Integrand size = 204, antiderivative size = 31 \[ \int \frac {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 x^4\right )} \, dx=\frac {2}{5-\left (-3+\frac {5-e^{6 x^4} (-5+x)+x}{x}\right )^2} \] Output:
2/(5-((5+x-exp(6*x^4)*(-5+x))/x-3)^2)
Time = 10.07 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.55 \[ \int \frac {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 x^4\right )} \, dx=-\frac {2 x^2}{25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )} \] Input:
Integrate[(-100*x + 40*x^2 + E^(12*x^4)*(-100*x + 20*x^2 + 2400*x^5 - 960* x^6 + 96*x^7) + E^(6*x^4)*(-200*x + 60*x^2 + 2400*x^5 - 1440*x^6 + 192*x^7 ))/(625 - 1000*x + 350*x^2 + 40*x^3 + x^4 + E^(6*x^4)*(2500 - 3500*x + 130 0*x^2 - 100*x^3 - 8*x^4) + E^(24*x^4)*(625 - 500*x + 150*x^2 - 20*x^3 + x^ 4) + E^(18*x^4)*(2500 - 2500*x + 900*x^2 - 140*x^3 + 8*x^4) + E^(12*x^4)*( 3750 - 4500*x + 1700*x^2 - 260*x^3 + 14*x^4)),x]
Output:
(-2*x^2)/(25 + E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {40 x^2+e^{12 x^4} \left (96 x^7-960 x^6+2400 x^5+20 x^2-100 x\right )+e^{6 x^4} \left (192 x^7-1440 x^6+2400 x^5+60 x^2-200 x\right )-100 x}{x^4+40 x^3+350 x^2+e^{6 x^4} \left (-8 x^4-100 x^3+1300 x^2-3500 x+2500\right )+e^{24 x^4} \left (x^4-20 x^3+150 x^2-500 x+625\right )+e^{18 x^4} \left (8 x^4-140 x^3+900 x^2-2500 x+2500\right )+e^{12 x^4} \left (14 x^4-260 x^3+1700 x^2-4500 x+3750\right )-1000 x+625} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 x \left (e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )+e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )+5 (2 x-5)\right )}{\left (e^{12 x^4} (x-5)^2-x^2+e^{6 x^4} \left (4 x^2-30 x+50\right )-20 x+25\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {x \left (5 (5-2 x)+e^{6 x^4} \left (-48 x^6+360 x^5-600 x^4-15 x+50\right )+e^{12 x^4} \left (-24 x^6+240 x^5-600 x^4-5 x+25\right )\right )}{\left (e^{12 x^4} (5-x)^2-x^2-20 x+2 e^{6 x^4} \left (2 x^2-15 x+25\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {x \left (5 (5-2 x)+e^{6 x^4} \left (-48 x^6+360 x^5-600 x^4-15 x+50\right )+e^{12 x^4} \left (-24 x^6+240 x^5-600 x^4-5 x+25\right )\right )}{\left (e^{12 x^4} (5-x)^2-x^2-20 x+2 e^{6 x^4} \left (2 x^2-15 x+25\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {x \left (-5 (2 x-5)-e^{12 x^4} \left (24 x^6-240 x^5+600 x^4+5 x-25\right )-e^{6 x^4} \left (48 x^6-360 x^5+600 x^4+15 x-50\right )\right )}{\left (e^{12 x^4} (x-5)^2-x^2-20 x+e^{6 x^4} \left (4 x^2-30 x+50\right )+25\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {x^2 \left (48 e^{6 x^4} x^6-24 x^6-600 e^{6 x^4} x^5-360 x^5+2400 e^{6 x^4} x^4+3000 x^4-3000 e^{6 x^4} x^3-3000 x^3+5 e^{6 x^4} x-15 x-25 e^{6 x^4}-25\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )^2}-\frac {x \left (24 x^5-120 x^4+5\right )}{(x-5) \left (4 e^{6 x^4} x^2+e^{12 x^4} x^2-x^2-30 e^{6 x^4} x-10 e^{12 x^4} x-20 x+50 e^{6 x^4}+25 e^{12 x^4}+25\right )}\right )dx\) |
Input:
Int[(-100*x + 40*x^2 + E^(12*x^4)*(-100*x + 20*x^2 + 2400*x^5 - 960*x^6 + 96*x^7) + E^(6*x^4)*(-200*x + 60*x^2 + 2400*x^5 - 1440*x^6 + 192*x^7))/(62 5 - 1000*x + 350*x^2 + 40*x^3 + x^4 + E^(6*x^4)*(2500 - 3500*x + 1300*x^2 - 100*x^3 - 8*x^4) + E^(24*x^4)*(625 - 500*x + 150*x^2 - 20*x^3 + x^4) + E ^(18*x^4)*(2500 - 2500*x + 900*x^2 - 140*x^3 + 8*x^4) + E^(12*x^4)*(3750 - 4500*x + 1700*x^2 - 260*x^3 + 14*x^4)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(72\) vs. \(2(30)=60\).
Time = 0.29 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.35
| method | result | size |
| risch | \(-\frac {2 x^{2}}{{\mathrm e}^{12 x^{4}} x^{2}-10 \,{\mathrm e}^{12 x^{4}} x +4 \,{\mathrm e}^{6 x^{4}} x^{2}+25 \,{\mathrm e}^{12 x^{4}}-30 \,{\mathrm e}^{6 x^{4}} x -x^{2}+50 \,{\mathrm e}^{6 x^{4}}-20 x +25}\) | \(73\) |
| parallelrisch | \(-\frac {2 x^{2}}{{\mathrm e}^{12 x^{4}} x^{2}-10 \,{\mathrm e}^{12 x^{4}} x +4 \,{\mathrm e}^{6 x^{4}} x^{2}+25 \,{\mathrm e}^{12 x^{4}}-30 \,{\mathrm e}^{6 x^{4}} x -x^{2}+50 \,{\mathrm e}^{6 x^{4}}-20 x +25}\) | \(79\) |
Input:
int(((96*x^7-960*x^6+2400*x^5+20*x^2-100*x)*exp(6*x^4)^2+(192*x^7-1440*x^6 +2400*x^5+60*x^2-200*x)*exp(6*x^4)+40*x^2-100*x)/((x^4-20*x^3+150*x^2-500* x+625)*exp(6*x^4)^4+(8*x^4-140*x^3+900*x^2-2500*x+2500)*exp(6*x^4)^3+(14*x ^4-260*x^3+1700*x^2-4500*x+3750)*exp(6*x^4)^2+(-8*x^4-100*x^3+1300*x^2-350 0*x+2500)*exp(6*x^4)+x^4+40*x^3+350*x^2-1000*x+625),x,method=_RETURNVERBOS E)
Output:
-2*x^2/(exp(12*x^4)*x^2-10*exp(12*x^4)*x+4*exp(6*x^4)*x^2+25*exp(12*x^4)-3 0*exp(6*x^4)*x-x^2+50*exp(6*x^4)-20*x+25)
Time = 0.10 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.58 \[ \int \frac {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 x^4\right )} \, dx=\frac {2 \, x^{2}}{x^{2} - {\left (x^{2} - 10 \, x + 25\right )} e^{\left (12 \, x^{4}\right )} - 2 \, {\left (2 \, x^{2} - 15 \, x + 25\right )} e^{\left (6 \, x^{4}\right )} + 20 \, x - 25} \] Input:
integrate(((96*x^7-960*x^6+2400*x^5+20*x^2-100*x)*exp(6*x^4)^2+(192*x^7-14 40*x^6+2400*x^5+60*x^2-200*x)*exp(6*x^4)+40*x^2-100*x)/((x^4-20*x^3+150*x^ 2-500*x+625)*exp(6*x^4)^4+(8*x^4-140*x^3+900*x^2-2500*x+2500)*exp(6*x^4)^3 +(14*x^4-260*x^3+1700*x^2-4500*x+3750)*exp(6*x^4)^2+(-8*x^4-100*x^3+1300*x ^2-3500*x+2500)*exp(6*x^4)+x^4+40*x^3+350*x^2-1000*x+625),x, algorithm="fr icas")
Output:
2*x^2/(x^2 - (x^2 - 10*x + 25)*e^(12*x^4) - 2*(2*x^2 - 15*x + 25)*e^(6*x^4 ) + 20*x - 25)
Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (20) = 40\).
Time = 0.37 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.48 \[ \int \frac {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 x^4\right )} \, dx=- \frac {2 x^{2}}{- x^{2} - 20 x + \left (x^{2} - 10 x + 25\right ) e^{12 x^{4}} + \left (4 x^{2} - 30 x + 50\right ) e^{6 x^{4}} + 25} \] Input:
integrate(((96*x**7-960*x**6+2400*x**5+20*x**2-100*x)*exp(6*x**4)**2+(192* x**7-1440*x**6+2400*x**5+60*x**2-200*x)*exp(6*x**4)+40*x**2-100*x)/((x**4- 20*x**3+150*x**2-500*x+625)*exp(6*x**4)**4+(8*x**4-140*x**3+900*x**2-2500* x+2500)*exp(6*x**4)**3+(14*x**4-260*x**3+1700*x**2-4500*x+3750)*exp(6*x**4 )**2+(-8*x**4-100*x**3+1300*x**2-3500*x+2500)*exp(6*x**4)+x**4+40*x**3+350 *x**2-1000*x+625),x)
Output:
-2*x**2/(-x**2 - 20*x + (x**2 - 10*x + 25)*exp(12*x**4) + (4*x**2 - 30*x + 50)*exp(6*x**4) + 25)
Time = 0.10 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.58 \[ \int \frac {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 x^4\right )} \, dx=\frac {2 \, x^{2}}{x^{2} - {\left (x^{2} - 10 \, x + 25\right )} e^{\left (12 \, x^{4}\right )} - 2 \, {\left (2 \, x^{2} - 15 \, x + 25\right )} e^{\left (6 \, x^{4}\right )} + 20 \, x - 25} \] Input:
integrate(((96*x^7-960*x^6+2400*x^5+20*x^2-100*x)*exp(6*x^4)^2+(192*x^7-14 40*x^6+2400*x^5+60*x^2-200*x)*exp(6*x^4)+40*x^2-100*x)/((x^4-20*x^3+150*x^ 2-500*x+625)*exp(6*x^4)^4+(8*x^4-140*x^3+900*x^2-2500*x+2500)*exp(6*x^4)^3 +(14*x^4-260*x^3+1700*x^2-4500*x+3750)*exp(6*x^4)^2+(-8*x^4-100*x^3+1300*x ^2-3500*x+2500)*exp(6*x^4)+x^4+40*x^3+350*x^2-1000*x+625),x, algorithm="ma xima")
Output:
2*x^2/(x^2 - (x^2 - 10*x + 25)*e^(12*x^4) - 2*(2*x^2 - 15*x + 25)*e^(6*x^4 ) + 20*x - 25)
Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (29) = 58\).
Time = 0.59 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.32 \[ \int \frac {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 x^4\right )} \, dx=-\frac {4 \, x^{2}}{x^{2} e^{\left (12 \, x^{4}\right )} + 4 \, x^{2} e^{\left (6 \, x^{4}\right )} - x^{2} - 10 \, x e^{\left (12 \, x^{4}\right )} - 30 \, x e^{\left (6 \, x^{4}\right )} - 20 \, x + 25 \, e^{\left (12 \, x^{4}\right )} + 50 \, e^{\left (6 \, x^{4}\right )} + 25} \] Input:
integrate(((96*x^7-960*x^6+2400*x^5+20*x^2-100*x)*exp(6*x^4)^2+(192*x^7-14 40*x^6+2400*x^5+60*x^2-200*x)*exp(6*x^4)+40*x^2-100*x)/((x^4-20*x^3+150*x^ 2-500*x+625)*exp(6*x^4)^4+(8*x^4-140*x^3+900*x^2-2500*x+2500)*exp(6*x^4)^3 +(14*x^4-260*x^3+1700*x^2-4500*x+3750)*exp(6*x^4)^2+(-8*x^4-100*x^3+1300*x ^2-3500*x+2500)*exp(6*x^4)+x^4+40*x^3+350*x^2-1000*x+625),x, algorithm="gi ac")
Output:
-4*x^2/(x^2*e^(12*x^4) + 4*x^2*e^(6*x^4) - x^2 - 10*x*e^(12*x^4) - 30*x*e^ (6*x^4) - 20*x + 25*e^(12*x^4) + 50*e^(6*x^4) + 25)
Timed out. \[ \int \frac {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 x^4\right )} \, dx=\int \frac {{\mathrm {e}}^{12\,x^4}\,\left (96\,x^7-960\,x^6+2400\,x^5+20\,x^2-100\,x\right )-100\,x+{\mathrm {e}}^{6\,x^4}\,\left (192\,x^7-1440\,x^6+2400\,x^5+60\,x^2-200\,x\right )+40\,x^2}{{\mathrm {e}}^{24\,x^4}\,\left (x^4-20\,x^3+150\,x^2-500\,x+625\right )-1000\,x+{\mathrm {e}}^{18\,x^4}\,\left (8\,x^4-140\,x^3+900\,x^2-2500\,x+2500\right )-{\mathrm {e}}^{6\,x^4}\,\left (8\,x^4+100\,x^3-1300\,x^2+3500\,x-2500\right )+{\mathrm {e}}^{12\,x^4}\,\left (14\,x^4-260\,x^3+1700\,x^2-4500\,x+3750\right )+350\,x^2+40\,x^3+x^4+625} \,d x \] Input:
int((exp(12*x^4)*(20*x^2 - 100*x + 2400*x^5 - 960*x^6 + 96*x^7) - 100*x + exp(6*x^4)*(60*x^2 - 200*x + 2400*x^5 - 1440*x^6 + 192*x^7) + 40*x^2)/(exp (24*x^4)*(150*x^2 - 500*x - 20*x^3 + x^4 + 625) - 1000*x + exp(18*x^4)*(90 0*x^2 - 2500*x - 140*x^3 + 8*x^4 + 2500) - exp(6*x^4)*(3500*x - 1300*x^2 + 100*x^3 + 8*x^4 - 2500) + exp(12*x^4)*(1700*x^2 - 4500*x - 260*x^3 + 14*x ^4 + 3750) + 350*x^2 + 40*x^3 + x^4 + 625),x)
Output:
int((exp(12*x^4)*(20*x^2 - 100*x + 2400*x^5 - 960*x^6 + 96*x^7) - 100*x + exp(6*x^4)*(60*x^2 - 200*x + 2400*x^5 - 1440*x^6 + 192*x^7) + 40*x^2)/(exp (24*x^4)*(150*x^2 - 500*x - 20*x^3 + x^4 + 625) - 1000*x + exp(18*x^4)*(90 0*x^2 - 2500*x - 140*x^3 + 8*x^4 + 2500) - exp(6*x^4)*(3500*x - 1300*x^2 + 100*x^3 + 8*x^4 - 2500) + exp(12*x^4)*(1700*x^2 - 4500*x - 260*x^3 + 14*x ^4 + 3750) + 350*x^2 + 40*x^3 + x^4 + 625), x)
\[ \int \frac {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 x^4\right )} \, dx=\text {too large to display} \] Input:
int(((96*x^7-960*x^6+2400*x^5+20*x^2-100*x)*exp(6*x^4)^2+(192*x^7-1440*x^6 +2400*x^5+60*x^2-200*x)*exp(6*x^4)+40*x^2-100*x)/((x^4-20*x^3+150*x^2-500* x+625)*exp(6*x^4)^4+(8*x^4-140*x^3+900*x^2-2500*x+2500)*exp(6*x^4)^3+(14*x ^4-260*x^3+1700*x^2-4500*x+3750)*exp(6*x^4)^2+(-8*x^4-100*x^3+1300*x^2-350 0*x+2500)*exp(6*x^4)+x^4+40*x^3+350*x^2-1000*x+625),x)
Output:
4*(10*int(x**2/(e**(24*x**4)*x**4 - 20*e**(24*x**4)*x**3 + 150*e**(24*x**4 )*x**2 - 500*e**(24*x**4)*x + 625*e**(24*x**4) + 8*e**(18*x**4)*x**4 - 140 *e**(18*x**4)*x**3 + 900*e**(18*x**4)*x**2 - 2500*e**(18*x**4)*x + 2500*e* *(18*x**4) + 14*e**(12*x**4)*x**4 - 260*e**(12*x**4)*x**3 + 1700*e**(12*x* *4)*x**2 - 4500*e**(12*x**4)*x + 3750*e**(12*x**4) - 8*e**(6*x**4)*x**4 - 100*e**(6*x**4)*x**3 + 1300*e**(6*x**4)*x**2 - 3500*e**(6*x**4)*x + 2500*e **(6*x**4) + x**4 + 40*x**3 + 350*x**2 - 1000*x + 625),x) + 24*int((e**(12 *x**4)*x**7)/(e**(24*x**4)*x**4 - 20*e**(24*x**4)*x**3 + 150*e**(24*x**4)* x**2 - 500*e**(24*x**4)*x + 625*e**(24*x**4) + 8*e**(18*x**4)*x**4 - 140*e **(18*x**4)*x**3 + 900*e**(18*x**4)*x**2 - 2500*e**(18*x**4)*x + 2500*e**( 18*x**4) + 14*e**(12*x**4)*x**4 - 260*e**(12*x**4)*x**3 + 1700*e**(12*x**4 )*x**2 - 4500*e**(12*x**4)*x + 3750*e**(12*x**4) - 8*e**(6*x**4)*x**4 - 10 0*e**(6*x**4)*x**3 + 1300*e**(6*x**4)*x**2 - 3500*e**(6*x**4)*x + 2500*e** (6*x**4) + x**4 + 40*x**3 + 350*x**2 - 1000*x + 625),x) - 240*int((e**(12* x**4)*x**6)/(e**(24*x**4)*x**4 - 20*e**(24*x**4)*x**3 + 150*e**(24*x**4)*x **2 - 500*e**(24*x**4)*x + 625*e**(24*x**4) + 8*e**(18*x**4)*x**4 - 140*e* *(18*x**4)*x**3 + 900*e**(18*x**4)*x**2 - 2500*e**(18*x**4)*x + 2500*e**(1 8*x**4) + 14*e**(12*x**4)*x**4 - 260*e**(12*x**4)*x**3 + 1700*e**(12*x**4) *x**2 - 4500*e**(12*x**4)*x + 3750*e**(12*x**4) - 8*e**(6*x**4)*x**4 - 100 *e**(6*x**4)*x**3 + 1300*e**(6*x**4)*x**2 - 3500*e**(6*x**4)*x + 2500*e...