Integrand size = 241, antiderivative size = 38 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=x+\frac {x^2}{3 \left (\frac {5}{-4+x}+e^{x^2} \log \left (5 \log \left (\frac {4}{3-x}\right )\right )\right )} \] Output:
x^2/(3*ln(5*ln(4/(3-x)))*exp(x^2)+15/(-4+x))+x
Time = 0.17 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.08 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\frac {1}{3} \left (3 (-3+x)+\frac {(-4+x) x^2}{5+e^{x^2} (-4+x) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )}\right ) \] Input:
Integrate[(E^x^2*(16*x^2 - 8*x^3 + x^4) + (-225 + 195*x - 85*x^2 + 15*x^3) *Log[-4/(-3 + x)] + E^x^2*(360 - 306*x + 110*x^2 + 74*x^3 - 78*x^4 + 22*x^ 5 - 2*x^6)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]] + E^(2*x^2)*(-144 + 12 0*x - 33*x^2 + 3*x^3)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]^2)/((-225 + 75*x)*Log[-4/(-3 + x)] + E^x^2*(360 - 210*x + 30*x^2)*Log[-4/(-3 + x)]*Lo g[5*Log[-4/(-3 + x)]] + E^(2*x^2)*(-144 + 120*x - 33*x^2 + 3*x^3)*Log[-4/( -3 + x)]*Log[5*Log[-4/(-3 + x)]]^2),x]
Output:
(3*(-3 + x) + ((-4 + x)*x^2)/(5 + E^x^2*(-4 + x)*Log[5*Log[-4/(-3 + x)]])) /3
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.
| \(\displaystyle \int \frac {e^{2 x^2} \left (3 x^3-33 x^2+120 x-144\right ) \log \left (-\frac {4}{x-3}\right ) \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+\left (15 x^3-85 x^2+195 x-225\right ) \log \left (-\frac {4}{x-3}\right )+e^{x^2} \left (x^4-8 x^3+16 x^2\right )+e^{x^2} \left (-2 x^6+22 x^5-78 x^4+74 x^3+110 x^2-306 x+360\right ) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )}{e^{x^2} \left (30 x^2-210 x+360\right ) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{2 x^2} \left (3 x^3-33 x^2+120 x-144\right ) \log \left (-\frac {4}{x-3}\right ) \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+(75 x-225) \log \left (-\frac {4}{x-3}\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-e^{2 x^2} \left (3 x^3-33 x^2+120 x-144\right ) \log \left (-\frac {4}{x-3}\right ) \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )-\left (15 x^3-85 x^2+195 x-225\right ) \log \left (-\frac {4}{x-3}\right )-e^{x^2} \left (x^4-8 x^3+16 x^2\right )-e^{x^2} \left (-2 x^6+22 x^5-78 x^4+74 x^3+110 x^2-306 x+360\right ) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )}{3 (3-x) \log \left (-\frac {4}{x-3}\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{3} \int -\frac {-3 e^{2 x^2} \left (-x^3+11 x^2-40 x+48\right ) \log \left (\frac {4}{3-x}\right ) \log ^2\left (5 \log \left (\frac {4}{3-x}\right )\right )+2 e^{x^2} \left (-x^6+11 x^5-39 x^4+37 x^3+55 x^2-153 x+180\right ) \log \left (\frac {4}{3-x}\right ) \log \left (5 \log \left (\frac {4}{3-x}\right )\right )+e^{x^2} \left (x^4-8 x^3+16 x^2\right )-5 \left (-3 x^3+17 x^2-39 x+45\right ) \log \left (\frac {4}{3-x}\right )}{(3-x) \log \left (\frac {4}{3-x}\right ) \left (-4 e^{x^2} \log \left (5 \log \left (\frac {4}{3-x}\right )\right )+e^{x^2} x \log \left (5 \log \left (\frac {4}{3-x}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{3} \int \frac {-3 e^{2 x^2} \left (-x^3+11 x^2-40 x+48\right ) \log \left (\frac {4}{3-x}\right ) \log ^2\left (5 \log \left (\frac {4}{3-x}\right )\right )+2 e^{x^2} \left (-x^6+11 x^5-39 x^4+37 x^3+55 x^2-153 x+180\right ) \log \left (\frac {4}{3-x}\right ) \log \left (5 \log \left (\frac {4}{3-x}\right )\right )+e^{x^2} \left (x^4-8 x^3+16 x^2\right )-5 \left (-3 x^3+17 x^2-39 x+45\right ) \log \left (\frac {4}{3-x}\right )}{(3-x) \log \left (\frac {4}{3-x}\right ) \left (-4 e^{x^2} \log \left (5 \log \left (\frac {4}{3-x}\right )\right )+e^{x^2} x \log \left (5 \log \left (\frac {4}{3-x}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{x^2} (x-4)^2 x^2-(x-3) \log \left (-\frac {4}{x-3}\right ) \left (-3 e^{2 x^2} (x-4)^2 \log ^2\left (5 \log \left (-\frac {4}{x-3}\right )\right )+2 e^{x^2} \left (x^5-8 x^4+15 x^3+8 x^2-31 x+60\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )-5 \left (3 x^2-8 x+15\right )\right )}{(3-x) \log \left (-\frac {4}{x-3}\right ) \left (e^{x^2} (x-4) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {5 \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-14 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2+25 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x-3 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+4\right ) x^2}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )^2}+\frac {(x-4) \left (2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^3-6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x^2-2 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) x-x+6 \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )\right ) x}{(x-3) \log \left (-\frac {4}{x-3}\right ) \log \left (5 \log \left (-\frac {4}{x-3}\right )\right ) \left (-4 e^{x^2} \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+e^{x^2} x \log \left (5 \log \left (-\frac {4}{x-3}\right )\right )+5\right )}-3\right )dx\) |
Input:
Int[(E^x^2*(16*x^2 - 8*x^3 + x^4) + (-225 + 195*x - 85*x^2 + 15*x^3)*Log[- 4/(-3 + x)] + E^x^2*(360 - 306*x + 110*x^2 + 74*x^3 - 78*x^4 + 22*x^5 - 2* x^6)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]] + E^(2*x^2)*(-144 + 120*x - 33*x^2 + 3*x^3)*Log[-4/(-3 + x)]*Log[5*Log[-4/(-3 + x)]]^2)/((-225 + 75*x) *Log[-4/(-3 + x)] + E^x^2*(360 - 210*x + 30*x^2)*Log[-4/(-3 + x)]*Log[5*Lo g[-4/(-3 + x)]] + E^(2*x^2)*(-144 + 120*x - 33*x^2 + 3*x^3)*Log[-4/(-3 + x )]*Log[5*Log[-4/(-3 + x)]]^2),x]
Output:
$Aborted
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 27.84 (sec) , antiderivative size = 111, normalized size of antiderivative = 2.92
| method | result | size |
| risch | \(x +\frac {x^{2} \left (x -4\right )}{3 x \,{\mathrm e}^{x^{2}} \ln \left (10 \ln \left (2\right )+5 i \pi -5 \ln \left (-3+x \right )+5 i \pi \operatorname {csgn}\left (\frac {i}{-3+x}\right )^{2} \left (\operatorname {csgn}\left (\frac {i}{-3+x}\right )-1\right )\right )-12 \,{\mathrm e}^{x^{2}} \ln \left (10 \ln \left (2\right )+5 i \pi -5 \ln \left (-3+x \right )+5 i \pi \operatorname {csgn}\left (\frac {i}{-3+x}\right )^{2} \left (\operatorname {csgn}\left (\frac {i}{-3+x}\right )-1\right )\right )+15}\) | \(111\) |
| parallelrisch | \(\frac {5400+990 \,{\mathrm e}^{x^{2}} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right ) x^{2}+330 x^{3}-2880 \,{\mathrm e}^{x^{2}} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right ) x -1320 x^{2}-4320 \,{\mathrm e}^{x^{2}} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right )+4950 x}{990 \,{\mathrm e}^{x^{2}} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right ) x -3960 \,{\mathrm e}^{x^{2}} \ln \left (5 \ln \left (-\frac {4}{-3+x}\right )\right )+4950}\) | \(111\) |
Input:
int(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x))) ^2+(-2*x^6+22*x^5-78*x^4+74*x^3+110*x^2-306*x+360)*exp(x^2)*ln(-4/(-3+x))* ln(5*ln(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*ln(-4/(-3+x))+(x^4-8*x^3+16* x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*ln(-4/(-3+x))*ln(5*ln( -4/(-3+x)))^2+(30*x^2-210*x+360)*exp(x^2)*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)) )+(75*x-225)*ln(-4/(-3+x))),x,method=_RETURNVERBOSE)
Output:
x+1/3*x^2*(x-4)/(x*exp(x^2)*ln(10*ln(2)+5*I*Pi-5*ln(-3+x)+5*I*Pi*csgn(I/(- 3+x))^2*(csgn(I/(-3+x))-1))-4*exp(x^2)*ln(10*ln(2)+5*I*Pi-5*ln(-3+x)+5*I*P i*csgn(I/(-3+x))^2*(csgn(I/(-3+x))-1))+5)
Time = 0.10 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.61 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\frac {x^{3} + 3 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{2}\right )} \log \left (5 \, \log \left (-\frac {4}{x - 3}\right )\right ) - 4 \, x^{2} + 15 \, x}{3 \, {\left ({\left (x - 4\right )} e^{\left (x^{2}\right )} \log \left (5 \, \log \left (-\frac {4}{x - 3}\right )\right ) + 5\right )}} \] Input:
integrate(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4 /(-3+x)))^2+(-2*x^6+22*x^5-78*x^4+74*x^3+110*x^2-306*x+360)*exp(x^2)*log(- 4/(-3+x))*log(5*log(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*log(-4/(-3+x))+( x^4-8*x^3+16*x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(- 3+x))*log(5*log(-4/(-3+x)))^2+(30*x^2-210*x+360)*exp(x^2)*log(-4/(-3+x))*l og(5*log(-4/(-3+x)))+(75*x-225)*log(-4/(-3+x))),x, algorithm="fricas")
Output:
1/3*(x^3 + 3*(x^2 - 4*x)*e^(x^2)*log(5*log(-4/(x - 3))) - 4*x^2 + 15*x)/(( x - 4)*e^(x^2)*log(5*log(-4/(x - 3))) + 5)
Time = 0.40 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.16 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=x + \frac {x^{3} - 4 x^{2}}{\left (3 x \log {\left (5 \log {\left (- \frac {4}{x - 3} \right )} \right )} - 12 \log {\left (5 \log {\left (- \frac {4}{x - 3} \right )} \right )}\right ) e^{x^{2}} + 15} \] Input:
integrate(((3*x**3-33*x**2+120*x-144)*exp(x**2)**2*ln(-4/(-3+x))*ln(5*ln(- 4/(-3+x)))**2+(-2*x**6+22*x**5-78*x**4+74*x**3+110*x**2-306*x+360)*exp(x** 2)*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)))+(15*x**3-85*x**2+195*x-225)*ln(-4/(-3 +x))+(x**4-8*x**3+16*x**2)*exp(x**2))/((3*x**3-33*x**2+120*x-144)*exp(x**2 )**2*ln(-4/(-3+x))*ln(5*ln(-4/(-3+x)))**2+(30*x**2-210*x+360)*exp(x**2)*ln (-4/(-3+x))*ln(5*ln(-4/(-3+x)))+(75*x-225)*ln(-4/(-3+x))),x)
Output:
x + (x**3 - 4*x**2)/((3*x*log(5*log(-4/(x - 3))) - 12*log(5*log(-4/(x - 3) )))*exp(x**2) + 15)
Result contains complex when optimal does not.
Time = 0.30 (sec) , antiderivative size = 112, normalized size of antiderivative = 2.95 \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\frac {x^{3} + 3 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{2}\right )} \log \left (-2 \, \log \left (2\right ) + \log \left (-x + 3\right )\right ) - 4 \, x^{2} - 3 \, {\left ({\left (-i \, \pi - \log \left (5\right )\right )} x^{2} + 4 \, {\left (i \, \pi + \log \left (5\right )\right )} x\right )} e^{\left (x^{2}\right )} + 15 \, x}{3 \, {\left ({\left (x - 4\right )} e^{\left (x^{2}\right )} \log \left (-2 \, \log \left (2\right ) + \log \left (-x + 3\right )\right ) + {\left (-4 i \, \pi + {\left (i \, \pi + \log \left (5\right )\right )} x - 4 \, \log \left (5\right )\right )} e^{\left (x^{2}\right )} + 5\right )}} \] Input:
integrate(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4 /(-3+x)))^2+(-2*x^6+22*x^5-78*x^4+74*x^3+110*x^2-306*x+360)*exp(x^2)*log(- 4/(-3+x))*log(5*log(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*log(-4/(-3+x))+( x^4-8*x^3+16*x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(- 3+x))*log(5*log(-4/(-3+x)))^2+(30*x^2-210*x+360)*exp(x^2)*log(-4/(-3+x))*l og(5*log(-4/(-3+x)))+(75*x-225)*log(-4/(-3+x))),x, algorithm="maxima")
Output:
1/3*(x^3 + 3*(x^2 - 4*x)*e^(x^2)*log(-2*log(2) + log(-x + 3)) - 4*x^2 - 3* ((-I*pi - log(5))*x^2 + 4*(I*pi + log(5))*x)*e^(x^2) + 15*x)/((x - 4)*e^(x ^2)*log(-2*log(2) + log(-x + 3)) + (-4*I*pi + (I*pi + log(5))*x - 4*log(5) )*e^(x^2) + 5)
Timed out. \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\text {Timed out} \] Input:
integrate(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4 /(-3+x)))^2+(-2*x^6+22*x^5-78*x^4+74*x^3+110*x^2-306*x+360)*exp(x^2)*log(- 4/(-3+x))*log(5*log(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*log(-4/(-3+x))+( x^4-8*x^3+16*x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(- 3+x))*log(5*log(-4/(-3+x)))^2+(30*x^2-210*x+360)*exp(x^2)*log(-4/(-3+x))*l og(5*log(-4/(-3+x)))+(75*x-225)*log(-4/(-3+x))),x, algorithm="giac")
Output:
Timed out
Timed out. \[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\int \frac {\ln \left (-\frac {4}{x-3}\right )\,{\mathrm {e}}^{2\,x^2}\,\left (3\,x^3-33\,x^2+120\,x-144\right )\,{\ln \left (5\,\ln \left (-\frac {4}{x-3}\right )\right )}^2+\ln \left (-\frac {4}{x-3}\right )\,{\mathrm {e}}^{x^2}\,\left (-2\,x^6+22\,x^5-78\,x^4+74\,x^3+110\,x^2-306\,x+360\right )\,\ln \left (5\,\ln \left (-\frac {4}{x-3}\right )\right )+\ln \left (-\frac {4}{x-3}\right )\,\left (15\,x^3-85\,x^2+195\,x-225\right )+{\mathrm {e}}^{x^2}\,\left (x^4-8\,x^3+16\,x^2\right )}{\ln \left (-\frac {4}{x-3}\right )\,{\mathrm {e}}^{2\,x^2}\,\left (3\,x^3-33\,x^2+120\,x-144\right )\,{\ln \left (5\,\ln \left (-\frac {4}{x-3}\right )\right )}^2+\ln \left (-\frac {4}{x-3}\right )\,{\mathrm {e}}^{x^2}\,\left (30\,x^2-210\,x+360\right )\,\ln \left (5\,\ln \left (-\frac {4}{x-3}\right )\right )+\ln \left (-\frac {4}{x-3}\right )\,\left (75\,x-225\right )} \,d x \] Input:
int((log(-4/(x - 3))*(195*x - 85*x^2 + 15*x^3 - 225) + exp(x^2)*(16*x^2 - 8*x^3 + x^4) + log(-4/(x - 3))*exp(x^2)*log(5*log(-4/(x - 3)))*(110*x^2 - 306*x + 74*x^3 - 78*x^4 + 22*x^5 - 2*x^6 + 360) + log(-4/(x - 3))*exp(2*x^ 2)*log(5*log(-4/(x - 3)))^2*(120*x - 33*x^2 + 3*x^3 - 144))/(log(-4/(x - 3 ))*(75*x - 225) + log(-4/(x - 3))*exp(2*x^2)*log(5*log(-4/(x - 3)))^2*(120 *x - 33*x^2 + 3*x^3 - 144) + log(-4/(x - 3))*exp(x^2)*log(5*log(-4/(x - 3) ))*(30*x^2 - 210*x + 360)),x)
Output:
int((log(-4/(x - 3))*(195*x - 85*x^2 + 15*x^3 - 225) + exp(x^2)*(16*x^2 - 8*x^3 + x^4) + log(-4/(x - 3))*exp(x^2)*log(5*log(-4/(x - 3)))*(110*x^2 - 306*x + 74*x^3 - 78*x^4 + 22*x^5 - 2*x^6 + 360) + log(-4/(x - 3))*exp(2*x^ 2)*log(5*log(-4/(x - 3)))^2*(120*x - 33*x^2 + 3*x^3 - 144))/(log(-4/(x - 3 ))*(75*x - 225) + log(-4/(x - 3))*exp(2*x^2)*log(5*log(-4/(x - 3)))^2*(120 *x - 33*x^2 + 3*x^3 - 144) + log(-4/(x - 3))*exp(x^2)*log(5*log(-4/(x - 3) ))*(30*x^2 - 210*x + 360)), x)
\[ \int \frac {e^{x^2} \left (16 x^2-8 x^3+x^4\right )+\left (-225+195 x-85 x^2+15 x^3\right ) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-306 x+110 x^2+74 x^3-78 x^4+22 x^5-2 x^6\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )}{(-225+75 x) \log \left (-\frac {4}{-3+x}\right )+e^{x^2} \left (360-210 x+30 x^2\right ) \log \left (-\frac {4}{-3+x}\right ) \log \left (5 \log \left (-\frac {4}{-3+x}\right )\right )+e^{2 x^2} \left (-144+120 x-33 x^2+3 x^3\right ) \log \left (-\frac {4}{-3+x}\right ) \log ^2\left (5 \log \left (-\frac {4}{-3+x}\right )\right )} \, dx=\int \frac {\left (3 x^{3}-33 x^{2}+120 x -144\right ) \left ({\mathrm e}^{x^{2}}\right )^{2} \mathrm {log}\left (-\frac {4}{x -3}\right ) \mathrm {log}\left (5 \,\mathrm {log}\left (-\frac {4}{x -3}\right )\right )^{2}+\left (-2 x^{6}+22 x^{5}-78 x^{4}+74 x^{3}+110 x^{2}-306 x +360\right ) {\mathrm e}^{x^{2}} \mathrm {log}\left (-\frac {4}{x -3}\right ) \mathrm {log}\left (5 \,\mathrm {log}\left (-\frac {4}{x -3}\right )\right )+\left (15 x^{3}-85 x^{2}+195 x -225\right ) \mathrm {log}\left (-\frac {4}{x -3}\right )+\left (x^{4}-8 x^{3}+16 x^{2}\right ) {\mathrm e}^{x^{2}}}{\left (3 x^{3}-33 x^{2}+120 x -144\right ) \left ({\mathrm e}^{x^{2}}\right )^{2} \mathrm {log}\left (-\frac {4}{x -3}\right ) \mathrm {log}\left (5 \,\mathrm {log}\left (-\frac {4}{x -3}\right )\right )^{2}+\left (30 x^{2}-210 x +360\right ) {\mathrm e}^{x^{2}} \mathrm {log}\left (-\frac {4}{x -3}\right ) \mathrm {log}\left (5 \,\mathrm {log}\left (-\frac {4}{x -3}\right )\right )+\left (75 x -225\right ) \mathrm {log}\left (-\frac {4}{x -3}\right )}d x \] Input:
int(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4/(-3+x )))^2+(-2*x^6+22*x^5-78*x^4+74*x^3+110*x^2-306*x+360)*exp(x^2)*log(-4/(-3+ x))*log(5*log(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*log(-4/(-3+x))+(x^4-8* x^3+16*x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))* log(5*log(-4/(-3+x)))^2+(30*x^2-210*x+360)*exp(x^2)*log(-4/(-3+x))*log(5*l og(-4/(-3+x)))+(75*x-225)*log(-4/(-3+x))),x)
Output:
int(((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))*log(5*log(-4/(-3+x )))^2+(-2*x^6+22*x^5-78*x^4+74*x^3+110*x^2-306*x+360)*exp(x^2)*log(-4/(-3+ x))*log(5*log(-4/(-3+x)))+(15*x^3-85*x^2+195*x-225)*log(-4/(-3+x))+(x^4-8* x^3+16*x^2)*exp(x^2))/((3*x^3-33*x^2+120*x-144)*exp(x^2)^2*log(-4/(-3+x))* log(5*log(-4/(-3+x)))^2+(30*x^2-210*x+360)*exp(x^2)*log(-4/(-3+x))*log(5*l og(-4/(-3+x)))+(75*x-225)*log(-4/(-3+x))),x)