Integrand size = 378, antiderivative size = 28 \[ \int \frac {e^{\frac {25 x^2-40 x^3+6 x^4+8 x^5+x^6+\left (-110 x+278 x^2-90 x^3-70 x^4-8 x^5\right ) \log ^2(x)+\left (121-418 x+273 x^2+152 x^3+16 x^4\right ) \log ^4(x)}{x^2-2 x^3+x^4+\left (-2 x+10 x^2-8 x^3\right ) \log ^2(x)+\left (1-8 x+16 x^2\right ) \log ^4(x)}} \left (10 x^3-28 x^4+24 x^5-4 x^6-2 x^7+\left (-120 x+216 x^2-72 x^3-24 x^4\right ) \log (x)+\left (60 x-210 x^2+282 x^3-222 x^4+66 x^5+24 x^6\right ) \log ^2(x)+\left (264-720 x+360 x^2+96 x^3\right ) \log ^3(x)+\left (-132+786 x-984 x^2+618 x^3-336 x^4-96 x^5\right ) \log ^4(x)+\left (-550+1126 x-456 x^2+544 x^3+128 x^4\right ) \log ^6(x)\right )}{x^3-3 x^4+3 x^5-x^6+\left (-3 x^2+18 x^3-27 x^4+12 x^5\right ) \log ^2(x)+\left (3 x-27 x^2+72 x^3-48 x^4\right ) \log ^4(x)+\left (-1+12 x-48 x^2+64 x^3\right ) \log ^6(x)} \, dx=e^{\left (5+x+\frac {6}{1-4 x+\frac {-x+x^2}{\log ^2(x)}}\right )^2} \] Output:
exp((6/((x^2-x)/ln(x)^2-4*x+1)+x+5)^2)
Time = 0.19 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75 \[ \int \frac {e^{\frac {25 x^2-40 x^3+6 x^4+8 x^5+x^6+\left (-110 x+278 x^2-90 x^3-70 x^4-8 x^5\right ) \log ^2(x)+\left (121-418 x+273 x^2+152 x^3+16 x^4\right ) \log ^4(x)}{x^2-2 x^3+x^4+\left (-2 x+10 x^2-8 x^3\right ) \log ^2(x)+\left (1-8 x+16 x^2\right ) \log ^4(x)}} \left (10 x^3-28 x^4+24 x^5-4 x^6-2 x^7+\left (-120 x+216 x^2-72 x^3-24 x^4\right ) \log (x)+\left (60 x-210 x^2+282 x^3-222 x^4+66 x^5+24 x^6\right ) \log ^2(x)+\left (264-720 x+360 x^2+96 x^3\right ) \log ^3(x)+\left (-132+786 x-984 x^2+618 x^3-336 x^4-96 x^5\right ) \log ^4(x)+\left (-550+1126 x-456 x^2+544 x^3+128 x^4\right ) \log ^6(x)\right )}{x^3-3 x^4+3 x^5-x^6+\left (-3 x^2+18 x^3-27 x^4+12 x^5\right ) \log ^2(x)+\left (3 x-27 x^2+72 x^3-48 x^4\right ) \log ^4(x)+\left (-1+12 x-48 x^2+64 x^3\right ) \log ^6(x)} \, dx=e^{\frac {\left (x \left (-5+4 x+x^2\right )+\left (11-19 x-4 x^2\right ) \log ^2(x)\right )^2}{\left ((-1+x) x+(1-4 x) \log ^2(x)\right )^2}} \] Input:
Integrate[(E^((25*x^2 - 40*x^3 + 6*x^4 + 8*x^5 + x^6 + (-110*x + 278*x^2 - 90*x^3 - 70*x^4 - 8*x^5)*Log[x]^2 + (121 - 418*x + 273*x^2 + 152*x^3 + 16 *x^4)*Log[x]^4)/(x^2 - 2*x^3 + x^4 + (-2*x + 10*x^2 - 8*x^3)*Log[x]^2 + (1 - 8*x + 16*x^2)*Log[x]^4))*(10*x^3 - 28*x^4 + 24*x^5 - 4*x^6 - 2*x^7 + (- 120*x + 216*x^2 - 72*x^3 - 24*x^4)*Log[x] + (60*x - 210*x^2 + 282*x^3 - 22 2*x^4 + 66*x^5 + 24*x^6)*Log[x]^2 + (264 - 720*x + 360*x^2 + 96*x^3)*Log[x ]^3 + (-132 + 786*x - 984*x^2 + 618*x^3 - 336*x^4 - 96*x^5)*Log[x]^4 + (-5 50 + 1126*x - 456*x^2 + 544*x^3 + 128*x^4)*Log[x]^6))/(x^3 - 3*x^4 + 3*x^5 - x^6 + (-3*x^2 + 18*x^3 - 27*x^4 + 12*x^5)*Log[x]^2 + (3*x - 27*x^2 + 72 *x^3 - 48*x^4)*Log[x]^4 + (-1 + 12*x - 48*x^2 + 64*x^3)*Log[x]^6),x]
Output:
E^((x*(-5 + 4*x + x^2) + (11 - 19*x - 4*x^2)*Log[x]^2)^2/((-1 + x)*x + (1 - 4*x)*Log[x]^2)^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.
| \(\displaystyle \int \frac {\left (-2 x^7-4 x^6+24 x^5-28 x^4+10 x^3+\left (96 x^3+360 x^2-720 x+264\right ) \log ^3(x)+\left (128 x^4+544 x^3-456 x^2+1126 x-550\right ) \log ^6(x)+\left (-24 x^4-72 x^3+216 x^2-120 x\right ) \log (x)+\left (-96 x^5-336 x^4+618 x^3-984 x^2+786 x-132\right ) \log ^4(x)+\left (24 x^6+66 x^5-222 x^4+282 x^3-210 x^2+60 x\right ) \log ^2(x)\right ) \exp \left (\frac {x^6+8 x^5+6 x^4-40 x^3+25 x^2+\left (16 x^4+152 x^3+273 x^2-418 x+121\right ) \log ^4(x)+\left (-8 x^5-70 x^4-90 x^3+278 x^2-110 x\right ) \log ^2(x)}{x^4-2 x^3+x^2+\left (16 x^2-8 x+1\right ) \log ^4(x)+\left (-8 x^3+10 x^2-2 x\right ) \log ^2(x)}\right )}{-x^6+3 x^5-3 x^4+x^3+\left (64 x^3-48 x^2+12 x-1\right ) \log ^6(x)+\left (-48 x^4+72 x^3-27 x^2+3 x\right ) \log ^4(x)+\left (12 x^5-27 x^4+18 x^3-3 x^2\right ) \log ^2(x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left ((x-1)^3 x^3 (x+5)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)+\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)\right ) \exp \left (\frac {\left (x \left (x^2+4 x-5\right )+\left (-4 x^2-19 x+11\right ) \log ^2(x)\right )^2}{\left ((x-1) x+(1-4 x) \log ^2(x)\right )^2}\right )}{\left ((x-1) x+(1-4 x) \log ^2(x)\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (x \left (-x^2-4 x+5\right )-\left (-4 x^2-19 x+11\right ) \log ^2(x)\right )^2}{\left ((1-x) x-(1-4 x) \log ^2(x)\right )^2}\right ) \left (-\left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)\right )-3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)+12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)+3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)-12 (1-x)^2 x (x+5) \log (x)+(1-x)^3 x^3 (x+5)\right )}{\left ((1-x) x-(1-4 x) \log ^2(x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (x \left (-x^2-4 x+5\right )-\left (-4 x^2-19 x+11\right ) \log ^2(x)\right )^2}{\left ((1-x) x-(1-4 x) \log ^2(x)\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (x \left (-x^2-4 x+5\right )-\left (-4 x^2-19 x+11\right ) \log ^2(x)\right )^2}{\left ((1-x) x-(1-4 x) \log ^2(x)\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (x \left (-x^2-4 x+5\right )-\left (-4 x^2-19 x+11\right ) \log ^2(x)\right )^2}{\left ((1-x) x-(1-4 x) \log ^2(x)\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (x \left (-x^2-4 x+5\right )-\left (-4 x^2-19 x+11\right ) \log ^2(x)\right )^2}{\left ((1-x) x-(1-4 x) \log ^2(x)\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {36 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) x \left (4 x^3-32 \log (x) x^2-2 x^2+16 \log (x) x+x-2 \log (x)\right ) (x-1)^2}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^3}-\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^5-128 \log (x) x^4+68 x^4-544 \log (x) x^3-78 x^3+648 \log (x) x^2+29 x^2-214 \log (x) x-17 x+22 \log (x)\right ) (x-1)}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )^2}+\frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (64 x^4+272 x^3-228 x^2+563 x-275\right )}{(4 x-1)^3}+\frac {6 \exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (16 x^4-16 x^3+75 x^2-28 x-11\right )}{(4 x-1)^3 \left (x^2-4 \log ^2(x) x-x+\log ^2(x)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {\left (\left (-4 x^2-19 x+11\right ) \log ^2(x)+x \left (x^2+4 x-5\right )\right )^2}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^2}\right ) \left (\left (-64 x^4-272 x^3+228 x^2-563 x+275\right ) \log ^6(x)+3 \left (16 x^5+56 x^4-103 x^3+164 x^2-131 x+22\right ) \log ^4(x)-12 \left (4 x^3+15 x^2-30 x+11\right ) \log ^3(x)-3 x \left (4 x^5+11 x^4-37 x^3+47 x^2-35 x+10\right ) \log ^2(x)+12 (x-1)^2 x (x+5) \log (x)+(x-1)^3 x^3 (x+5)\right )}{\left ((1-4 x) \log ^2(x)+(x-1) x\right )^3}dx\) |
Input:
Int[(E^((25*x^2 - 40*x^3 + 6*x^4 + 8*x^5 + x^6 + (-110*x + 278*x^2 - 90*x^ 3 - 70*x^4 - 8*x^5)*Log[x]^2 + (121 - 418*x + 273*x^2 + 152*x^3 + 16*x^4)* Log[x]^4)/(x^2 - 2*x^3 + x^4 + (-2*x + 10*x^2 - 8*x^3)*Log[x]^2 + (1 - 8*x + 16*x^2)*Log[x]^4))*(10*x^3 - 28*x^4 + 24*x^5 - 4*x^6 - 2*x^7 + (-120*x + 216*x^2 - 72*x^3 - 24*x^4)*Log[x] + (60*x - 210*x^2 + 282*x^3 - 222*x^4 + 66*x^5 + 24*x^6)*Log[x]^2 + (264 - 720*x + 360*x^2 + 96*x^3)*Log[x]^3 + (-132 + 786*x - 984*x^2 + 618*x^3 - 336*x^4 - 96*x^5)*Log[x]^4 + (-550 + 1 126*x - 456*x^2 + 544*x^3 + 128*x^4)*Log[x]^6))/(x^3 - 3*x^4 + 3*x^5 - x^6 + (-3*x^2 + 18*x^3 - 27*x^4 + 12*x^5)*Log[x]^2 + (3*x - 27*x^2 + 72*x^3 - 48*x^4)*Log[x]^4 + (-1 + 12*x - 48*x^2 + 64*x^3)*Log[x]^6),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(62\) vs. \(2(27)=54\).
Time = 0.05 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.25
\[{\mathrm e}^{\frac {\left (4 x^{2} \ln \left (x \right )^{2}+19 x \ln \left (x \right )^{2}-x^{3}-11 \ln \left (x \right )^{2}-4 x^{2}+5 x \right )^{2}}{\left (4 x \ln \left (x \right )^{2}-\ln \left (x \right )^{2}-x^{2}+x \right )^{2}}}\]
Input:
int(((128*x^4+544*x^3-456*x^2+1126*x-550)*ln(x)^6+(-96*x^5-336*x^4+618*x^3 -984*x^2+786*x-132)*ln(x)^4+(96*x^3+360*x^2-720*x+264)*ln(x)^3+(24*x^6+66* x^5-222*x^4+282*x^3-210*x^2+60*x)*ln(x)^2+(-24*x^4-72*x^3+216*x^2-120*x)*l n(x)-2*x^7-4*x^6+24*x^5-28*x^4+10*x^3)*exp(((16*x^4+152*x^3+273*x^2-418*x+ 121)*ln(x)^4+(-8*x^5-70*x^4-90*x^3+278*x^2-110*x)*ln(x)^2+x^6+8*x^5+6*x^4- 40*x^3+25*x^2)/((16*x^2-8*x+1)*ln(x)^4+(-8*x^3+10*x^2-2*x)*ln(x)^2+x^4-2*x ^3+x^2))/((64*x^3-48*x^2+12*x-1)*ln(x)^6+(-48*x^4+72*x^3-27*x^2+3*x)*ln(x) ^4+(12*x^5-27*x^4+18*x^3-3*x^2)*ln(x)^2-x^6+3*x^5-3*x^4+x^3),x)
Output:
exp((4*x^2*ln(x)^2+19*x*ln(x)^2-x^3-11*ln(x)^2-4*x^2+5*x)^2/(4*x*ln(x)^2-l n(x)^2-x^2+x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 128 vs. \(2 (28) = 56\).
Time = 0.10 (sec) , antiderivative size = 128, normalized size of antiderivative = 4.57 \[ \int \frac {e^{\frac {25 x^2-40 x^3+6 x^4+8 x^5+x^6+\left (-110 x+278 x^2-90 x^3-70 x^4-8 x^5\right ) \log ^2(x)+\left (121-418 x+273 x^2+152 x^3+16 x^4\right ) \log ^4(x)}{x^2-2 x^3+x^4+\left (-2 x+10 x^2-8 x^3\right ) \log ^2(x)+\left (1-8 x+16 x^2\right ) \log ^4(x)}} \left (10 x^3-28 x^4+24 x^5-4 x^6-2 x^7+\left (-120 x+216 x^2-72 x^3-24 x^4\right ) \log (x)+\left (60 x-210 x^2+282 x^3-222 x^4+66 x^5+24 x^6\right ) \log ^2(x)+\left (264-720 x+360 x^2+96 x^3\right ) \log ^3(x)+\left (-132+786 x-984 x^2+618 x^3-336 x^4-96 x^5\right ) \log ^4(x)+\left (-550+1126 x-456 x^2+544 x^3+128 x^4\right ) \log ^6(x)\right )}{x^3-3 x^4+3 x^5-x^6+\left (-3 x^2+18 x^3-27 x^4+12 x^5\right ) \log ^2(x)+\left (3 x-27 x^2+72 x^3-48 x^4\right ) \log ^4(x)+\left (-1+12 x-48 x^2+64 x^3\right ) \log ^6(x)} \, dx=e^{\left (\frac {x^{6} + 8 \, x^{5} + {\left (16 \, x^{4} + 152 \, x^{3} + 273 \, x^{2} - 418 \, x + 121\right )} \log \left (x\right )^{4} + 6 \, x^{4} - 40 \, x^{3} - 2 \, {\left (4 \, x^{5} + 35 \, x^{4} + 45 \, x^{3} - 139 \, x^{2} + 55 \, x\right )} \log \left (x\right )^{2} + 25 \, x^{2}}{{\left (16 \, x^{2} - 8 \, x + 1\right )} \log \left (x\right )^{4} + x^{4} - 2 \, x^{3} - 2 \, {\left (4 \, x^{3} - 5 \, x^{2} + x\right )} \log \left (x\right )^{2} + x^{2}}\right )} \] Input:
integrate(((128*x^4+544*x^3-456*x^2+1126*x-550)*log(x)^6+(-96*x^5-336*x^4+ 618*x^3-984*x^2+786*x-132)*log(x)^4+(96*x^3+360*x^2-720*x+264)*log(x)^3+(2 4*x^6+66*x^5-222*x^4+282*x^3-210*x^2+60*x)*log(x)^2+(-24*x^4-72*x^3+216*x^ 2-120*x)*log(x)-2*x^7-4*x^6+24*x^5-28*x^4+10*x^3)*exp(((16*x^4+152*x^3+273 *x^2-418*x+121)*log(x)^4+(-8*x^5-70*x^4-90*x^3+278*x^2-110*x)*log(x)^2+x^6 +8*x^5+6*x^4-40*x^3+25*x^2)/((16*x^2-8*x+1)*log(x)^4+(-8*x^3+10*x^2-2*x)*l og(x)^2+x^4-2*x^3+x^2))/((64*x^3-48*x^2+12*x-1)*log(x)^6+(-48*x^4+72*x^3-2 7*x^2+3*x)*log(x)^4+(12*x^5-27*x^4+18*x^3-3*x^2)*log(x)^2-x^6+3*x^5-3*x^4+ x^3),x, algorithm="fricas")
Output:
e^((x^6 + 8*x^5 + (16*x^4 + 152*x^3 + 273*x^2 - 418*x + 121)*log(x)^4 + 6* x^4 - 40*x^3 - 2*(4*x^5 + 35*x^4 + 45*x^3 - 139*x^2 + 55*x)*log(x)^2 + 25* x^2)/((16*x^2 - 8*x + 1)*log(x)^4 + x^4 - 2*x^3 - 2*(4*x^3 - 5*x^2 + x)*lo g(x)^2 + x^2))
Leaf count of result is larger than twice the leaf count of optimal. 124 vs. \(2 (22) = 44\).
Time = 2.83 (sec) , antiderivative size = 124, normalized size of antiderivative = 4.43 \[ \int \frac {e^{\frac {25 x^2-40 x^3+6 x^4+8 x^5+x^6+\left (-110 x+278 x^2-90 x^3-70 x^4-8 x^5\right ) \log ^2(x)+\left (121-418 x+273 x^2+152 x^3+16 x^4\right ) \log ^4(x)}{x^2-2 x^3+x^4+\left (-2 x+10 x^2-8 x^3\right ) \log ^2(x)+\left (1-8 x+16 x^2\right ) \log ^4(x)}} \left (10 x^3-28 x^4+24 x^5-4 x^6-2 x^7+\left (-120 x+216 x^2-72 x^3-24 x^4\right ) \log (x)+\left (60 x-210 x^2+282 x^3-222 x^4+66 x^5+24 x^6\right ) \log ^2(x)+\left (264-720 x+360 x^2+96 x^3\right ) \log ^3(x)+\left (-132+786 x-984 x^2+618 x^3-336 x^4-96 x^5\right ) \log ^4(x)+\left (-550+1126 x-456 x^2+544 x^3+128 x^4\right ) \log ^6(x)\right )}{x^3-3 x^4+3 x^5-x^6+\left (-3 x^2+18 x^3-27 x^4+12 x^5\right ) \log ^2(x)+\left (3 x-27 x^2+72 x^3-48 x^4\right ) \log ^4(x)+\left (-1+12 x-48 x^2+64 x^3\right ) \log ^6(x)} \, dx=e^{\frac {x^{6} + 8 x^{5} + 6 x^{4} - 40 x^{3} + 25 x^{2} + \left (16 x^{4} + 152 x^{3} + 273 x^{2} - 418 x + 121\right ) \log {\left (x \right )}^{4} + \left (- 8 x^{5} - 70 x^{4} - 90 x^{3} + 278 x^{2} - 110 x\right ) \log {\left (x \right )}^{2}}{x^{4} - 2 x^{3} + x^{2} + \left (16 x^{2} - 8 x + 1\right ) \log {\left (x \right )}^{4} + \left (- 8 x^{3} + 10 x^{2} - 2 x\right ) \log {\left (x \right )}^{2}}} \] Input:
integrate(((128*x**4+544*x**3-456*x**2+1126*x-550)*ln(x)**6+(-96*x**5-336* x**4+618*x**3-984*x**2+786*x-132)*ln(x)**4+(96*x**3+360*x**2-720*x+264)*ln (x)**3+(24*x**6+66*x**5-222*x**4+282*x**3-210*x**2+60*x)*ln(x)**2+(-24*x** 4-72*x**3+216*x**2-120*x)*ln(x)-2*x**7-4*x**6+24*x**5-28*x**4+10*x**3)*exp (((16*x**4+152*x**3+273*x**2-418*x+121)*ln(x)**4+(-8*x**5-70*x**4-90*x**3+ 278*x**2-110*x)*ln(x)**2+x**6+8*x**5+6*x**4-40*x**3+25*x**2)/((16*x**2-8*x +1)*ln(x)**4+(-8*x**3+10*x**2-2*x)*ln(x)**2+x**4-2*x**3+x**2))/((64*x**3-4 8*x**2+12*x-1)*ln(x)**6+(-48*x**4+72*x**3-27*x**2+3*x)*ln(x)**4+(12*x**5-2 7*x**4+18*x**3-3*x**2)*ln(x)**2-x**6+3*x**5-3*x**4+x**3),x)
Output:
exp((x**6 + 8*x**5 + 6*x**4 - 40*x**3 + 25*x**2 + (16*x**4 + 152*x**3 + 27 3*x**2 - 418*x + 121)*log(x)**4 + (-8*x**5 - 70*x**4 - 90*x**3 + 278*x**2 - 110*x)*log(x)**2)/(x**4 - 2*x**3 + x**2 + (16*x**2 - 8*x + 1)*log(x)**4 + (-8*x**3 + 10*x**2 - 2*x)*log(x)**2))
Leaf count of result is larger than twice the leaf count of optimal. 113 vs. \(2 (28) = 56\).
Time = 6.80 (sec) , antiderivative size = 113, normalized size of antiderivative = 4.04 \[ \int \frac {e^{\frac {25 x^2-40 x^3+6 x^4+8 x^5+x^6+\left (-110 x+278 x^2-90 x^3-70 x^4-8 x^5\right ) \log ^2(x)+\left (121-418 x+273 x^2+152 x^3+16 x^4\right ) \log ^4(x)}{x^2-2 x^3+x^4+\left (-2 x+10 x^2-8 x^3\right ) \log ^2(x)+\left (1-8 x+16 x^2\right ) \log ^4(x)}} \left (10 x^3-28 x^4+24 x^5-4 x^6-2 x^7+\left (-120 x+216 x^2-72 x^3-24 x^4\right ) \log (x)+\left (60 x-210 x^2+282 x^3-222 x^4+66 x^5+24 x^6\right ) \log ^2(x)+\left (264-720 x+360 x^2+96 x^3\right ) \log ^3(x)+\left (-132+786 x-984 x^2+618 x^3-336 x^4-96 x^5\right ) \log ^4(x)+\left (-550+1126 x-456 x^2+544 x^3+128 x^4\right ) \log ^6(x)\right )}{x^3-3 x^4+3 x^5-x^6+\left (-3 x^2+18 x^3-27 x^4+12 x^5\right ) \log ^2(x)+\left (3 x-27 x^2+72 x^3-48 x^4\right ) \log ^4(x)+\left (-1+12 x-48 x^2+64 x^3\right ) \log ^6(x)} \, dx=e^{\left (\frac {36 \, \log \left (x\right )^{4}}{{\left (16 \, x^{2} - 8 \, x + 1\right )} \log \left (x\right )^{4} + x^{4} - 2 \, x^{3} - 2 \, {\left (4 \, x^{3} - 5 \, x^{2} + x\right )} \log \left (x\right )^{2} + x^{2}} + x^{2} - \frac {12 \, x \log \left (x\right )^{2}}{{\left (4 \, x - 1\right )} \log \left (x\right )^{2} - x^{2} + x} + 10 \, x - \frac {60 \, \log \left (x\right )^{2}}{{\left (4 \, x - 1\right )} \log \left (x\right )^{2} - x^{2} + x} + 25\right )} \] Input:
integrate(((128*x^4+544*x^3-456*x^2+1126*x-550)*log(x)^6+(-96*x^5-336*x^4+ 618*x^3-984*x^2+786*x-132)*log(x)^4+(96*x^3+360*x^2-720*x+264)*log(x)^3+(2 4*x^6+66*x^5-222*x^4+282*x^3-210*x^2+60*x)*log(x)^2+(-24*x^4-72*x^3+216*x^ 2-120*x)*log(x)-2*x^7-4*x^6+24*x^5-28*x^4+10*x^3)*exp(((16*x^4+152*x^3+273 *x^2-418*x+121)*log(x)^4+(-8*x^5-70*x^4-90*x^3+278*x^2-110*x)*log(x)^2+x^6 +8*x^5+6*x^4-40*x^3+25*x^2)/((16*x^2-8*x+1)*log(x)^4+(-8*x^3+10*x^2-2*x)*l og(x)^2+x^4-2*x^3+x^2))/((64*x^3-48*x^2+12*x-1)*log(x)^6+(-48*x^4+72*x^3-2 7*x^2+3*x)*log(x)^4+(12*x^5-27*x^4+18*x^3-3*x^2)*log(x)^2-x^6+3*x^5-3*x^4+ x^3),x, algorithm="maxima")
Output:
e^(36*log(x)^4/((16*x^2 - 8*x + 1)*log(x)^4 + x^4 - 2*x^3 - 2*(4*x^3 - 5*x ^2 + x)*log(x)^2 + x^2) + x^2 - 12*x*log(x)^2/((4*x - 1)*log(x)^2 - x^2 + x) + 10*x - 60*log(x)^2/((4*x - 1)*log(x)^2 - x^2 + x) + 25)
Leaf count of result is larger than twice the leaf count of optimal. 994 vs. \(2 (28) = 56\).
Time = 1.43 (sec) , antiderivative size = 994, normalized size of antiderivative = 35.50 \[ \int \frac {e^{\frac {25 x^2-40 x^3+6 x^4+8 x^5+x^6+\left (-110 x+278 x^2-90 x^3-70 x^4-8 x^5\right ) \log ^2(x)+\left (121-418 x+273 x^2+152 x^3+16 x^4\right ) \log ^4(x)}{x^2-2 x^3+x^4+\left (-2 x+10 x^2-8 x^3\right ) \log ^2(x)+\left (1-8 x+16 x^2\right ) \log ^4(x)}} \left (10 x^3-28 x^4+24 x^5-4 x^6-2 x^7+\left (-120 x+216 x^2-72 x^3-24 x^4\right ) \log (x)+\left (60 x-210 x^2+282 x^3-222 x^4+66 x^5+24 x^6\right ) \log ^2(x)+\left (264-720 x+360 x^2+96 x^3\right ) \log ^3(x)+\left (-132+786 x-984 x^2+618 x^3-336 x^4-96 x^5\right ) \log ^4(x)+\left (-550+1126 x-456 x^2+544 x^3+128 x^4\right ) \log ^6(x)\right )}{x^3-3 x^4+3 x^5-x^6+\left (-3 x^2+18 x^3-27 x^4+12 x^5\right ) \log ^2(x)+\left (3 x-27 x^2+72 x^3-48 x^4\right ) \log ^4(x)+\left (-1+12 x-48 x^2+64 x^3\right ) \log ^6(x)} \, dx=\text {Too large to display} \] Input:
integrate(((128*x^4+544*x^3-456*x^2+1126*x-550)*log(x)^6+(-96*x^5-336*x^4+ 618*x^3-984*x^2+786*x-132)*log(x)^4+(96*x^3+360*x^2-720*x+264)*log(x)^3+(2 4*x^6+66*x^5-222*x^4+282*x^3-210*x^2+60*x)*log(x)^2+(-24*x^4-72*x^3+216*x^ 2-120*x)*log(x)-2*x^7-4*x^6+24*x^5-28*x^4+10*x^3)*exp(((16*x^4+152*x^3+273 *x^2-418*x+121)*log(x)^4+(-8*x^5-70*x^4-90*x^3+278*x^2-110*x)*log(x)^2+x^6 +8*x^5+6*x^4-40*x^3+25*x^2)/((16*x^2-8*x+1)*log(x)^4+(-8*x^3+10*x^2-2*x)*l og(x)^2+x^4-2*x^3+x^2))/((64*x^3-48*x^2+12*x-1)*log(x)^6+(-48*x^4+72*x^3-2 7*x^2+3*x)*log(x)^4+(12*x^5-27*x^4+18*x^3-3*x^2)*log(x)^2-x^6+3*x^5-3*x^4+ x^3),x, algorithm="giac")
Output:
e^(16*x^4*log(x)^4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) - 8*x^5*log(x)^ 2/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 152*x^3*log(x)^4/(16*x^2*log(x )^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2 *x^3 - 2*x*log(x)^2 + x^2) + x^6/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*l og(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) - 70*x^4*log(x)^2/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 273*x^2*log(x)^ 4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 8*x^5/(16*x^2*log(x)^4 - 8*x^3 *log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x* log(x)^2 + x^2) - 90*x^3*log(x)^2/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x* log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) - 418*x*log(x)^4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 6*x^4/(16*x^2*l og(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 278*x^2*log(x)^2/(16*x^2*log(x)^4 - 8*x^3 *log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x* log(x)^2 + x^2) + 121*log(x)^4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*...
Time = 2.51 (sec) , antiderivative size = 1008, normalized size of antiderivative = 36.00 \[ \int \frac {e^{\frac {25 x^2-40 x^3+6 x^4+8 x^5+x^6+\left (-110 x+278 x^2-90 x^3-70 x^4-8 x^5\right ) \log ^2(x)+\left (121-418 x+273 x^2+152 x^3+16 x^4\right ) \log ^4(x)}{x^2-2 x^3+x^4+\left (-2 x+10 x^2-8 x^3\right ) \log ^2(x)+\left (1-8 x+16 x^2\right ) \log ^4(x)}} \left (10 x^3-28 x^4+24 x^5-4 x^6-2 x^7+\left (-120 x+216 x^2-72 x^3-24 x^4\right ) \log (x)+\left (60 x-210 x^2+282 x^3-222 x^4+66 x^5+24 x^6\right ) \log ^2(x)+\left (264-720 x+360 x^2+96 x^3\right ) \log ^3(x)+\left (-132+786 x-984 x^2+618 x^3-336 x^4-96 x^5\right ) \log ^4(x)+\left (-550+1126 x-456 x^2+544 x^3+128 x^4\right ) \log ^6(x)\right )}{x^3-3 x^4+3 x^5-x^6+\left (-3 x^2+18 x^3-27 x^4+12 x^5\right ) \log ^2(x)+\left (3 x-27 x^2+72 x^3-48 x^4\right ) \log ^4(x)+\left (-1+12 x-48 x^2+64 x^3\right ) \log ^6(x)} \, dx=\text {Too large to display} \] Input:
int(-(exp((log(x)^4*(273*x^2 - 418*x + 152*x^3 + 16*x^4 + 121) - log(x)^2* (110*x - 278*x^2 + 90*x^3 + 70*x^4 + 8*x^5) + 25*x^2 - 40*x^3 + 6*x^4 + 8* x^5 + x^6)/(log(x)^4*(16*x^2 - 8*x + 1) - log(x)^2*(2*x - 10*x^2 + 8*x^3) + x^2 - 2*x^3 + x^4))*(log(x)*(120*x - 216*x^2 + 72*x^3 + 24*x^4) - log(x) ^3*(360*x^2 - 720*x + 96*x^3 + 264) - log(x)^6*(1126*x - 456*x^2 + 544*x^3 + 128*x^4 - 550) + log(x)^4*(984*x^2 - 786*x - 618*x^3 + 336*x^4 + 96*x^5 + 132) - 10*x^3 + 28*x^4 - 24*x^5 + 4*x^6 + 2*x^7 - log(x)^2*(60*x - 210* x^2 + 282*x^3 - 222*x^4 + 66*x^5 + 24*x^6)))/(log(x)^6*(12*x - 48*x^2 + 64 *x^3 - 1) + log(x)^4*(3*x - 27*x^2 + 72*x^3 - 48*x^4) + x^3 - 3*x^4 + 3*x^ 5 - x^6 - log(x)^2*(3*x^2 - 18*x^3 + 27*x^4 - 12*x^5)),x)
Output:
exp(-(110*x*log(x)^2)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log (x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp(-(418*x *log(x)^4)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x ^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp(x^6/(log(x)^4 - 8* x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log( x)^4 + x^2 - 2*x^3 + x^4))*exp((6*x^4)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log( x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((8*x^5)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^ 2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((25*x^2)/(l og(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp(-(40*x^3)/(log(x)^4 - 8*x*log(x )^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp(-(8*x^5*log(x)^2)/(log(x)^4 - 8*x*log(x)^4 - 2*x*l og(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((16*x^4*log(x)^4)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 1 0*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*ex p(-(70*x^4*log(x)^2)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log( x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp(-(90*x^3 *log(x)^2)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x ^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((152*x^3*log(x)...
\[ \int \frac {e^{\frac {25 x^2-40 x^3+6 x^4+8 x^5+x^6+\left (-110 x+278 x^2-90 x^3-70 x^4-8 x^5\right ) \log ^2(x)+\left (121-418 x+273 x^2+152 x^3+16 x^4\right ) \log ^4(x)}{x^2-2 x^3+x^4+\left (-2 x+10 x^2-8 x^3\right ) \log ^2(x)+\left (1-8 x+16 x^2\right ) \log ^4(x)}} \left (10 x^3-28 x^4+24 x^5-4 x^6-2 x^7+\left (-120 x+216 x^2-72 x^3-24 x^4\right ) \log (x)+\left (60 x-210 x^2+282 x^3-222 x^4+66 x^5+24 x^6\right ) \log ^2(x)+\left (264-720 x+360 x^2+96 x^3\right ) \log ^3(x)+\left (-132+786 x-984 x^2+618 x^3-336 x^4-96 x^5\right ) \log ^4(x)+\left (-550+1126 x-456 x^2+544 x^3+128 x^4\right ) \log ^6(x)\right )}{x^3-3 x^4+3 x^5-x^6+\left (-3 x^2+18 x^3-27 x^4+12 x^5\right ) \log ^2(x)+\left (3 x-27 x^2+72 x^3-48 x^4\right ) \log ^4(x)+\left (-1+12 x-48 x^2+64 x^3\right ) \log ^6(x)} \, dx=\text {too large to display} \] Input:
int(((128*x^4+544*x^3-456*x^2+1126*x-550)*log(x)^6+(-96*x^5-336*x^4+618*x^ 3-984*x^2+786*x-132)*log(x)^4+(96*x^3+360*x^2-720*x+264)*log(x)^3+(24*x^6+ 66*x^5-222*x^4+282*x^3-210*x^2+60*x)*log(x)^2+(-24*x^4-72*x^3+216*x^2-120* x)*log(x)-2*x^7-4*x^6+24*x^5-28*x^4+10*x^3)*exp(((16*x^4+152*x^3+273*x^2-4 18*x+121)*log(x)^4+(-8*x^5-70*x^4-90*x^3+278*x^2-110*x)*log(x)^2+x^6+8*x^5 +6*x^4-40*x^3+25*x^2)/((16*x^2-8*x+1)*log(x)^4+(-8*x^3+10*x^2-2*x)*log(x)^ 2+x^4-2*x^3+x^2))/((64*x^3-48*x^2+12*x-1)*log(x)^6+(-48*x^4+72*x^3-27*x^2+ 3*x)*log(x)^4+(12*x^5-27*x^4+18*x^3-3*x^2)*log(x)^2-x^6+3*x^5-3*x^4+x^3),x )
Output:
2*e**22*(64*int((e**((16*log(x)**4*x**4 + 152*log(x)**4*x**3 - 79*log(x)** 4*x**2 + 10*log(x)**4*x + 99*log(x)**4 - 8*log(x)**2*x**5 - 70*log(x)**2*x **4 + 98*log(x)**2*x**3 + 58*log(x)**2*x**2 + x**6 + 8*x**5 - 16*x**4 + 10 *x**3 + 3*x**2)/(16*log(x)**4*x**2 - 8*log(x)**4*x + log(x)**4 - 8*log(x)* *2*x**3 + 10*log(x)**2*x**2 - 2*log(x)**2*x + x**4 - 2*x**3 + x**2))*log(x )**6*x**4)/(64*e**((252*log(x)**4*x + 12*log(x)**2*x**3 + 66*log(x)**2*x + 6*x**3)/(16*log(x)**4*x**2 - 8*log(x)**4*x + log(x)**4 - 8*log(x)**2*x**3 + 10*log(x)**2*x**2 - 2*log(x)**2*x + x**4 - 2*x**3 + x**2))*log(x)**6*x* *3 - 48*e**((252*log(x)**4*x + 12*log(x)**2*x**3 + 66*log(x)**2*x + 6*x**3 )/(16*log(x)**4*x**2 - 8*log(x)**4*x + log(x)**4 - 8*log(x)**2*x**3 + 10*l og(x)**2*x**2 - 2*log(x)**2*x + x**4 - 2*x**3 + x**2))*log(x)**6*x**2 + 12 *e**((252*log(x)**4*x + 12*log(x)**2*x**3 + 66*log(x)**2*x + 6*x**3)/(16*l og(x)**4*x**2 - 8*log(x)**4*x + log(x)**4 - 8*log(x)**2*x**3 + 10*log(x)** 2*x**2 - 2*log(x)**2*x + x**4 - 2*x**3 + x**2))*log(x)**6*x - e**((252*log (x)**4*x + 12*log(x)**2*x**3 + 66*log(x)**2*x + 6*x**3)/(16*log(x)**4*x**2 - 8*log(x)**4*x + log(x)**4 - 8*log(x)**2*x**3 + 10*log(x)**2*x**2 - 2*lo g(x)**2*x + x**4 - 2*x**3 + x**2))*log(x)**6 - 48*e**((252*log(x)**4*x + 1 2*log(x)**2*x**3 + 66*log(x)**2*x + 6*x**3)/(16*log(x)**4*x**2 - 8*log(x)* *4*x + log(x)**4 - 8*log(x)**2*x**3 + 10*log(x)**2*x**2 - 2*log(x)**2*x + x**4 - 2*x**3 + x**2))*log(x)**4*x**4 + 72*e**((252*log(x)**4*x + 12*lo...