + 3*x^3 + E^(20 + x)*(3 - 6*x + 3*x^2))*Log[(36 - 72*x + 36*x^2)/(81 - 252*x + 250*x^2 - 84*x^3 + 9*x^4 + E^(40 + 2*x)*(9 - 18*x + 9*x^2) + E^( 20 + x)*(-54 + 138*x - 102*x^2 + 18*x^3))])/((-9 + 23*x - 17*x^2 + 3*x^3 + E^(20 + x)*(3 - 6*x + 3*x^2))*Log[(36 - 72*x + 36*x^2)/(81 - 252*x + 250* x^2 - 84*x^3 + 9*x^4 + E^(40 + 2*x)*(9 - 18*x + 9*x^2) + E^(20 + x)*(-54 + 138*x - 102*x^2 + 18*x^3))]),x]
3.14.78.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(74\) vs. \(2(26)=52\).
Time = 0.73 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.78
| method | result | size |
| norman | \(x +\ln \left (\ln \left (\frac {36 x^{2}-72 x +36}{\left (9 x^{2}-18 x +9\right ) {\mathrm e}^{40+2 x}+\left (18 x^{3}-102 x^{2}+138 x -54\right ) {\mathrm e}^{20+x}+9 x^{4}-84 x^{3}+250 x^{2}-252 x +81}\right )\right )\) | \(75\) |
| parallelrisch | \(4+\ln \left (\ln \left (\frac {36 x^{2}-72 x +36}{18 \,{\mathrm e}^{20+x} x^{3}+9 x^{4}-102 \,{\mathrm e}^{20+x} x^{2}+9 \,{\mathrm e}^{40+2 x} x^{2}-84 x^{3}+138 \,{\mathrm e}^{20+x} x -18 \,{\mathrm e}^{40+2 x} x +250 x^{2}-54 \,{\mathrm e}^{20+x}+9 \,{\mathrm e}^{40+2 x}-252 x +81}\right )\right )+x\) | \(97\) |
| risch | \(x +\ln \left (\ln \left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )+\frac {i \left (\pi \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )-2 \pi \,\operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2}+\pi \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3}+\pi \,\operatorname {csgn}\left (i \left (-1+x \right )^{2}\right ) \operatorname {csgn}\left (\frac {i}{\left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )^{2}}\right ) \operatorname {csgn}\left (\frac {i \left (-1+x \right )^{2}}{\left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )^{2}}\right )-\pi \,\operatorname {csgn}\left (i \left (-1+x \right )^{2}\right ) \operatorname {csgn}\left (\frac {i \left (-1+x \right )^{2}}{\left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )^{2}}\right )^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{\left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )^{2}}\right ) \operatorname {csgn}\left (\frac {i \left (-1+x \right )^{2}}{\left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )^{2}}\right )^{2}-\pi {\operatorname {csgn}\left (i \left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )\right )}^{2} \operatorname {csgn}\left (i \left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )^{2}\right )+2 \pi \,\operatorname {csgn}\left (i \left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )\right ) {\operatorname {csgn}\left (i \left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )^{2}\right )}^{2}-\pi {\operatorname {csgn}\left (i \left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )^{2}\right )}^{3}+\pi \operatorname {csgn}\left (\frac {i \left (-1+x \right )^{2}}{\left (x^{2}+\left ({\mathrm e}^{20+x}-\frac {14}{3}\right ) x -{\mathrm e}^{20+x}+3\right )^{2}}\right )^{3}+4 i \ln \left (-1+x \right )+4 i \ln \left (2\right )\right )}{4}\right )\) | \(435\) |
int((((3*x^2-6*x+3)*exp(20+x)+3*x^3-17*x^2+23*x-9)*ln((36*x^2-72*x+36)/((9 *x^2-18*x+9)*exp(20+x)^2+(18*x^3-102*x^2+138*x-54)*exp(20+x)+9*x^4-84*x^3+ 250*x^2-252*x+81))+(-6*x^2+12*x-6)*exp(20+x)-6*x^2+12*x-10)/((3*x^2-6*x+3) *exp(20+x)+3*x^3-17*x^2+23*x-9)/ln((36*x^2-72*x+36)/((9*x^2-18*x+9)*exp(20 +x)^2+(18*x^3-102*x^2+138*x-54)*exp(20+x)+9*x^4-84*x^3+250*x^2-252*x+81)), x,method=_RETURNVERBOSE)
x+ln(ln((36*x^2-72*x+36)/((9*x^2-18*x+9)*exp(20+x)^2+(18*x^3-102*x^2+138*x -54)*exp(20+x)+9*x^4-84*x^3+250*x^2-252*x+81)))
Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (28) = 56\).
Time = 0.26 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.70 \[ \int \frac {-10+12 x-6 x^2+e^{20+x} \left (-6+12 x-6 x^2\right )+\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )}{\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )} \, dx=x + \log \left (\log \left (\frac {36 \, {\left (x^{2} - 2 \, x + 1\right )}}{9 \, x^{4} - 84 \, x^{3} + 250 \, x^{2} + 9 \, {\left (x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x + 40\right )} + 6 \, {\left (3 \, x^{3} - 17 \, x^{2} + 23 \, x - 9\right )} e^{\left (x + 20\right )} - 252 \, x + 81}\right )\right ) \]
integrate((((3*x^2-6*x+3)*exp(20+x)+3*x^3-17*x^2+23*x-9)*log((36*x^2-72*x+ 36)/((9*x^2-18*x+9)*exp(20+x)^2+(18*x^3-102*x^2+138*x-54)*exp(20+x)+9*x^4- 84*x^3+250*x^2-252*x+81))+(-6*x^2+12*x-6)*exp(20+x)-6*x^2+12*x-10)/((3*x^2 -6*x+3)*exp(20+x)+3*x^3-17*x^2+23*x-9)/log((36*x^2-72*x+36)/((9*x^2-18*x+9 )*exp(20+x)^2+(18*x^3-102*x^2+138*x-54)*exp(20+x)+9*x^4-84*x^3+250*x^2-252 *x+81)),x, algorithm=\
x + log(log(36*(x^2 - 2*x + 1)/(9*x^4 - 84*x^3 + 250*x^2 + 9*(x^2 - 2*x + 1)*e^(2*x + 40) + 6*(3*x^3 - 17*x^2 + 23*x - 9)*e^(x + 20) - 252*x + 81)))
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (22) = 44\).
Time = 0.63 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.63 \[ \int \frac {-10+12 x-6 x^2+e^{20+x} \left (-6+12 x-6 x^2\right )+\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )}{\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )} \, dx=x + \log {\left (\log {\left (\frac {36 x^{2} - 72 x + 36}{9 x^{4} - 84 x^{3} + 250 x^{2} - 252 x + \left (9 x^{2} - 18 x + 9\right ) e^{2 x + 40} + \left (18 x^{3} - 102 x^{2} + 138 x - 54\right ) e^{x + 20} + 81} \right )} \right )} \]
integrate((((3*x**2-6*x+3)*exp(20+x)+3*x**3-17*x**2+23*x-9)*ln((36*x**2-72 *x+36)/((9*x**2-18*x+9)*exp(20+x)**2+(18*x**3-102*x**2+138*x-54)*exp(20+x) +9*x**4-84*x**3+250*x**2-252*x+81))+(-6*x**2+12*x-6)*exp(20+x)-6*x**2+12*x -10)/((3*x**2-6*x+3)*exp(20+x)+3*x**3-17*x**2+23*x-9)/ln((36*x**2-72*x+36) /((9*x**2-18*x+9)*exp(20+x)**2+(18*x**3-102*x**2+138*x-54)*exp(20+x)+9*x** 4-84*x**3+250*x**2-252*x+81)),x)
x + log(log((36*x**2 - 72*x + 36)/(9*x**4 - 84*x**3 + 250*x**2 - 252*x + ( 9*x**2 - 18*x + 9)*exp(2*x + 40) + (18*x**3 - 102*x**2 + 138*x - 54)*exp(x + 20) + 81)))
Time = 7.16 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.56 \[ \int \frac {-10+12 x-6 x^2+e^{20+x} \left (-6+12 x-6 x^2\right )+\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )}{\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )} \, dx=x + \log \left (-\log \left (3\right ) - \log \left (2\right ) + \log \left (3 \, x^{2} + 3 \, {\left (x e^{20} - e^{20}\right )} e^{x} - 14 \, x + 9\right ) - \log \left (x - 1\right )\right ) \]
integrate((((3*x^2-6*x+3)*exp(20+x)+3*x^3-17*x^2+23*x-9)*log((36*x^2-72*x+ 36)/((9*x^2-18*x+9)*exp(20+x)^2+(18*x^3-102*x^2+138*x-54)*exp(20+x)+9*x^4- 84*x^3+250*x^2-252*x+81))+(-6*x^2+12*x-6)*exp(20+x)-6*x^2+12*x-10)/((3*x^2 -6*x+3)*exp(20+x)+3*x^3-17*x^2+23*x-9)/log((36*x^2-72*x+36)/((9*x^2-18*x+9 )*exp(20+x)^2+(18*x^3-102*x^2+138*x-54)*exp(20+x)+9*x^4-84*x^3+250*x^2-252 *x+81)),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 97 vs. \(2 (28) = 56\).
Time = 5.63 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.59 \[ \int \frac {-10+12 x-6 x^2+e^{20+x} \left (-6+12 x-6 x^2\right )+\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )}{\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )} \, dx=x + \log \left (-\log \left (9 \, x^{4} + 18 \, x^{3} e^{\left (x + 20\right )} - 84 \, x^{3} + 9 \, x^{2} e^{\left (2 \, x + 40\right )} - 102 \, x^{2} e^{\left (x + 20\right )} + 250 \, x^{2} - 18 \, x e^{\left (2 \, x + 40\right )} + 138 \, x e^{\left (x + 20\right )} - 252 \, x + 9 \, e^{\left (2 \, x + 40\right )} - 54 \, e^{\left (x + 20\right )} + 81\right ) + \log \left (36 \, x^{2} - 72 \, x + 36\right )\right ) \]
integrate((((3*x^2-6*x+3)*exp(20+x)+3*x^3-17*x^2+23*x-9)*log((36*x^2-72*x+ 36)/((9*x^2-18*x+9)*exp(20+x)^2+(18*x^3-102*x^2+138*x-54)*exp(20+x)+9*x^4- 84*x^3+250*x^2-252*x+81))+(-6*x^2+12*x-6)*exp(20+x)-6*x^2+12*x-10)/((3*x^2 -6*x+3)*exp(20+x)+3*x^3-17*x^2+23*x-9)/log((36*x^2-72*x+36)/((9*x^2-18*x+9 )*exp(20+x)^2+(18*x^3-102*x^2+138*x-54)*exp(20+x)+9*x^4-84*x^3+250*x^2-252 *x+81)),x, algorithm=\
x + log(-log(9*x^4 + 18*x^3*e^(x + 20) - 84*x^3 + 9*x^2*e^(2*x + 40) - 102 *x^2*e^(x + 20) + 250*x^2 - 18*x*e^(2*x + 40) + 138*x*e^(x + 20) - 252*x + 9*e^(2*x + 40) - 54*e^(x + 20) + 81) + log(36*x^2 - 72*x + 36))
Time = 10.03 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.74 \[ \int \frac {-10+12 x-6 x^2+e^{20+x} \left (-6+12 x-6 x^2\right )+\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )}{\left (-9+23 x-17 x^2+3 x^3+e^{20+x} \left (3-6 x+3 x^2\right )\right ) \log \left (\frac {36-72 x+36 x^2}{81-252 x+250 x^2-84 x^3+9 x^4+e^{40+2 x} \left (9-18 x+9 x^2\right )+e^{20+x} \left (-54+138 x-102 x^2+18 x^3\right )}\right )} \, dx=x+\ln \left (\ln \left (\frac {36\,x^2-72\,x+36}{250\,x^2-252\,x-84\,x^3+9\,x^4+{\mathrm {e}}^{20}\,{\mathrm {e}}^x\,\left (18\,x^3-102\,x^2+138\,x-54\right )+{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{40}\,\left (9\,x^2-18\,x+9\right )+81}\right )\right ) \]
int(-(exp(x + 20)*(6*x^2 - 12*x + 6) - 12*x - log((36*x^2 - 72*x + 36)/(ex p(x + 20)*(138*x - 102*x^2 + 18*x^3 - 54) - 252*x + exp(2*x + 40)*(9*x^2 - 18*x + 9) + 250*x^2 - 84*x^3 + 9*x^4 + 81))*(23*x + exp(x + 20)*(3*x^2 - 6*x + 3) - 17*x^2 + 3*x^3 - 9) + 6*x^2 + 10)/(log((36*x^2 - 72*x + 36)/(ex p(x + 20)*(138*x - 102*x^2 + 18*x^3 - 54) - 252*x + exp(2*x + 40)*(9*x^2 - 18*x + 9) + 250*x^2 - 84*x^3 + 9*x^4 + 81))*(23*x + exp(x + 20)*(3*x^2 - 6*x + 3) - 17*x^2 + 3*x^3 - 9)),x)