Integrand size = 178, antiderivative size = 30 \[ \int \frac {34 x^2+15 x^3+e^{2 x} \left (-36+51 x+18 x^2\right )+e^x \left (18 x-66 x^2-18 x^3\right )+\left (-9 x^2-6 x^3+e^{2 x} \left (9-18 x-6 x^2\right )+e^x \left (24 x^2+6 x^3\right )\right ) \log (x)}{-43 x^3-9 x^4+e^{2 x} \left (-27 x-9 x^2\right )+e^x \left (54 x^2+18 x^3\right )+\left (9 x^3+3 x^4+e^{2 x} \left (9 x+3 x^2\right )+e^x \left (-18 x^2-6 x^3\right )\right ) \log (x)} \, dx=\log \left (\frac {1}{x+\frac {3 \left (e^x-x\right )^2 (3+x) (3-\log (x))}{16 x}}\right ) \] Output:
ln(1/(x+3/4*(3-ln(x))*(3+x)*(exp(x)-x)*(1/4*exp(x)-1/4*x)/x))
Leaf count is larger than twice the leaf count of optimal. \(97\) vs. \(2(30)=60\).
Time = 0.15 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.23 \[ \int \frac {34 x^2+15 x^3+e^{2 x} \left (-36+51 x+18 x^2\right )+e^x \left (18 x-66 x^2-18 x^3\right )+\left (-9 x^2-6 x^3+e^{2 x} \left (9-18 x-6 x^2\right )+e^x \left (24 x^2+6 x^3\right )\right ) \log (x)}{-43 x^3-9 x^4+e^{2 x} \left (-27 x-9 x^2\right )+e^x \left (54 x^2+18 x^3\right )+\left (9 x^3+3 x^4+e^{2 x} \left (9 x+3 x^2\right )+e^x \left (-18 x^2-6 x^3\right )\right ) \log (x)} \, dx=\log (x)-\log \left (-27 e^{2 x}+54 e^x x-9 e^{2 x} x-43 x^2+18 e^x x^2-9 x^3+9 e^{2 x} \log (x)-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 x^2 \log (x)-6 e^x x^2 \log (x)+3 x^3 \log (x)\right ) \] Input:
Integrate[(34*x^2 + 15*x^3 + E^(2*x)*(-36 + 51*x + 18*x^2) + E^x*(18*x - 6 6*x^2 - 18*x^3) + (-9*x^2 - 6*x^3 + E^(2*x)*(9 - 18*x - 6*x^2) + E^x*(24*x ^2 + 6*x^3))*Log[x])/(-43*x^3 - 9*x^4 + E^(2*x)*(-27*x - 9*x^2) + E^x*(54* x^2 + 18*x^3) + (9*x^3 + 3*x^4 + E^(2*x)*(9*x + 3*x^2) + E^x*(-18*x^2 - 6* x^3))*Log[x]),x]
Output:
Log[x] - Log[-27*E^(2*x) + 54*E^x*x - 9*E^(2*x)*x - 43*x^2 + 18*E^x*x^2 - 9*x^3 + 9*E^(2*x)*Log[x] - 18*E^x*x*Log[x] + 3*E^(2*x)*x*Log[x] + 9*x^2*Lo g[x] - 6*E^x*x^2*Log[x] + 3*x^3*Log[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.
| \(\displaystyle \int \frac {15 x^3+34 x^2+e^{2 x} \left (18 x^2+51 x-36\right )+e^x \left (-18 x^3-66 x^2+18 x\right )+\left (-6 x^3-9 x^2+e^{2 x} \left (-6 x^2-18 x+9\right )+e^x \left (6 x^3+24 x^2\right )\right ) \log (x)}{-9 x^4-43 x^3+e^{2 x} \left (-9 x^2-27 x\right )+e^x \left (18 x^3+54 x^2\right )+\left (3 x^4+9 x^3+e^{2 x} \left (3 x^2+9 x\right )+e^x \left (-6 x^3-18 x^2\right )\right ) \log (x)} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2-2 x^2 \log (x)+17 x-6 x \log (x)+3 \log (x)-12}{x (x+3) (\log (x)-3)}+\frac {2 \left (27 x^4+3 x^4 \log ^2(x)-18 x^4 \log (x)-27 e^x x^3+183 x^3-3 e^x x^3 \log ^2(x)+15 x^3 \log ^2(x)+18 e^x x^3 \log (x)-106 x^3 \log (x)-135 e^x x^2+193 x^2-15 e^x x^2 \log ^2(x)+9 x^2 \log ^2(x)+90 e^x x^2 \log (x)-94 x^2 \log (x)-81 e^x x-411 x+243 e^x-9 e^x x \log ^2(x)-27 x \log ^2(x)+27 e^x \log ^2(x)+54 e^x x \log (x)+210 x \log (x)-162 e^x \log (x)\right )}{(x+3) (\log (x)-3) \left (-9 x^3+3 x^3 \log (x)+18 e^x x^2-43 x^2-6 e^x x^2 \log (x)+9 x^2 \log (x)+54 e^x x-9 e^{2 x} x-27 e^{2 x}-18 e^x x \log (x)+3 e^{2 x} x \log (x)+9 e^{2 x} \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left ((15 x+34) x^2\right )+6 e^x \left (3 x^2+11 x-3\right ) x-3 e^{2 x} \left (6 x^2+17 x-12\right )+3 \left (-2 e^x (x+4) x^2+(2 x+3) x^2+e^{2 x} \left (2 x^2+6 x-3\right )\right ) \log (x)}{x \left (x^2 (9 x+43)+9 e^{2 x} (x+3)-18 e^x x (x+3)-3 (x+3) \left (e^x-x\right )^2 \log (x)\right )}dx\) |
Input:
Int[(34*x^2 + 15*x^3 + E^(2*x)*(-36 + 51*x + 18*x^2) + E^x*(18*x - 66*x^2 - 18*x^3) + (-9*x^2 - 6*x^3 + E^(2*x)*(9 - 18*x - 6*x^2) + E^x*(24*x^2 + 6 *x^3))*Log[x])/(-43*x^3 - 9*x^4 + E^(2*x)*(-27*x - 9*x^2) + E^x*(54*x^2 + 18*x^3) + (9*x^3 + 3*x^4 + E^(2*x)*(9*x + 3*x^2) + E^x*(-18*x^2 - 6*x^3))* Log[x]),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(87\) vs. \(2(33)=66\).
Time = 61.58 (sec) , antiderivative size = 88, normalized size of antiderivative = 2.93
| method | result | size |
| parallelrisch | \(-\ln \left (x^{3} \ln \left (x \right )-2 x^{2} {\mathrm e}^{x} \ln \left (x \right )+\ln \left (x \right ) {\mathrm e}^{2 x} x -3 x^{3}+3 x^{2} \ln \left (x \right )+6 \,{\mathrm e}^{x} x^{2}-6 x \,{\mathrm e}^{x} \ln \left (x \right )-3 x \,{\mathrm e}^{2 x}+3 \ln \left (x \right ) {\mathrm e}^{2 x}-\frac {43 x^{2}}{3}+18 \,{\mathrm e}^{x} x -9 \,{\mathrm e}^{2 x}\right )+\ln \left (x \right )\) | \(88\) |
| risch | \(\ln \left (x \right )-\ln \left (3+x \right )-2 \ln \left ({\mathrm e}^{x}-x \right )-\ln \left (\ln \left (x \right )-\frac {9 x^{3}-18 \,{\mathrm e}^{x} x^{2}+9 x \,{\mathrm e}^{2 x}+43 x^{2}-54 \,{\mathrm e}^{x} x +27 \,{\mathrm e}^{2 x}}{3 \left (x^{3}-2 \,{\mathrm e}^{x} x^{2}+x \,{\mathrm e}^{2 x}+3 x^{2}-6 \,{\mathrm e}^{x} x +3 \,{\mathrm e}^{2 x}\right )}\right )\) | \(98\) |
Input:
int((((-6*x^2-18*x+9)*exp(x)^2+(6*x^3+24*x^2)*exp(x)-6*x^3-9*x^2)*ln(x)+(1 8*x^2+51*x-36)*exp(x)^2+(-18*x^3-66*x^2+18*x)*exp(x)+15*x^3+34*x^2)/(((3*x ^2+9*x)*exp(x)^2+(-6*x^3-18*x^2)*exp(x)+3*x^4+9*x^3)*ln(x)+(-9*x^2-27*x)*e xp(x)^2+(18*x^3+54*x^2)*exp(x)-9*x^4-43*x^3),x,method=_RETURNVERBOSE)
Output:
-ln(x^3*ln(x)-2*x^2*exp(x)*ln(x)+x*exp(x)^2*ln(x)-3*x^3+3*x^2*ln(x)+6*exp( x)*x^2-6*x*exp(x)*ln(x)-3*x*exp(x)^2+3*exp(x)^2*ln(x)-43/3*x^2+18*exp(x)*x -9*exp(x)^2)+ln(x)
Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (29) = 58\).
Time = 0.08 (sec) , antiderivative size = 116, normalized size of antiderivative = 3.87 \[ \int \frac {34 x^2+15 x^3+e^{2 x} \left (-36+51 x+18 x^2\right )+e^x \left (18 x-66 x^2-18 x^3\right )+\left (-9 x^2-6 x^3+e^{2 x} \left (9-18 x-6 x^2\right )+e^x \left (24 x^2+6 x^3\right )\right ) \log (x)}{-43 x^3-9 x^4+e^{2 x} \left (-27 x-9 x^2\right )+e^x \left (54 x^2+18 x^3\right )+\left (9 x^3+3 x^4+e^{2 x} \left (9 x+3 x^2\right )+e^x \left (-18 x^2-6 x^3\right )\right ) \log (x)} \, dx=-\log \left (x + 3\right ) + \log \left (x\right ) - 2 \, \log \left (-x + e^{x}\right ) - \log \left (-\frac {9 \, x^{3} + 43 \, x^{2} + 9 \, {\left (x + 3\right )} e^{\left (2 \, x\right )} - 18 \, {\left (x^{2} + 3 \, x\right )} e^{x} - 3 \, {\left (x^{3} + 3 \, x^{2} + {\left (x + 3\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{2} + 3 \, x\right )} e^{x}\right )} \log \left (x\right )}{x^{3} + 3 \, x^{2} + {\left (x + 3\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{2} + 3 \, x\right )} e^{x}}\right ) \] Input:
integrate((((-6*x^2-18*x+9)*exp(x)^2+(6*x^3+24*x^2)*exp(x)-6*x^3-9*x^2)*lo g(x)+(18*x^2+51*x-36)*exp(x)^2+(-18*x^3-66*x^2+18*x)*exp(x)+15*x^3+34*x^2) /(((3*x^2+9*x)*exp(x)^2+(-6*x^3-18*x^2)*exp(x)+3*x^4+9*x^3)*log(x)+(-9*x^2 -27*x)*exp(x)^2+(18*x^3+54*x^2)*exp(x)-9*x^4-43*x^3),x, algorithm="fricas" )
Output:
-log(x + 3) + log(x) - 2*log(-x + e^x) - log(-(9*x^3 + 43*x^2 + 9*(x + 3)* e^(2*x) - 18*(x^2 + 3*x)*e^x - 3*(x^3 + 3*x^2 + (x + 3)*e^(2*x) - 2*(x^2 + 3*x)*e^x)*log(x))/(x^3 + 3*x^2 + (x + 3)*e^(2*x) - 2*(x^2 + 3*x)*e^x))
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (32) = 64\).
Time = 2.59 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.37 \[ \int \frac {34 x^2+15 x^3+e^{2 x} \left (-36+51 x+18 x^2\right )+e^x \left (18 x-66 x^2-18 x^3\right )+\left (-9 x^2-6 x^3+e^{2 x} \left (9-18 x-6 x^2\right )+e^x \left (24 x^2+6 x^3\right )\right ) \log (x)}{-43 x^3-9 x^4+e^{2 x} \left (-27 x-9 x^2\right )+e^x \left (54 x^2+18 x^3\right )+\left (9 x^3+3 x^4+e^{2 x} \left (9 x+3 x^2\right )+e^x \left (-18 x^2-6 x^3\right )\right ) \log (x)} \, dx=\log {\left (x \right )} - \log {\left (x + 3 \right )} - \log {\left (\log {\left (x \right )} - 3 \right )} - \log {\left (- 2 x e^{x} + e^{2 x} + \frac {3 x^{3} \log {\left (x \right )} - 9 x^{3} + 9 x^{2} \log {\left (x \right )} - 43 x^{2}}{3 x \log {\left (x \right )} - 9 x + 9 \log {\left (x \right )} - 27} \right )} \] Input:
integrate((((-6*x**2-18*x+9)*exp(x)**2+(6*x**3+24*x**2)*exp(x)-6*x**3-9*x* *2)*ln(x)+(18*x**2+51*x-36)*exp(x)**2+(-18*x**3-66*x**2+18*x)*exp(x)+15*x* *3+34*x**2)/(((3*x**2+9*x)*exp(x)**2+(-6*x**3-18*x**2)*exp(x)+3*x**4+9*x** 3)*ln(x)+(-9*x**2-27*x)*exp(x)**2+(18*x**3+54*x**2)*exp(x)-9*x**4-43*x**3) ,x)
Output:
log(x) - log(x + 3) - log(log(x) - 3) - log(-2*x*exp(x) + exp(2*x) + (3*x* *3*log(x) - 9*x**3 + 9*x**2*log(x) - 43*x**2)/(3*x*log(x) - 9*x + 9*log(x) - 27))
Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (29) = 58\).
Time = 0.12 (sec) , antiderivative size = 99, normalized size of antiderivative = 3.30 \[ \int \frac {34 x^2+15 x^3+e^{2 x} \left (-36+51 x+18 x^2\right )+e^x \left (18 x-66 x^2-18 x^3\right )+\left (-9 x^2-6 x^3+e^{2 x} \left (9-18 x-6 x^2\right )+e^x \left (24 x^2+6 x^3\right )\right ) \log (x)}{-43 x^3-9 x^4+e^{2 x} \left (-27 x-9 x^2\right )+e^x \left (54 x^2+18 x^3\right )+\left (9 x^3+3 x^4+e^{2 x} \left (9 x+3 x^2\right )+e^x \left (-18 x^2-6 x^3\right )\right ) \log (x)} \, dx=-\log \left (x + 3\right ) + \log \left (x\right ) - \log \left (-\frac {9 \, x^{3} + 43 \, x^{2} - 3 \, {\left ({\left (x + 3\right )} \log \left (x\right ) - 3 \, x - 9\right )} e^{\left (2 \, x\right )} - 6 \, {\left (3 \, x^{2} - {\left (x^{2} + 3 \, x\right )} \log \left (x\right ) + 9 \, x\right )} e^{x} - 3 \, {\left (x^{3} + 3 \, x^{2}\right )} \log \left (x\right )}{3 \, {\left ({\left (x + 3\right )} \log \left (x\right ) - 3 \, x - 9\right )}}\right ) - \log \left (\log \left (x\right ) - 3\right ) \] Input:
integrate((((-6*x^2-18*x+9)*exp(x)^2+(6*x^3+24*x^2)*exp(x)-6*x^3-9*x^2)*lo g(x)+(18*x^2+51*x-36)*exp(x)^2+(-18*x^3-66*x^2+18*x)*exp(x)+15*x^3+34*x^2) /(((3*x^2+9*x)*exp(x)^2+(-6*x^3-18*x^2)*exp(x)+3*x^4+9*x^3)*log(x)+(-9*x^2 -27*x)*exp(x)^2+(18*x^3+54*x^2)*exp(x)-9*x^4-43*x^3),x, algorithm="maxima" )
Output:
-log(x + 3) + log(x) - log(-1/3*(9*x^3 + 43*x^2 - 3*((x + 3)*log(x) - 3*x - 9)*e^(2*x) - 6*(3*x^2 - (x^2 + 3*x)*log(x) + 9*x)*e^x - 3*(x^3 + 3*x^2)* log(x))/((x + 3)*log(x) - 3*x - 9)) - log(log(x) - 3)
Leaf count of result is larger than twice the leaf count of optimal. 89 vs. \(2 (29) = 58\).
Time = 0.20 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.97 \[ \int \frac {34 x^2+15 x^3+e^{2 x} \left (-36+51 x+18 x^2\right )+e^x \left (18 x-66 x^2-18 x^3\right )+\left (-9 x^2-6 x^3+e^{2 x} \left (9-18 x-6 x^2\right )+e^x \left (24 x^2+6 x^3\right )\right ) \log (x)}{-43 x^3-9 x^4+e^{2 x} \left (-27 x-9 x^2\right )+e^x \left (54 x^2+18 x^3\right )+\left (9 x^3+3 x^4+e^{2 x} \left (9 x+3 x^2\right )+e^x \left (-18 x^2-6 x^3\right )\right ) \log (x)} \, dx=-\log \left (3 \, x^{3} \log \left (x\right ) - 6 \, x^{2} e^{x} \log \left (x\right ) - 9 \, x^{3} + 18 \, x^{2} e^{x} + 9 \, x^{2} \log \left (x\right ) + 3 \, x e^{\left (2 \, x\right )} \log \left (x\right ) - 18 \, x e^{x} \log \left (x\right ) - 43 \, x^{2} - 9 \, x e^{\left (2 \, x\right )} + 54 \, x e^{x} + 9 \, e^{\left (2 \, x\right )} \log \left (x\right ) - 27 \, e^{\left (2 \, x\right )}\right ) + \log \left (x\right ) \] Input:
integrate((((-6*x^2-18*x+9)*exp(x)^2+(6*x^3+24*x^2)*exp(x)-6*x^3-9*x^2)*lo g(x)+(18*x^2+51*x-36)*exp(x)^2+(-18*x^3-66*x^2+18*x)*exp(x)+15*x^3+34*x^2) /(((3*x^2+9*x)*exp(x)^2+(-6*x^3-18*x^2)*exp(x)+3*x^4+9*x^3)*log(x)+(-9*x^2 -27*x)*exp(x)^2+(18*x^3+54*x^2)*exp(x)-9*x^4-43*x^3),x, algorithm="giac")
Output:
-log(3*x^3*log(x) - 6*x^2*e^x*log(x) - 9*x^3 + 18*x^2*e^x + 9*x^2*log(x) + 3*x*e^(2*x)*log(x) - 18*x*e^x*log(x) - 43*x^2 - 9*x*e^(2*x) + 54*x*e^x + 9*e^(2*x)*log(x) - 27*e^(2*x)) + log(x)
Timed out. \[ \int \frac {34 x^2+15 x^3+e^{2 x} \left (-36+51 x+18 x^2\right )+e^x \left (18 x-66 x^2-18 x^3\right )+\left (-9 x^2-6 x^3+e^{2 x} \left (9-18 x-6 x^2\right )+e^x \left (24 x^2+6 x^3\right )\right ) \log (x)}{-43 x^3-9 x^4+e^{2 x} \left (-27 x-9 x^2\right )+e^x \left (54 x^2+18 x^3\right )+\left (9 x^3+3 x^4+e^{2 x} \left (9 x+3 x^2\right )+e^x \left (-18 x^2-6 x^3\right )\right ) \log (x)} \, dx=\int -\frac {{\mathrm {e}}^{2\,x}\,\left (18\,x^2+51\,x-36\right )-\ln \left (x\right )\,\left ({\mathrm {e}}^{2\,x}\,\left (6\,x^2+18\,x-9\right )-{\mathrm {e}}^x\,\left (6\,x^3+24\,x^2\right )+9\,x^2+6\,x^3\right )+34\,x^2+15\,x^3-{\mathrm {e}}^x\,\left (18\,x^3+66\,x^2-18\,x\right )}{{\mathrm {e}}^{2\,x}\,\left (9\,x^2+27\,x\right )-{\mathrm {e}}^x\,\left (18\,x^3+54\,x^2\right )-\ln \left (x\right )\,\left ({\mathrm {e}}^{2\,x}\,\left (3\,x^2+9\,x\right )-{\mathrm {e}}^x\,\left (6\,x^3+18\,x^2\right )+9\,x^3+3\,x^4\right )+43\,x^3+9\,x^4} \,d x \] Input:
int(-(exp(2*x)*(51*x + 18*x^2 - 36) - log(x)*(exp(2*x)*(18*x + 6*x^2 - 9) - exp(x)*(24*x^2 + 6*x^3) + 9*x^2 + 6*x^3) + 34*x^2 + 15*x^3 - exp(x)*(66* x^2 - 18*x + 18*x^3))/(exp(2*x)*(27*x + 9*x^2) - exp(x)*(54*x^2 + 18*x^3) - log(x)*(exp(2*x)*(9*x + 3*x^2) - exp(x)*(18*x^2 + 6*x^3) + 9*x^3 + 3*x^4 ) + 43*x^3 + 9*x^4),x)
Output:
int(-(exp(2*x)*(51*x + 18*x^2 - 36) - log(x)*(exp(2*x)*(18*x + 6*x^2 - 9) - exp(x)*(24*x^2 + 6*x^3) + 9*x^2 + 6*x^3) + 34*x^2 + 15*x^3 - exp(x)*(66* x^2 - 18*x + 18*x^3))/(exp(2*x)*(27*x + 9*x^2) - exp(x)*(54*x^2 + 18*x^3) - log(x)*(exp(2*x)*(9*x + 3*x^2) - exp(x)*(18*x^2 + 6*x^3) + 9*x^3 + 3*x^4 ) + 43*x^3 + 9*x^4), x)
Time = 0.25 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.23 \[ \int \frac {34 x^2+15 x^3+e^{2 x} \left (-36+51 x+18 x^2\right )+e^x \left (18 x-66 x^2-18 x^3\right )+\left (-9 x^2-6 x^3+e^{2 x} \left (9-18 x-6 x^2\right )+e^x \left (24 x^2+6 x^3\right )\right ) \log (x)}{-43 x^3-9 x^4+e^{2 x} \left (-27 x-9 x^2\right )+e^x \left (54 x^2+18 x^3\right )+\left (9 x^3+3 x^4+e^{2 x} \left (9 x+3 x^2\right )+e^x \left (-18 x^2-6 x^3\right )\right ) \log (x)} \, dx=-\mathrm {log}\left (3 e^{2 x} \mathrm {log}\left (x \right ) x +9 e^{2 x} \mathrm {log}\left (x \right )-9 e^{2 x} x -27 e^{2 x}-6 e^{x} \mathrm {log}\left (x \right ) x^{2}-18 e^{x} \mathrm {log}\left (x \right ) x +18 e^{x} x^{2}+54 e^{x} x +3 \,\mathrm {log}\left (x \right ) x^{3}+9 \,\mathrm {log}\left (x \right ) x^{2}-9 x^{3}-43 x^{2}\right )+\mathrm {log}\left (x \right ) \] Input:
int((((-6*x^2-18*x+9)*exp(x)^2+(6*x^3+24*x^2)*exp(x)-6*x^3-9*x^2)*log(x)+( 18*x^2+51*x-36)*exp(x)^2+(-18*x^3-66*x^2+18*x)*exp(x)+15*x^3+34*x^2)/(((3* x^2+9*x)*exp(x)^2+(-6*x^3-18*x^2)*exp(x)+3*x^4+9*x^3)*log(x)+(-9*x^2-27*x) *exp(x)^2+(18*x^3+54*x^2)*exp(x)-9*x^4-43*x^3),x)
Output:
- log(3*e**(2*x)*log(x)*x + 9*e**(2*x)*log(x) - 9*e**(2*x)*x - 27*e**(2*x ) - 6*e**x*log(x)*x**2 - 18*e**x*log(x)*x + 18*e**x*x**2 + 54*e**x*x + 3*l og(x)*x**3 + 9*log(x)*x**2 - 9*x**3 - 43*x**2) + log(x)