Integrand size = 507, antiderivative size = 33 \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\frac {2 \log \left (1+5 \left (-2+e^x\right )\right )}{x \left (-x+\left (x+\log \left (e^3-x\right )\right )^2\right )} \] Output:
ln(5*exp(x)-9)/x/(1/2*(ln(-x+exp(3))+x)^2-1/2*x)
Time = 0.15 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.30 \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\frac {2 \log \left (-9+5 e^x\right )}{x \left (-x+x^2+2 x \log \left (e^3-x\right )+\log ^2\left (e^3-x\right )\right )} \] Input:
Integrate[(E^x*(10*x^3 - 10*x^4 + E^3*(-10*x^2 + 10*x^3)) + E^x*(20*E^3*x^ 2 - 20*x^3)*Log[E^3 - x] + E^x*(10*E^3*x - 10*x^2)*Log[E^3 - x]^2 + Log[-9 + 5*E^x]*(-54*x^3 + E^3*(-36*x + 54*x^2) + E^x*(30*x^3 + E^3*(20*x - 30*x ^2)) + (-36*x + 72*E^3*x - 72*x^2 + E^x*(20*x - 40*E^3*x + 40*x^2))*Log[E^ 3 - x] + (18*E^3 - 18*x + E^x*(-10*E^3 + 10*x))*Log[E^3 - x]^2))/(9*x^5 - 18*x^6 + 9*x^7 + E^3*(-9*x^4 + 18*x^5 - 9*x^6) + E^x*(-5*x^5 + 10*x^6 - 5* x^7 + E^3*(5*x^4 - 10*x^5 + 5*x^6)) + (-36*x^5 + 36*x^6 + E^3*(36*x^4 - 36 *x^5) + E^x*(20*x^5 - 20*x^6 + E^3*(-20*x^4 + 20*x^5)))*Log[E^3 - x] + (-1 8*x^4 + 54*x^5 + E^3*(18*x^3 - 54*x^4) + E^x*(10*x^4 - 30*x^5 + E^3*(-10*x ^3 + 30*x^4)))*Log[E^3 - x]^2 + (-36*E^3*x^3 + 36*x^4 + E^x*(20*E^3*x^3 - 20*x^4))*Log[E^3 - x]^3 + (-9*E^3*x^2 + 9*x^3 + E^x*(5*E^3*x^2 - 5*x^3))*L og[E^3 - x]^4),x]
Output:
(2*Log[-9 + 5*E^x])/(x*(-x + x^2 + 2*x*Log[E^3 - x] + Log[E^3 - x]^2))
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.
| \(\displaystyle \int \frac {e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (5 e^x-9\right ) \left (-54 x^3+e^3 \left (54 x^2-36 x\right )+\left (-72 x^2+e^x \left (40 x^2-40 e^3 x+20 x\right )+72 e^3 x-36 x\right ) \log \left (e^3-x\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-18 x+e^x \left (10 x-10 e^3\right )+18 e^3\right ) \log ^2\left (e^3-x\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (-10 x^4+10 x^3+e^3 \left (10 x^3-10 x^2\right )\right )}{9 x^7-18 x^6+9 x^5+\left (36 x^4-36 e^3 x^3+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (9 x^3-9 e^3 x^2+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )+e^3 \left (-9 x^6+18 x^5-9 x^4\right )+\left (36 x^6-36 x^5+e^3 \left (36 x^4-36 x^5\right )+e^x \left (-20 x^6+20 x^5+e^3 \left (20 x^5-20 x^4\right )\right )\right ) \log \left (e^3-x\right )+\left (54 x^5-18 x^4+e^3 \left (18 x^3-54 x^4\right )+e^x \left (-30 x^5+10 x^4+e^3 \left (30 x^4-10 x^3\right )\right )\right ) \log ^2\left (e^3-x\right )+e^x \left (-5 x^7+10 x^6-5 x^5+e^3 \left (5 x^6-10 x^5+5 x^4\right )\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (\frac {5 e^x x \left ((x-1) x+\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )\right )}{5 e^x-9}-\frac {\log \left (5 e^x-9\right ) \left (-3 x^3+e^3 (3 x-2) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )-2 \left (2 x-2 e^3+1\right ) x \log \left (e^3-x\right )\right )}{e^3-x}\right )}{x^2 \left ((x-1) x+\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {\frac {5 e^x x \left (-\log ^2\left (e^3-x\right )-2 x \log \left (e^3-x\right )+(1-x) x\right )}{9-5 e^x}+\frac {\log \left (-9+5 e^x\right ) \left (3 x^3+e^3 (2-3 x) x+2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x-\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )}{e^3-x}}{x^2 \left (-\log ^2\left (e^3-x\right )-2 x \log \left (e^3-x\right )+(1-x) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {-x^4+3 \log \left (-9+5 e^x\right ) x^3-2 \log \left (e^3-x\right ) x^3+\left (1+e^3\right ) x^3-\log ^2\left (e^3-x\right ) x^2-3 e^3 \log \left (-9+5 e^x\right ) x^2+4 \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x^2+2 e^3 \log \left (e^3-x\right ) x^2-e^3 x^2+\log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right ) x+e^3 \log ^2\left (e^3-x\right ) x+2 e^3 \log \left (-9+5 e^x\right ) x+2 \left (1-2 e^3\right ) \log \left (-9+5 e^x\right ) \log \left (e^3-x\right ) x-e^3 \log \left (-9+5 e^x\right ) \log ^2\left (e^3-x\right )}{\left (e^3-x\right ) x^2 \left (-x^2-2 \log \left (e^3-x\right ) x+x-\log ^2\left (e^3-x\right )\right )^2}+\frac {9}{\left (-9+5 e^x\right ) x \left (x^2+2 \log \left (e^3-x\right ) x-x+\log ^2\left (e^3-x\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-9+5 e^x\right ) \log \left (-9+5 e^x\right ) \left (-3 x^3+e^3 (3 x-2) x-2 \left (2 x-2 e^3+1\right ) \log \left (e^3-x\right ) x+\left (e^3-x\right ) \log ^2\left (e^3-x\right )\right )-5 e^x \left (e^3-x\right ) x \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )}{\left (9-5 e^x\right ) \left (e^3-x\right ) x^2 \left (\log ^2\left (e^3-x\right )+2 x \log \left (e^3-x\right )+(x-1) x\right )^2}dx\) |
Input:
Int[(E^x*(10*x^3 - 10*x^4 + E^3*(-10*x^2 + 10*x^3)) + E^x*(20*E^3*x^2 - 20 *x^3)*Log[E^3 - x] + E^x*(10*E^3*x - 10*x^2)*Log[E^3 - x]^2 + Log[-9 + 5*E ^x]*(-54*x^3 + E^3*(-36*x + 54*x^2) + E^x*(30*x^3 + E^3*(20*x - 30*x^2)) + (-36*x + 72*E^3*x - 72*x^2 + E^x*(20*x - 40*E^3*x + 40*x^2))*Log[E^3 - x] + (18*E^3 - 18*x + E^x*(-10*E^3 + 10*x))*Log[E^3 - x]^2))/(9*x^5 - 18*x^6 + 9*x^7 + E^3*(-9*x^4 + 18*x^5 - 9*x^6) + E^x*(-5*x^5 + 10*x^6 - 5*x^7 + E^3*(5*x^4 - 10*x^5 + 5*x^6)) + (-36*x^5 + 36*x^6 + E^3*(36*x^4 - 36*x^5) + E^x*(20*x^5 - 20*x^6 + E^3*(-20*x^4 + 20*x^5)))*Log[E^3 - x] + (-18*x^4 + 54*x^5 + E^3*(18*x^3 - 54*x^4) + E^x*(10*x^4 - 30*x^5 + E^3*(-10*x^3 + 3 0*x^4)))*Log[E^3 - x]^2 + (-36*E^3*x^3 + 36*x^4 + E^x*(20*E^3*x^3 - 20*x^4 ))*Log[E^3 - x]^3 + (-9*E^3*x^2 + 9*x^3 + E^x*(5*E^3*x^2 - 5*x^3))*Log[E^3 - x]^4),x]
Output:
$Aborted
Time = 0.07 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.24
\[\frac {2 \ln \left (5 \,{\mathrm e}^{x}-9\right )}{x \left (x^{2}+2 \ln \left (-x +{\mathrm e}^{3}\right ) x +\ln \left (-x +{\mathrm e}^{3}\right )^{2}-x \right )}\]
Input:
int(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*ln(-x+exp(3))^2+((-40*x*ex p(3)+40*x^2+20*x)*exp(x)+72*x*exp(3)-72*x^2-36*x)*ln(-x+exp(3))+((-30*x^2+ 20*x)*exp(3)+30*x^3)*exp(x)+(54*x^2-36*x)*exp(3)-54*x^3)*ln(5*exp(x)-9)+(1 0*x*exp(3)-10*x^2)*exp(x)*ln(-x+exp(3))^2+(20*x^2*exp(3)-20*x^3)*exp(x)*ln (-x+exp(3))+((10*x^3-10*x^2)*exp(3)-10*x^4+10*x^3)*exp(x))/(((5*x^2*exp(3) -5*x^3)*exp(x)-9*x^2*exp(3)+9*x^3)*ln(-x+exp(3))^4+((20*x^3*exp(3)-20*x^4) *exp(x)-36*x^3*exp(3)+36*x^4)*ln(-x+exp(3))^3+(((30*x^4-10*x^3)*exp(3)-30* x^5+10*x^4)*exp(x)+(-54*x^4+18*x^3)*exp(3)+54*x^5-18*x^4)*ln(-x+exp(3))^2+ (((20*x^5-20*x^4)*exp(3)-20*x^6+20*x^5)*exp(x)+(-36*x^5+36*x^4)*exp(3)+36* x^6-36*x^5)*ln(-x+exp(3))+((5*x^6-10*x^5+5*x^4)*exp(3)-5*x^7+10*x^6-5*x^5) *exp(x)+(-9*x^6+18*x^5-9*x^4)*exp(3)+9*x^7-18*x^6+9*x^5),x)
Output:
2/x/(x^2+2*ln(-x+exp(3))*x+ln(-x+exp(3))^2-x)*ln(5*exp(x)-9)
Time = 0.10 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.30 \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\frac {2 \, \log \left (5 \, e^{x} - 9\right )}{x^{3} + 2 \, x^{2} \log \left (-x + e^{3}\right ) + x \log \left (-x + e^{3}\right )^{2} - x^{2}} \] Input:
integrate(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*log(-x+exp(3))^2+((- 40*x*exp(3)+40*x^2+20*x)*exp(x)+72*x*exp(3)-72*x^2-36*x)*log(-x+exp(3))+(( -30*x^2+20*x)*exp(3)+30*x^3)*exp(x)+(54*x^2-36*x)*exp(3)-54*x^3)*log(5*exp (x)-9)+(10*x*exp(3)-10*x^2)*exp(x)*log(-x+exp(3))^2+(20*x^2*exp(3)-20*x^3) *exp(x)*log(-x+exp(3))+((10*x^3-10*x^2)*exp(3)-10*x^4+10*x^3)*exp(x))/(((5 *x^2*exp(3)-5*x^3)*exp(x)-9*x^2*exp(3)+9*x^3)*log(-x+exp(3))^4+((20*x^3*ex p(3)-20*x^4)*exp(x)-36*x^3*exp(3)+36*x^4)*log(-x+exp(3))^3+(((30*x^4-10*x^ 3)*exp(3)-30*x^5+10*x^4)*exp(x)+(-54*x^4+18*x^3)*exp(3)+54*x^5-18*x^4)*log (-x+exp(3))^2+(((20*x^5-20*x^4)*exp(3)-20*x^6+20*x^5)*exp(x)+(-36*x^5+36*x ^4)*exp(3)+36*x^6-36*x^5)*log(-x+exp(3))+((5*x^6-10*x^5+5*x^4)*exp(3)-5*x^ 7+10*x^6-5*x^5)*exp(x)+(-9*x^6+18*x^5-9*x^4)*exp(3)+9*x^7-18*x^6+9*x^5),x, algorithm="fricas")
Output:
2*log(5*e^x - 9)/(x^3 + 2*x^2*log(-x + e^3) + x*log(-x + e^3)^2 - x^2)
Exception generated. \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*ln(-x+exp(3))**2+((- 40*x*exp(3)+40*x**2+20*x)*exp(x)+72*x*exp(3)-72*x**2-36*x)*ln(-x+exp(3))+( (-30*x**2+20*x)*exp(3)+30*x**3)*exp(x)+(54*x**2-36*x)*exp(3)-54*x**3)*ln(5 *exp(x)-9)+(10*x*exp(3)-10*x**2)*exp(x)*ln(-x+exp(3))**2+(20*x**2*exp(3)-2 0*x**3)*exp(x)*ln(-x+exp(3))+((10*x**3-10*x**2)*exp(3)-10*x**4+10*x**3)*ex p(x))/(((5*x**2*exp(3)-5*x**3)*exp(x)-9*x**2*exp(3)+9*x**3)*ln(-x+exp(3))* *4+((20*x**3*exp(3)-20*x**4)*exp(x)-36*x**3*exp(3)+36*x**4)*ln(-x+exp(3))* *3+(((30*x**4-10*x**3)*exp(3)-30*x**5+10*x**4)*exp(x)+(-54*x**4+18*x**3)*e xp(3)+54*x**5-18*x**4)*ln(-x+exp(3))**2+(((20*x**5-20*x**4)*exp(3)-20*x**6 +20*x**5)*exp(x)+(-36*x**5+36*x**4)*exp(3)+36*x**6-36*x**5)*ln(-x+exp(3))+ ((5*x**6-10*x**5+5*x**4)*exp(3)-5*x**7+10*x**6-5*x**5)*exp(x)+(-9*x**6+18* x**5-9*x**4)*exp(3)+9*x**7-18*x**6+9*x**5),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
Time = 0.30 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.30 \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\frac {2 \, \log \left (5 \, e^{x} - 9\right )}{x^{3} + 2 \, x^{2} \log \left (-x + e^{3}\right ) + x \log \left (-x + e^{3}\right )^{2} - x^{2}} \] Input:
integrate(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*log(-x+exp(3))^2+((- 40*x*exp(3)+40*x^2+20*x)*exp(x)+72*x*exp(3)-72*x^2-36*x)*log(-x+exp(3))+(( -30*x^2+20*x)*exp(3)+30*x^3)*exp(x)+(54*x^2-36*x)*exp(3)-54*x^3)*log(5*exp (x)-9)+(10*x*exp(3)-10*x^2)*exp(x)*log(-x+exp(3))^2+(20*x^2*exp(3)-20*x^3) *exp(x)*log(-x+exp(3))+((10*x^3-10*x^2)*exp(3)-10*x^4+10*x^3)*exp(x))/(((5 *x^2*exp(3)-5*x^3)*exp(x)-9*x^2*exp(3)+9*x^3)*log(-x+exp(3))^4+((20*x^3*ex p(3)-20*x^4)*exp(x)-36*x^3*exp(3)+36*x^4)*log(-x+exp(3))^3+(((30*x^4-10*x^ 3)*exp(3)-30*x^5+10*x^4)*exp(x)+(-54*x^4+18*x^3)*exp(3)+54*x^5-18*x^4)*log (-x+exp(3))^2+(((20*x^5-20*x^4)*exp(3)-20*x^6+20*x^5)*exp(x)+(-36*x^5+36*x ^4)*exp(3)+36*x^6-36*x^5)*log(-x+exp(3))+((5*x^6-10*x^5+5*x^4)*exp(3)-5*x^ 7+10*x^6-5*x^5)*exp(x)+(-9*x^6+18*x^5-9*x^4)*exp(3)+9*x^7-18*x^6+9*x^5),x, algorithm="maxima")
Output:
2*log(5*e^x - 9)/(x^3 + 2*x^2*log(-x + e^3) + x*log(-x + e^3)^2 - x^2)
Timed out. \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\text {Timed out} \] Input:
integrate(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*log(-x+exp(3))^2+((- 40*x*exp(3)+40*x^2+20*x)*exp(x)+72*x*exp(3)-72*x^2-36*x)*log(-x+exp(3))+(( -30*x^2+20*x)*exp(3)+30*x^3)*exp(x)+(54*x^2-36*x)*exp(3)-54*x^3)*log(5*exp (x)-9)+(10*x*exp(3)-10*x^2)*exp(x)*log(-x+exp(3))^2+(20*x^2*exp(3)-20*x^3) *exp(x)*log(-x+exp(3))+((10*x^3-10*x^2)*exp(3)-10*x^4+10*x^3)*exp(x))/(((5 *x^2*exp(3)-5*x^3)*exp(x)-9*x^2*exp(3)+9*x^3)*log(-x+exp(3))^4+((20*x^3*ex p(3)-20*x^4)*exp(x)-36*x^3*exp(3)+36*x^4)*log(-x+exp(3))^3+(((30*x^4-10*x^ 3)*exp(3)-30*x^5+10*x^4)*exp(x)+(-54*x^4+18*x^3)*exp(3)+54*x^5-18*x^4)*log (-x+exp(3))^2+(((20*x^5-20*x^4)*exp(3)-20*x^6+20*x^5)*exp(x)+(-36*x^5+36*x ^4)*exp(3)+36*x^6-36*x^5)*log(-x+exp(3))+((5*x^6-10*x^5+5*x^4)*exp(3)-5*x^ 7+10*x^6-5*x^5)*exp(x)+(-9*x^6+18*x^5-9*x^4)*exp(3)+9*x^7-18*x^6+9*x^5),x, algorithm="giac")
Output:
Timed out
Time = 3.62 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.21 \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\frac {2\,\ln \left (5\,{\mathrm {e}}^x-9\right )}{x\,\left (x^2+2\,x\,\ln \left ({\mathrm {e}}^3-x\right )-x+{\ln \left ({\mathrm {e}}^3-x\right )}^2\right )} \] Input:
int(-(log(5*exp(x) - 9)*(exp(3)*(36*x - 54*x^2) - exp(x)*(exp(3)*(20*x - 3 0*x^2) + 30*x^3) + 54*x^3 + log(exp(3) - x)*(36*x - 72*x*exp(3) + 72*x^2 - exp(x)*(20*x - 40*x*exp(3) + 40*x^2)) - log(exp(3) - x)^2*(18*exp(3) - 18 *x + exp(x)*(10*x - 10*exp(3)))) + exp(x)*(exp(3)*(10*x^2 - 10*x^3) - 10*x ^3 + 10*x^4) - log(exp(3) - x)^2*exp(x)*(10*x*exp(3) - 10*x^2) - log(exp(3 ) - x)*exp(x)*(20*x^2*exp(3) - 20*x^3))/(exp(x)*(exp(3)*(5*x^4 - 10*x^5 + 5*x^6) - 5*x^5 + 10*x^6 - 5*x^7) + log(exp(3) - x)*(exp(3)*(36*x^4 - 36*x^ 5) - exp(x)*(exp(3)*(20*x^4 - 20*x^5) - 20*x^5 + 20*x^6) - 36*x^5 + 36*x^6 ) + log(exp(3) - x)^4*(exp(x)*(5*x^2*exp(3) - 5*x^3) - 9*x^2*exp(3) + 9*x^ 3) + log(exp(3) - x)^3*(exp(x)*(20*x^3*exp(3) - 20*x^4) - 36*x^3*exp(3) + 36*x^4) + log(exp(3) - x)^2*(exp(3)*(18*x^3 - 54*x^4) - exp(x)*(exp(3)*(10 *x^3 - 30*x^4) - 10*x^4 + 30*x^5) - 18*x^4 + 54*x^5) - exp(3)*(9*x^4 - 18* x^5 + 9*x^6) + 9*x^5 - 18*x^6 + 9*x^7),x)
Output:
(2*log(5*exp(x) - 9))/(x*(log(exp(3) - x)^2 - x + x^2 + 2*x*log(exp(3) - x )))
Time = 0.27 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.30 \[ \int \frac {e^x \left (10 x^3-10 x^4+e^3 \left (-10 x^2+10 x^3\right )\right )+e^x \left (20 e^3 x^2-20 x^3\right ) \log \left (e^3-x\right )+e^x \left (10 e^3 x-10 x^2\right ) \log ^2\left (e^3-x\right )+\log \left (-9+5 e^x\right ) \left (-54 x^3+e^3 \left (-36 x+54 x^2\right )+e^x \left (30 x^3+e^3 \left (20 x-30 x^2\right )\right )+\left (-36 x+72 e^3 x-72 x^2+e^x \left (20 x-40 e^3 x+40 x^2\right )\right ) \log \left (e^3-x\right )+\left (18 e^3-18 x+e^x \left (-10 e^3+10 x\right )\right ) \log ^2\left (e^3-x\right )\right )}{9 x^5-18 x^6+9 x^7+e^3 \left (-9 x^4+18 x^5-9 x^6\right )+e^x \left (-5 x^5+10 x^6-5 x^7+e^3 \left (5 x^4-10 x^5+5 x^6\right )\right )+\left (-36 x^5+36 x^6+e^3 \left (36 x^4-36 x^5\right )+e^x \left (20 x^5-20 x^6+e^3 \left (-20 x^4+20 x^5\right )\right )\right ) \log \left (e^3-x\right )+\left (-18 x^4+54 x^5+e^3 \left (18 x^3-54 x^4\right )+e^x \left (10 x^4-30 x^5+e^3 \left (-10 x^3+30 x^4\right )\right )\right ) \log ^2\left (e^3-x\right )+\left (-36 e^3 x^3+36 x^4+e^x \left (20 e^3 x^3-20 x^4\right )\right ) \log ^3\left (e^3-x\right )+\left (-9 e^3 x^2+9 x^3+e^x \left (5 e^3 x^2-5 x^3\right )\right ) \log ^4\left (e^3-x\right )} \, dx=\frac {2 \,\mathrm {log}\left (5 e^{x}-9\right )}{x \left (\mathrm {log}\left (e^{3}-x \right )^{2}+2 \,\mathrm {log}\left (e^{3}-x \right ) x +x^{2}-x \right )} \] Input:
int(((((-10*exp(3)+10*x)*exp(x)+18*exp(3)-18*x)*log(-x+exp(3))^2+((-40*x*e xp(3)+40*x^2+20*x)*exp(x)+72*x*exp(3)-72*x^2-36*x)*log(-x+exp(3))+((-30*x^ 2+20*x)*exp(3)+30*x^3)*exp(x)+(54*x^2-36*x)*exp(3)-54*x^3)*log(5*exp(x)-9) +(10*x*exp(3)-10*x^2)*exp(x)*log(-x+exp(3))^2+(20*x^2*exp(3)-20*x^3)*exp(x )*log(-x+exp(3))+((10*x^3-10*x^2)*exp(3)-10*x^4+10*x^3)*exp(x))/(((5*x^2*e xp(3)-5*x^3)*exp(x)-9*x^2*exp(3)+9*x^3)*log(-x+exp(3))^4+((20*x^3*exp(3)-2 0*x^4)*exp(x)-36*x^3*exp(3)+36*x^4)*log(-x+exp(3))^3+(((30*x^4-10*x^3)*exp (3)-30*x^5+10*x^4)*exp(x)+(-54*x^4+18*x^3)*exp(3)+54*x^5-18*x^4)*log(-x+ex p(3))^2+(((20*x^5-20*x^4)*exp(3)-20*x^6+20*x^5)*exp(x)+(-36*x^5+36*x^4)*ex p(3)+36*x^6-36*x^5)*log(-x+exp(3))+((5*x^6-10*x^5+5*x^4)*exp(3)-5*x^7+10*x ^6-5*x^5)*exp(x)+(-9*x^6+18*x^5-9*x^4)*exp(3)+9*x^7-18*x^6+9*x^5),x)
Output:
(2*log(5*e**x - 9))/(x*(log(e**3 - x)**2 + 2*log(e**3 - x)*x + x**2 - x))