Integrand size = 905, antiderivative size = 34 \[ \int \frac {-400-100 x-800 x^2+1240 x^3-816 x^4+774 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-40-170 x-152 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-480 x+120 x^2-204 x^3+696 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )+\left (-400+100 x-1600 x^2+2560 x^3-1968 x^4+2272 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-80-320 x-496 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-960 x+320 x^2-832 x^3+2128 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log (-4+x)+\left (-800 x^2+1320 x^3-1408 x^4+2202 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-40-150 x-536 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-480 x+200 x^2-1012 x^3+2168 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log ^2(-4+x)+\left (-256 x^4+704 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-192 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-384 x^3+736 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )\right ) \log ^3(-4+x)+\left (-200-150 x-320 x^2+520 x^3-240 x^4+30 x^5+e^{2 x} \left (-90 x+20 x^2\right )+e^x \left (-160 x+100 x^3-20 x^4\right )+\left (-200+50 x-640 x^2+1080 x^3-520 x^4+70 x^5+e^{2 x} \left (-170 x+40 x^2\right )+e^x \left (-320 x+40 x^2+180 x^3-40 x^4\right )\right ) \log (-4+x)+\left (-320 x^2+560 x^3-280 x^4+40 x^5+e^{2 x} \left (-80 x+20 x^2\right )+e^x \left (-160 x+40 x^2+80 x^3-20 x^4\right )\right ) \log ^2(-4+x)\right ) \log (x)-50 x \log ^2(x)}{-100 x+25 x^2+\left (-300 x+75 x^2\right ) \log (-4+x)+\left (-300 x+75 x^2\right ) \log ^2(-4+x)+\left (-100 x+25 x^2\right ) \log ^3(-4+x)} \, dx=\left (\frac {1}{5} \left (e^x+2 x-x^2\right )^2+\frac {2+\log (x)}{1+\log (-4+x)}\right )^2 \] Output:
((ln(x)+2)/(ln(-4+x)+1)+1/5*(exp(x)-x^2+2*x)^2)^2
Leaf count is larger than twice the leaf count of optimal. \(69\) vs. \(2(34)=68\).
Time = 0.61 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.03 \[ \int \frac {-400-100 x-800 x^2+1240 x^3-816 x^4+774 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-40-170 x-152 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-480 x+120 x^2-204 x^3+696 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )+\left (-400+100 x-1600 x^2+2560 x^3-1968 x^4+2272 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-80-320 x-496 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-960 x+320 x^2-832 x^3+2128 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log (-4+x)+\left (-800 x^2+1320 x^3-1408 x^4+2202 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-40-150 x-536 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-480 x+200 x^2-1012 x^3+2168 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log ^2(-4+x)+\left (-256 x^4+704 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-192 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-384 x^3+736 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )\right ) \log ^3(-4+x)+\left (-200-150 x-320 x^2+520 x^3-240 x^4+30 x^5+e^{2 x} \left (-90 x+20 x^2\right )+e^x \left (-160 x+100 x^3-20 x^4\right )+\left (-200+50 x-640 x^2+1080 x^3-520 x^4+70 x^5+e^{2 x} \left (-170 x+40 x^2\right )+e^x \left (-320 x+40 x^2+180 x^3-40 x^4\right )\right ) \log (-4+x)+\left (-320 x^2+560 x^3-280 x^4+40 x^5+e^{2 x} \left (-80 x+20 x^2\right )+e^x \left (-160 x+40 x^2+80 x^3-20 x^4\right )\right ) \log ^2(-4+x)\right ) \log (x)-50 x \log ^2(x)}{-100 x+25 x^2+\left (-300 x+75 x^2\right ) \log (-4+x)+\left (-300 x+75 x^2\right ) \log ^2(-4+x)+\left (-100 x+25 x^2\right ) \log ^3(-4+x)} \, dx=\frac {\left (10+e^{2 x}+4 e^x x+4 x^2-2 e^x x^2-4 x^3+x^4+\left (e^x-(-2+x) x\right )^2 \log (-4+x)+5 \log (x)\right )^2}{25 (1+\log (-4+x))^2} \] Input:
Integrate[(-400 - 100*x - 800*x^2 + 1240*x^3 - 816*x^4 + 774*x^5 - 736*x^6 + 368*x^7 - 88*x^8 + 8*x^9 + E^(4*x)*(-16*x + 4*x^2) + E^(3*x)*(-32*x - 5 6*x^2 + 64*x^3 - 12*x^4) + E^(2*x)*(-40 - 170*x - 152*x^2 + 144*x^3 + 72*x ^4 - 72*x^5 + 12*x^6) + E^x*(-480*x + 120*x^2 - 204*x^3 + 696*x^4 - 448*x^ 5 + 72*x^6 + 16*x^7 - 4*x^8) + (-400 + 100*x - 1600*x^2 + 2560*x^3 - 1968* x^4 + 2272*x^5 - 2208*x^6 + 1104*x^7 - 264*x^8 + 24*x^9 + E^(4*x)*(-48*x + 12*x^2) + E^(3*x)*(-96*x - 168*x^2 + 192*x^3 - 36*x^4) + E^(2*x)*(-80 - 3 20*x - 496*x^2 + 432*x^3 + 216*x^4 - 216*x^5 + 36*x^6) + E^x*(-960*x + 320 *x^2 - 832*x^3 + 2128*x^4 - 1344*x^5 + 216*x^6 + 48*x^7 - 12*x^8))*Log[-4 + x] + (-800*x^2 + 1320*x^3 - 1408*x^4 + 2202*x^5 - 2208*x^6 + 1104*x^7 - 264*x^8 + 24*x^9 + E^(4*x)*(-48*x + 12*x^2) + E^(3*x)*(-96*x - 168*x^2 + 1 92*x^3 - 36*x^4) + E^(2*x)*(-40 - 150*x - 536*x^2 + 432*x^3 + 216*x^4 - 21 6*x^5 + 36*x^6) + E^x*(-480*x + 200*x^2 - 1012*x^3 + 2168*x^4 - 1344*x^5 + 216*x^6 + 48*x^7 - 12*x^8))*Log[-4 + x]^2 + (-256*x^4 + 704*x^5 - 736*x^6 + 368*x^7 - 88*x^8 + 8*x^9 + E^(4*x)*(-16*x + 4*x^2) + E^(3*x)*(-32*x - 5 6*x^2 + 64*x^3 - 12*x^4) + E^(2*x)*(-192*x^2 + 144*x^3 + 72*x^4 - 72*x^5 + 12*x^6) + E^x*(-384*x^3 + 736*x^4 - 448*x^5 + 72*x^6 + 16*x^7 - 4*x^8))*L og[-4 + x]^3 + (-200 - 150*x - 320*x^2 + 520*x^3 - 240*x^4 + 30*x^5 + E^(2 *x)*(-90*x + 20*x^2) + E^x*(-160*x + 100*x^3 - 20*x^4) + (-200 + 50*x - 64 0*x^2 + 1080*x^3 - 520*x^4 + 70*x^5 + E^(2*x)*(-170*x + 40*x^2) + E^x*(-32 0*x + 40*x^2 + 180*x^3 - 40*x^4))*Log[-4 + x] + (-320*x^2 + 560*x^3 - 280* x^4 + 40*x^5 + E^(2*x)*(-80*x + 20*x^2) + E^x*(-160*x + 40*x^2 + 80*x^3 - 20*x^4))*Log[-4 + x]^2)*Log[x] - 50*x*Log[x]^2)/(-100*x + 25*x^2 + (-300*x + 75*x^2)*Log[-4 + x] + (-300*x + 75*x^2)*Log[-4 + x]^2 + (-100*x + 25*x^ 2)*Log[-4 + x]^3),x]
Output:
(10 + E^(2*x) + 4*E^x*x + 4*x^2 - 2*E^x*x^2 - 4*x^3 + x^4 + (E^x - (-2 + x )*x)^2*Log[-4 + x] + 5*Log[x])^2/(25*(1 + Log[-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.
| \(\displaystyle \int \frac {8 x^9-88 x^8+368 x^7-736 x^6+774 x^5-816 x^4+1240 x^3-800 x^2-50 \log ^2(x) x-100 x+\left (8 x^9-88 x^8+368 x^7-736 x^6+704 x^5-256 x^4+e^{4 x} \left (4 x^2-16 x\right )+e^{3 x} \left (-12 x^4+64 x^3-56 x^2-32 x\right )+e^{2 x} \left (12 x^6-72 x^5+72 x^4+144 x^3-192 x^2\right )+e^x \left (-4 x^8+16 x^7+72 x^6-448 x^5+736 x^4-384 x^3\right )\right ) \log ^3(x-4)+\left (24 x^9-264 x^8+1104 x^7-2208 x^6+2202 x^5-1408 x^4+1320 x^3-800 x^2+e^{4 x} \left (12 x^2-48 x\right )+e^{3 x} \left (-36 x^4+192 x^3-168 x^2-96 x\right )+e^{2 x} \left (36 x^6-216 x^5+216 x^4+432 x^3-536 x^2-150 x-40\right )+e^x \left (-12 x^8+48 x^7+216 x^6-1344 x^5+2168 x^4-1012 x^3+200 x^2-480 x\right )\right ) \log ^2(x-4)+e^{4 x} \left (4 x^2-16 x\right )+e^{3 x} \left (-12 x^4+64 x^3-56 x^2-32 x\right )+e^{2 x} \left (12 x^6-72 x^5+72 x^4+144 x^3-152 x^2-170 x-40\right )+e^x \left (-4 x^8+16 x^7+72 x^6-448 x^5+696 x^4-204 x^3+120 x^2-480 x\right )+\left (24 x^9-264 x^8+1104 x^7-2208 x^6+2272 x^5-1968 x^4+2560 x^3-1600 x^2+100 x+e^{4 x} \left (12 x^2-48 x\right )+e^{3 x} \left (-36 x^4+192 x^3-168 x^2-96 x\right )+e^{2 x} \left (36 x^6-216 x^5+216 x^4+432 x^3-496 x^2-320 x-80\right )+e^x \left (-12 x^8+48 x^7+216 x^6-1344 x^5+2128 x^4-832 x^3+320 x^2-960 x\right )-400\right ) \log (x-4)+\left (30 x^5-240 x^4+520 x^3-320 x^2-150 x+\left (40 x^5-280 x^4+560 x^3-320 x^2+e^{2 x} \left (20 x^2-80 x\right )+e^x \left (-20 x^4+80 x^3+40 x^2-160 x\right )\right ) \log ^2(x-4)+e^{2 x} \left (20 x^2-90 x\right )+e^x \left (-20 x^4+100 x^3-160 x\right )+\left (70 x^5-520 x^4+1080 x^3-640 x^2+50 x+e^{2 x} \left (40 x^2-170 x\right )+e^x \left (-40 x^4+180 x^3+40 x^2-320 x\right )-200\right ) \log (x-4)-200\right ) \log (x)-400}{\left (25 x^2-100 x\right ) \log ^3(x-4)+\left (75 x^2-300 x\right ) \log ^2(x-4)+\left (75 x^2-300 x\right ) \log (x-4)+25 x^2-100 x} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-8 x^9+88 x^8-368 x^7+736 x^6-774 x^5+816 x^4-1240 x^3+800 x^2+50 \log ^2(x) x+100 x-\left (8 x^9-88 x^8+368 x^7-736 x^6+704 x^5-256 x^4+e^{4 x} \left (4 x^2-16 x\right )+e^{3 x} \left (-12 x^4+64 x^3-56 x^2-32 x\right )+e^{2 x} \left (12 x^6-72 x^5+72 x^4+144 x^3-192 x^2\right )+e^x \left (-4 x^8+16 x^7+72 x^6-448 x^5+736 x^4-384 x^3\right )\right ) \log ^3(x-4)-\left (24 x^9-264 x^8+1104 x^7-2208 x^6+2202 x^5-1408 x^4+1320 x^3-800 x^2+e^{4 x} \left (12 x^2-48 x\right )+e^{3 x} \left (-36 x^4+192 x^3-168 x^2-96 x\right )+e^{2 x} \left (36 x^6-216 x^5+216 x^4+432 x^3-536 x^2-150 x-40\right )+e^x \left (-12 x^8+48 x^7+216 x^6-1344 x^5+2168 x^4-1012 x^3+200 x^2-480 x\right )\right ) \log ^2(x-4)-e^{4 x} \left (4 x^2-16 x\right )-e^{3 x} \left (-12 x^4+64 x^3-56 x^2-32 x\right )-e^{2 x} \left (12 x^6-72 x^5+72 x^4+144 x^3-152 x^2-170 x-40\right )-e^x \left (-4 x^8+16 x^7+72 x^6-448 x^5+696 x^4-204 x^3+120 x^2-480 x\right )-\left (24 x^9-264 x^8+1104 x^7-2208 x^6+2272 x^5-1968 x^4+2560 x^3-1600 x^2+100 x+e^{4 x} \left (12 x^2-48 x\right )+e^{3 x} \left (-36 x^4+192 x^3-168 x^2-96 x\right )+e^{2 x} \left (36 x^6-216 x^5+216 x^4+432 x^3-496 x^2-320 x-80\right )+e^x \left (-12 x^8+48 x^7+216 x^6-1344 x^5+2128 x^4-832 x^3+320 x^2-960 x\right )-400\right ) \log (x-4)-\left (30 x^5-240 x^4+520 x^3-320 x^2-150 x+\left (40 x^5-280 x^4+560 x^3-320 x^2+e^{2 x} \left (20 x^2-80 x\right )+e^x \left (-20 x^4+80 x^3+40 x^2-160 x\right )\right ) \log ^2(x-4)+e^{2 x} \left (20 x^2-90 x\right )+e^x \left (-20 x^4+100 x^3-160 x\right )+\left (70 x^5-520 x^4+1080 x^3-640 x^2+50 x+e^{2 x} \left (40 x^2-170 x\right )+e^x \left (-40 x^4+180 x^3+40 x^2-320 x\right )-200\right ) \log (x-4)-200\right ) \log (x)+400}{25 (4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{25} \int \frac {2 \left (-4 x^9+44 x^8-184 x^7+368 x^6-387 x^5+408 x^4-620 x^3+400 x^2+25 \log ^2(x) x+50 x+2 \left (-2 x^9+22 x^8-92 x^7+184 x^6-176 x^5+64 x^4+e^{4 x} \left (4 x-x^2\right )+e^{3 x} \left (3 x^4-16 x^3+14 x^2+8 x\right )+3 e^{2 x} \left (-x^6+6 x^5-6 x^4-12 x^3+16 x^2\right )+e^x \left (x^8-4 x^7-18 x^6+112 x^5-184 x^4+96 x^3\right )\right ) \log ^3(x-4)+\left (-12 x^9+132 x^8-552 x^7+1104 x^6-1101 x^5+704 x^4-660 x^3+400 x^2+6 e^{4 x} \left (4 x-x^2\right )+6 e^{3 x} \left (3 x^4-16 x^3+14 x^2+8 x\right )+e^{2 x} \left (-18 x^6+108 x^5-108 x^4-216 x^3+268 x^2+75 x+20\right )+2 e^x \left (3 x^8-12 x^7-54 x^6+336 x^5-542 x^4+253 x^3-50 x^2+120 x\right )\right ) \log ^2(x-4)+2 e^{4 x} \left (4 x-x^2\right )+2 e^{3 x} \left (3 x^4-16 x^3+14 x^2+8 x\right )+e^{2 x} \left (-6 x^6+36 x^5-36 x^4-72 x^3+76 x^2+85 x+20\right )+2 e^x \left (x^8-4 x^7-18 x^6+112 x^5-174 x^4+51 x^3-30 x^2+120 x\right )+2 \left (-6 x^9+66 x^8-276 x^7+552 x^6-568 x^5+492 x^4-640 x^3+400 x^2-25 x+3 e^{4 x} \left (4 x-x^2\right )+3 e^{3 x} \left (3 x^4-16 x^3+14 x^2+8 x\right )+e^{2 x} \left (-9 x^6+54 x^5-54 x^4-108 x^3+124 x^2+80 x+20\right )+e^x \left (3 x^8-12 x^7-54 x^6+336 x^5-532 x^4+208 x^3-80 x^2+240 x\right )+100\right ) \log (x-4)+5 \left (-3 x^5+24 x^4-52 x^3+32 x^2+15 x+2 \left (-2 x^5+14 x^4-28 x^3+16 x^2+e^{2 x} \left (4 x-x^2\right )+e^x \left (x^4-4 x^3-2 x^2+8 x\right )\right ) \log ^2(x-4)+e^{2 x} \left (9 x-2 x^2\right )+2 e^x \left (x^4-5 x^3+8 x\right )+\left (-7 x^5+52 x^4-108 x^3+64 x^2-5 x+e^{2 x} \left (17 x-4 x^2\right )+2 e^x \left (2 x^4-9 x^3-2 x^2+16 x\right )+20\right ) \log (x-4)+20\right ) \log (x)+200\right )}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+44 x^8-184 x^7+368 x^6-387 x^5+408 x^4-620 x^3+400 x^2+25 \log ^2(x) x+50 x+2 \left (-2 x^9+22 x^8-92 x^7+184 x^6-176 x^5+64 x^4+e^{4 x} \left (4 x-x^2\right )+e^{3 x} \left (3 x^4-16 x^3+14 x^2+8 x\right )+3 e^{2 x} \left (-x^6+6 x^5-6 x^4-12 x^3+16 x^2\right )+e^x \left (x^8-4 x^7-18 x^6+112 x^5-184 x^4+96 x^3\right )\right ) \log ^3(x-4)+\left (-12 x^9+132 x^8-552 x^7+1104 x^6-1101 x^5+704 x^4-660 x^3+400 x^2+6 e^{4 x} \left (4 x-x^2\right )+6 e^{3 x} \left (3 x^4-16 x^3+14 x^2+8 x\right )+e^{2 x} \left (-18 x^6+108 x^5-108 x^4-216 x^3+268 x^2+75 x+20\right )+2 e^x \left (3 x^8-12 x^7-54 x^6+336 x^5-542 x^4+253 x^3-50 x^2+120 x\right )\right ) \log ^2(x-4)+2 e^{4 x} \left (4 x-x^2\right )+2 e^{3 x} \left (3 x^4-16 x^3+14 x^2+8 x\right )+e^{2 x} \left (-6 x^6+36 x^5-36 x^4-72 x^3+76 x^2+85 x+20\right )+2 e^x \left (x^8-4 x^7-18 x^6+112 x^5-174 x^4+51 x^3-30 x^2+120 x\right )+2 \left (-6 x^9+66 x^8-276 x^7+552 x^6-568 x^5+492 x^4-640 x^3+400 x^2-25 x+3 e^{4 x} \left (4 x-x^2\right )+3 e^{3 x} \left (3 x^4-16 x^3+14 x^2+8 x\right )+e^{2 x} \left (-9 x^6+54 x^5-54 x^4-108 x^3+124 x^2+80 x+20\right )+e^x \left (3 x^8-12 x^7-54 x^6+336 x^5-532 x^4+208 x^3-80 x^2+240 x\right )+100\right ) \log (x-4)+5 \left (-3 x^5+24 x^4-52 x^3+32 x^2+15 x+2 \left (-2 x^5+14 x^4-28 x^3+16 x^2+e^{2 x} \left (4 x-x^2\right )+e^x \left (x^4-4 x^3-2 x^2+8 x\right )\right ) \log ^2(x-4)+e^{2 x} \left (9 x-2 x^2\right )+2 e^x \left (x^4-5 x^3+8 x\right )+\left (-7 x^5+52 x^4-108 x^3+64 x^2-5 x+e^{2 x} \left (17 x-4 x^2\right )+2 e^x \left (2 x^4-9 x^3-2 x^2+16 x\right )+20\right ) \log (x-4)+20\right ) \log (x)+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {4 \log ^3(x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {12 \log ^2(x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {44 \log ^3(x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log ^2(x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {184 \log ^3(x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log ^2(x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {368 \log ^3(x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log ^2(x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {20 \log ^2(x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {352 \log ^3(x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {1101 \log ^2(x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {140 \log ^2(x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {128 \log ^3(x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {704 \log ^2(x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {280 \log ^2(x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {660 \log ^2(x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log ^2(x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 \log ^2(x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2}{25} \int \frac {-4 x^9+2 e^x x^8+44 x^8-8 e^x x^7-184 x^7-36 e^x x^6-6 e^{2 x} x^6+368 x^6+224 e^x x^5+36 e^{2 x} x^5-387 x^5-348 e^x x^4-36 e^{2 x} x^4+6 e^{3 x} x^4+408 x^4+102 e^x x^3-72 e^{2 x} x^3-32 e^{3 x} x^3-620 x^3-60 e^x x^2+76 e^{2 x} x^2+28 e^{3 x} x^2-2 e^{4 x} x^2+400 x^2+240 e^x x+85 e^{2 x} x+16 e^{3 x} x+8 e^{4 x} x-2 \left (-2 x+e^x+2\right ) (x-4) \left (e^x-(x-2) x\right )^3 \log ^3(x-4) x+25 \log ^2(x) x+50 x+20 e^{2 x}-5 \left (3 x^5-2 \left (12+e^x\right ) x^4+2 \left (26+5 e^x\right ) x^3+2 \left (-16+e^{2 x}\right ) x^2-\left (15+16 e^x+9 e^{2 x}\right ) x-20\right ) \log (x)-(x-4) \left (e^x-(x-2) x\right ) \log ^2(x-4) \left (6 e^{3 x} x-12 e^{2 x} \left (x^2-x-1\right ) x+\left (-12 x^5+60 x^4-96 x^3+48 x^2-45 x+50\right ) x-10 \left (2 x-e^x-2\right ) \log (x) x+e^x \left (6 x^5-48 x^3+48 x^2+20 x+5\right )\right )-\log (x-4) \left (2 \left (6 x^9-66 x^8+276 x^7-552 x^6+568 x^5-492 x^4+640 x^3-400 x^2+3 e^{4 x} (x-4) x-3 e^{3 x} \left (3 x^3-16 x^2+14 x+8\right ) x-e^x \left (3 x^7-12 x^6-54 x^5+336 x^4-532 x^3+208 x^2-80 x+240\right ) x+25 x+e^{2 x} \left (9 x^6-54 x^5+54 x^4+108 x^3-124 x^2-80 x-20\right )-100\right )+5 \left (7 x^5-4 \left (13+e^x\right ) x^4+18 \left (6+e^x\right ) x^3+4 \left (-16+e^x+e^{2 x}\right ) x^2+\left (5-32 e^x-17 e^{2 x}\right ) x-20\right ) \log (x)\right )+200}{(4-x) x (\log (x-4)+1)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{25} \int \left (\frac {12 \log (x-4) x^8}{(x-4) (\log (x-4)+1)^3}+\frac {4 x^8}{(x-4) (\log (x-4)+1)^3}-\frac {132 \log (x-4) x^7}{(x-4) (\log (x-4)+1)^3}-\frac {44 x^7}{(x-4) (\log (x-4)+1)^3}+\frac {552 \log (x-4) x^6}{(x-4) (\log (x-4)+1)^3}+\frac {184 x^6}{(x-4) (\log (x-4)+1)^3}-\frac {1104 \log (x-4) x^5}{(x-4) (\log (x-4)+1)^3}-\frac {368 x^5}{(x-4) (\log (x-4)+1)^3}+\frac {35 \log (x-4) \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {15 \log (x) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {4 (x-2)^3 \log ^3(x-4) x^4}{(\log (x-4)+1)^3}+\frac {1136 \log (x-4) x^4}{(x-4) (\log (x-4)+1)^3}+\frac {387 x^4}{(x-4) (\log (x-4)+1)^3}-\frac {260 \log (x-4) \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {120 \log (x) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {4 (x-2)^3 \log ^3(x-4) x^3}{(\log (x-4)+1)^3}-\frac {984 \log (x-4) x^3}{(x-4) (\log (x-4)+1)^3}-\frac {408 x^3}{(x-4) (\log (x-4)+1)^3}+\frac {20 (x-2) \log ^2(x-4) \log (x) x^2}{(\log (x-4)+1)^3}+\frac {540 \log (x-4) \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {260 \log (x) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {1280 \log (x-4) x^2}{(x-4) (\log (x-4)+1)^3}+\frac {620 x^2}{(x-4) (\log (x-4)+1)^3}-\frac {20 (x-2) \log ^2(x-4) \log (x) x}{(\log (x-4)+1)^3}-\frac {320 \log (x-4) \log (x) x}{(x-4) (\log (x-4)+1)^3}-\frac {160 \log (x) x}{(x-4) (\log (x-4)+1)^3}+\frac {(x-2) \left (12 x^5-60 x^4+96 x^3-48 x^2+45 x-50\right ) \log ^2(x-4) x}{(\log (x-4)+1)^3}-\frac {800 \log (x-4) x}{(x-4) (\log (x-4)+1)^3}-\frac {400 x}{(x-4) (\log (x-4)+1)^3}+2 e^{4 x}-\frac {25 \log ^2(x)}{(x-4) (\log (x-4)+1)^3}-2 e^{3 x} \left (3 x^2-4 x-2\right )+\frac {25 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {75 \log (x)}{(x-4) (\log (x-4)+1)^3}-\frac {2 e^x \left (\log ^2(x-4) x^7+2 \log (x-4) x^7+x^7-4 \log ^2(x-4) x^6-8 \log (x-4) x^6-4 x^6-18 \log ^2(x-4) x^5-36 \log (x-4) x^5-18 x^5+112 \log ^2(x-4) x^4+224 \log (x-4) x^4+112 x^4-184 \log ^2(x-4) x^3-358 \log (x-4) x^3+5 \log (x-4) \log (x) x^3+5 \log (x) x^3-174 x^3+96 \log ^2(x-4) x^2+157 \log (x-4) x^2-20 \log (x-4) \log (x) x^2-25 \log (x) x^2+51 x^2-50 \log (x-4) x-10 \log (x-4) \log (x) x-30 x+120 \log (x-4)+40 \log (x-4) \log (x)+40 \log (x)+120\right )}{(x-4) (\log (x-4)+1)^2}+\frac {50 \log (x-4)}{(x-4) (\log (x-4)+1)^3}-\frac {50}{(x-4) (\log (x-4)+1)^3}-\frac {100 \log (x-4) \log (x)}{(x-4) (\log (x-4)+1)^3 x}-\frac {100 \log (x)}{(x-4) (\log (x-4)+1)^3 x}+\frac {e^{2 x} \left (6 \log ^2(x-4) x^6+12 \log (x-4) x^6+6 x^6-36 \log ^2(x-4) x^5-72 \log (x-4) x^5-36 x^5+36 \log ^2(x-4) x^4+72 \log (x-4) x^4+36 x^4+72 \log ^2(x-4) x^3+144 \log (x-4) x^3+72 x^3-96 \log ^2(x-4) x^2-172 \log (x-4) x^2+10 \log (x-4) \log (x) x^2+10 \log (x) x^2-76 x^2-75 \log (x-4) x-40 \log (x-4) \log (x) x-45 \log (x) x-85 x-20 \log (x-4)-20\right )}{(x-4) (\log (x-4)+1)^2 x}-\frac {200 \log (x-4)}{(x-4) (\log (x-4)+1)^3 x}-\frac {200}{(x-4) (\log (x-4)+1)^3 x}\right )dx\) |
Input:
Int[(-400 - 100*x - 800*x^2 + 1240*x^3 - 816*x^4 + 774*x^5 - 736*x^6 + 368 *x^7 - 88*x^8 + 8*x^9 + E^(4*x)*(-16*x + 4*x^2) + E^(3*x)*(-32*x - 56*x^2 + 64*x^3 - 12*x^4) + E^(2*x)*(-40 - 170*x - 152*x^2 + 144*x^3 + 72*x^4 - 7 2*x^5 + 12*x^6) + E^x*(-480*x + 120*x^2 - 204*x^3 + 696*x^4 - 448*x^5 + 72 *x^6 + 16*x^7 - 4*x^8) + (-400 + 100*x - 1600*x^2 + 2560*x^3 - 1968*x^4 + 2272*x^5 - 2208*x^6 + 1104*x^7 - 264*x^8 + 24*x^9 + E^(4*x)*(-48*x + 12*x^ 2) + E^(3*x)*(-96*x - 168*x^2 + 192*x^3 - 36*x^4) + E^(2*x)*(-80 - 320*x - 496*x^2 + 432*x^3 + 216*x^4 - 216*x^5 + 36*x^6) + E^x*(-960*x + 320*x^2 - 832*x^3 + 2128*x^4 - 1344*x^5 + 216*x^6 + 48*x^7 - 12*x^8))*Log[-4 + x] + (-800*x^2 + 1320*x^3 - 1408*x^4 + 2202*x^5 - 2208*x^6 + 1104*x^7 - 264*x^ 8 + 24*x^9 + E^(4*x)*(-48*x + 12*x^2) + E^(3*x)*(-96*x - 168*x^2 + 192*x^3 - 36*x^4) + E^(2*x)*(-40 - 150*x - 536*x^2 + 432*x^3 + 216*x^4 - 216*x^5 + 36*x^6) + E^x*(-480*x + 200*x^2 - 1012*x^3 + 2168*x^4 - 1344*x^5 + 216*x ^6 + 48*x^7 - 12*x^8))*Log[-4 + x]^2 + (-256*x^4 + 704*x^5 - 736*x^6 + 368 *x^7 - 88*x^8 + 8*x^9 + E^(4*x)*(-16*x + 4*x^2) + E^(3*x)*(-32*x - 56*x^2 + 64*x^3 - 12*x^4) + E^(2*x)*(-192*x^2 + 144*x^3 + 72*x^4 - 72*x^5 + 12*x^ 6) + E^x*(-384*x^3 + 736*x^4 - 448*x^5 + 72*x^6 + 16*x^7 - 4*x^8))*Log[-4 + x]^3 + (-200 - 150*x - 320*x^2 + 520*x^3 - 240*x^4 + 30*x^5 + E^(2*x)*(- 90*x + 20*x^2) + E^x*(-160*x + 100*x^3 - 20*x^4) + (-200 + 50*x - 640*x^2 + 1080*x^3 - 520*x^4 + 70*x^5 + E^(2*x)*(-170*x + 40*x^2) + E^x*(-320*x + 40*x^2 + 180*x^3 - 40*x^4))*Log[-4 + x] + (-320*x^2 + 560*x^3 - 280*x^4 + 40*x^5 + E^(2*x)*(-80*x + 20*x^2) + E^x*(-160*x + 40*x^2 + 80*x^3 - 20*x^4 ))*Log[-4 + x]^2)*Log[x] - 50*x*Log[x]^2)/(-100*x + 25*x^2 + (-300*x + 75* x^2)*Log[-4 + x] + (-300*x + 75*x^2)*Log[-4 + x]^2 + (-100*x + 25*x^2)*Log [-4 + x]^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(329\) vs. \(2(31)=62\).
Time = 0.43 (sec) , antiderivative size = 330, normalized size of antiderivative = 9.71
\[\frac {x^{8}}{25}-\frac {8 x^{7}}{25}+\frac {24 x^{6}}{25}-\frac {32 x^{5}}{25}+\frac {16 x^{4}}{25}+\frac {{\mathrm e}^{4 x}}{25}+\frac {8 x \,{\mathrm e}^{3 x}}{25}-\frac {4 x^{2} {\mathrm e}^{3 x}}{25}+\frac {24 \,{\mathrm e}^{2 x} x^{2}}{25}-\frac {24 \,{\mathrm e}^{2 x} x^{3}}{25}+\frac {6 x^{4} {\mathrm e}^{2 x}}{25}+\frac {32 \,{\mathrm e}^{x} x^{3}}{25}-\frac {48 \,{\mathrm e}^{x} x^{4}}{25}+\frac {24 x^{5} {\mathrm e}^{x}}{25}-\frac {4 x^{6} {\mathrm e}^{x}}{25}+\frac {20-8 \ln \left (x \right ) \ln \left (x -4\right ) x^{3}+2 x^{4} \ln \left (x \right )-8 \,{\mathrm e}^{x} x^{2}-16 x^{3} \ln \left (x -4\right )+8 \ln \left (x \right ) {\mathrm e}^{x} \ln \left (x -4\right ) x -4 \ln \left (x \right ) {\mathrm e}^{x} \ln \left (x -4\right ) x^{2}+2 \,{\mathrm e}^{2 x} \ln \left (x \right )-4 x^{2} {\mathrm e}^{x} \ln \left (x \right )+8 x \,{\mathrm e}^{x} \ln \left (x \right )-8 x^{3} \ln \left (x \right )+16 \,{\mathrm e}^{x} x +8 x^{2} \ln \left (x \right )+4 \,{\mathrm e}^{2 x}+20 \ln \left (x \right )+5 \ln \left (x \right )^{2}+16 x^{2}-16 x^{3}+4 x^{4}+16 x^{2} \ln \left (x -4\right )+4 \ln \left (x -4\right ) x^{4}+2 \ln \left (x \right ) \ln \left (x -4\right ) x^{4}+8 \ln \left (x \right ) \ln \left (x -4\right ) x^{2}-8 \,{\mathrm e}^{x} \ln \left (x -4\right ) x^{2}+16 \,{\mathrm e}^{x} \ln \left (x -4\right ) x +2 \,{\mathrm e}^{2 x} \ln \left (x \right ) \ln \left (x -4\right )+4 \,{\mathrm e}^{2 x} \ln \left (x -4\right )}{5 \left (\ln \left (x -4\right )+1\right )^{2}}\]
Input:
int((-50*x*ln(x)^2+(((20*x^2-80*x)*exp(x)^2+(-20*x^4+80*x^3+40*x^2-160*x)* exp(x)+40*x^5-280*x^4+560*x^3-320*x^2)*ln(x-4)^2+((40*x^2-170*x)*exp(x)^2+ (-40*x^4+180*x^3+40*x^2-320*x)*exp(x)+70*x^5-520*x^4+1080*x^3-640*x^2+50*x -200)*ln(x-4)+(20*x^2-90*x)*exp(x)^2+(-20*x^4+100*x^3-160*x)*exp(x)+30*x^5 -240*x^4+520*x^3-320*x^2-150*x-200)*ln(x)+((4*x^2-16*x)*exp(x)^4+(-12*x^4+ 64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-192*x^2)*exp(x) ^2+(-4*x^8+16*x^7+72*x^6-448*x^5+736*x^4-384*x^3)*exp(x)+8*x^9-88*x^8+368* x^7-736*x^6+704*x^5-256*x^4)*ln(x-4)^3+((12*x^2-48*x)*exp(x)^4+(-36*x^4+19 2*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-536*x^2-150*x -40)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2168*x^4-1012*x^3+200*x^2-4 80*x)*exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2202*x^5-1408*x^4+1320*x^3-8 00*x^2)*ln(x-4)^2+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3-168*x^2-96*x)*e xp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-496*x^2-320*x-80)*exp(x)^2+(-12*x^ 8+48*x^7+216*x^6-1344*x^5+2128*x^4-832*x^3+320*x^2-960*x)*exp(x)+24*x^9-26 4*x^8+1104*x^7-2208*x^6+2272*x^5-1968*x^4+2560*x^3-1600*x^2+100*x-400)*ln( x-4)+(4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-7 2*x^5+72*x^4+144*x^3-152*x^2-170*x-40)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448* x^5+696*x^4-204*x^3+120*x^2-480*x)*exp(x)+8*x^9-88*x^8+368*x^7-736*x^6+774 *x^5-816*x^4+1240*x^3-800*x^2-100*x-400)/((25*x^2-100*x)*ln(x-4)^3+(75*x^2 -300*x)*ln(x-4)^2+(75*x^2-300*x)*ln(x-4)+25*x^2-100*x),x)
Output:
1/25*x^8-8/25*x^7+24/25*x^6-32/25*x^5+16/25*x^4+1/25*exp(x)^4+8/25*x*exp(x )^3-4/25*x^2*exp(x)^3+24/25*exp(x)^2*x^2-24/25*exp(x)^2*x^3+6/25*exp(x)^2* x^4+32/25*exp(x)*x^3-48/25*exp(x)*x^4+24/25*x^5*exp(x)-4/25*x^6*exp(x)+1/5 *(20-8*ln(x)*ln(x-4)*x^3+2*x^4*ln(x)-8*exp(x)*x^2-16*x^3*ln(x-4)+2*exp(x)^ 2*ln(x)+8*ln(x)*exp(x)*ln(x-4)*x-4*ln(x)*exp(x)*ln(x-4)*x^2-4*x^2*exp(x)*l n(x)+8*x*exp(x)*ln(x)+4*exp(x)^2-8*x^3*ln(x)+16*exp(x)*x+8*x^2*ln(x)+20*ln (x)+5*ln(x)^2+16*x^2-16*x^3+4*x^4+16*x^2*ln(x-4)+4*ln(x-4)*x^4+2*ln(x)*ln( x-4)*x^4+8*ln(x)*ln(x-4)*x^2-8*exp(x)*ln(x-4)*x^2+16*exp(x)*ln(x-4)*x+4*ex p(x)^2*ln(x-4)+2*exp(x)^2*ln(x)*ln(x-4))/(ln(x-4)+1)^2
Leaf count of result is larger than twice the leaf count of optimal. 400 vs. \(2 (32) = 64\).
Time = 0.11 (sec) , antiderivative size = 400, normalized size of antiderivative = 11.76 \[ \int \frac {-400-100 x-800 x^2+1240 x^3-816 x^4+774 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-40-170 x-152 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-480 x+120 x^2-204 x^3+696 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )+\left (-400+100 x-1600 x^2+2560 x^3-1968 x^4+2272 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-80-320 x-496 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-960 x+320 x^2-832 x^3+2128 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log (-4+x)+\left (-800 x^2+1320 x^3-1408 x^4+2202 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-40-150 x-536 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-480 x+200 x^2-1012 x^3+2168 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log ^2(-4+x)+\left (-256 x^4+704 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-192 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-384 x^3+736 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )\right ) \log ^3(-4+x)+\left (-200-150 x-320 x^2+520 x^3-240 x^4+30 x^5+e^{2 x} \left (-90 x+20 x^2\right )+e^x \left (-160 x+100 x^3-20 x^4\right )+\left (-200+50 x-640 x^2+1080 x^3-520 x^4+70 x^5+e^{2 x} \left (-170 x+40 x^2\right )+e^x \left (-320 x+40 x^2+180 x^3-40 x^4\right )\right ) \log (-4+x)+\left (-320 x^2+560 x^3-280 x^4+40 x^5+e^{2 x} \left (-80 x+20 x^2\right )+e^x \left (-160 x+40 x^2+80 x^3-20 x^4\right )\right ) \log ^2(-4+x)\right ) \log (x)-50 x \log ^2(x)}{-100 x+25 x^2+\left (-300 x+75 x^2\right ) \log (-4+x)+\left (-300 x+75 x^2\right ) \log ^2(-4+x)+\left (-100 x+25 x^2\right ) \log ^3(-4+x)} \, dx=\frac {x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 36 \, x^{4} - 80 \, x^{3} + {\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 16 \, x^{4} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3}\right )} e^{x} + e^{\left (4 \, x\right )}\right )} \log \left (x - 4\right )^{2} + 80 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 2 \, {\left (3 \, x^{4} - 12 \, x^{3} + 12 \, x^{2} + 10\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3} + 10 \, x^{2} - 20 \, x\right )} e^{x} + 2 \, {\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 26 \, x^{4} - 40 \, x^{3} + 40 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 2 \, {\left (3 \, x^{4} - 12 \, x^{3} + 12 \, x^{2} + 5\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3} + 5 \, x^{2} - 10 \, x\right )} e^{x} + e^{\left (4 \, x\right )}\right )} \log \left (x - 4\right ) + 10 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2} - 2 \, {\left (x^{2} - 2 \, x\right )} e^{x} + {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2} - 2 \, {\left (x^{2} - 2 \, x\right )} e^{x} + e^{\left (2 \, x\right )}\right )} \log \left (x - 4\right ) + e^{\left (2 \, x\right )} + 10\right )} \log \left (x\right ) + 25 \, \log \left (x\right )^{2} + e^{\left (4 \, x\right )} + 100}{25 \, {\left (\log \left (x - 4\right )^{2} + 2 \, \log \left (x - 4\right ) + 1\right )}} \] Input:
integrate((-50*x*log(x)^2+(((20*x^2-80*x)*exp(x)^2+(-20*x^4+80*x^3+40*x^2- 160*x)*exp(x)+40*x^5-280*x^4+560*x^3-320*x^2)*log(-4+x)^2+((40*x^2-170*x)* exp(x)^2+(-40*x^4+180*x^3+40*x^2-320*x)*exp(x)+70*x^5-520*x^4+1080*x^3-640 *x^2+50*x-200)*log(-4+x)+(20*x^2-90*x)*exp(x)^2+(-20*x^4+100*x^3-160*x)*ex p(x)+30*x^5-240*x^4+520*x^3-320*x^2-150*x-200)*log(x)+((4*x^2-16*x)*exp(x) ^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-192 *x^2)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+736*x^4-384*x^3)*exp(x)+8*x^9 -88*x^8+368*x^7-736*x^6+704*x^5-256*x^4)*log(-4+x)^3+((12*x^2-48*x)*exp(x) ^4+(-36*x^4+192*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3 -536*x^2-150*x-40)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2168*x^4-1012 *x^3+200*x^2-480*x)*exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2202*x^5-1408* x^4+1320*x^3-800*x^2)*log(-4+x)^2+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3 -168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-496*x^2-320*x-80)* exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2128*x^4-832*x^3+320*x^2-960*x)* exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2272*x^5-1968*x^4+2560*x^3-1600*x^ 2+100*x-400)*log(-4+x)+(4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)* exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-152*x^2-170*x-40)*exp(x)^2+(-4*x^8+ 16*x^7+72*x^6-448*x^5+696*x^4-204*x^3+120*x^2-480*x)*exp(x)+8*x^9-88*x^8+3 68*x^7-736*x^6+774*x^5-816*x^4+1240*x^3-800*x^2-100*x-400)/((25*x^2-100*x) *log(-4+x)^3+(75*x^2-300*x)*log(-4+x)^2+(75*x^2-300*x)*log(-4+x)+25*x^2-10 0*x),x, algorithm="fricas")
Output:
1/25*(x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 36*x^4 - 80*x^3 + (x^8 - 8*x^7 + 24* x^6 - 32*x^5 + 16*x^4 - 4*(x^2 - 2*x)*e^(3*x) + 6*(x^4 - 4*x^3 + 4*x^2)*e^ (2*x) - 4*(x^6 - 6*x^5 + 12*x^4 - 8*x^3)*e^x + e^(4*x))*log(x - 4)^2 + 80* x^2 - 4*(x^2 - 2*x)*e^(3*x) + 2*(3*x^4 - 12*x^3 + 12*x^2 + 10)*e^(2*x) - 4 *(x^6 - 6*x^5 + 12*x^4 - 8*x^3 + 10*x^2 - 20*x)*e^x + 2*(x^8 - 8*x^7 + 24* x^6 - 32*x^5 + 26*x^4 - 40*x^3 + 40*x^2 - 4*(x^2 - 2*x)*e^(3*x) + 2*(3*x^4 - 12*x^3 + 12*x^2 + 5)*e^(2*x) - 4*(x^6 - 6*x^5 + 12*x^4 - 8*x^3 + 5*x^2 - 10*x)*e^x + e^(4*x))*log(x - 4) + 10*(x^4 - 4*x^3 + 4*x^2 - 2*(x^2 - 2*x )*e^x + (x^4 - 4*x^3 + 4*x^2 - 2*(x^2 - 2*x)*e^x + e^(2*x))*log(x - 4) + e ^(2*x) + 10)*log(x) + 25*log(x)^2 + e^(4*x) + 100)/(log(x - 4)^2 + 2*log(x - 4) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 532 vs. \(2 (26) = 52\).
Time = 0.90 (sec) , antiderivative size = 532, normalized size of antiderivative = 15.65 \[ \int \frac {-400-100 x-800 x^2+1240 x^3-816 x^4+774 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-40-170 x-152 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-480 x+120 x^2-204 x^3+696 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )+\left (-400+100 x-1600 x^2+2560 x^3-1968 x^4+2272 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-80-320 x-496 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-960 x+320 x^2-832 x^3+2128 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log (-4+x)+\left (-800 x^2+1320 x^3-1408 x^4+2202 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-40-150 x-536 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-480 x+200 x^2-1012 x^3+2168 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log ^2(-4+x)+\left (-256 x^4+704 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-192 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-384 x^3+736 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )\right ) \log ^3(-4+x)+\left (-200-150 x-320 x^2+520 x^3-240 x^4+30 x^5+e^{2 x} \left (-90 x+20 x^2\right )+e^x \left (-160 x+100 x^3-20 x^4\right )+\left (-200+50 x-640 x^2+1080 x^3-520 x^4+70 x^5+e^{2 x} \left (-170 x+40 x^2\right )+e^x \left (-320 x+40 x^2+180 x^3-40 x^4\right )\right ) \log (-4+x)+\left (-320 x^2+560 x^3-280 x^4+40 x^5+e^{2 x} \left (-80 x+20 x^2\right )+e^x \left (-160 x+40 x^2+80 x^3-20 x^4\right )\right ) \log ^2(-4+x)\right ) \log (x)-50 x \log ^2(x)}{-100 x+25 x^2+\left (-300 x+75 x^2\right ) \log (-4+x)+\left (-300 x+75 x^2\right ) \log ^2(-4+x)+\left (-100 x+25 x^2\right ) \log ^3(-4+x)} \, dx =\text {Too large to display} \] Input:
integrate((-50*x*ln(x)**2+(((20*x**2-80*x)*exp(x)**2+(-20*x**4+80*x**3+40* x**2-160*x)*exp(x)+40*x**5-280*x**4+560*x**3-320*x**2)*ln(-4+x)**2+((40*x* *2-170*x)*exp(x)**2+(-40*x**4+180*x**3+40*x**2-320*x)*exp(x)+70*x**5-520*x **4+1080*x**3-640*x**2+50*x-200)*ln(-4+x)+(20*x**2-90*x)*exp(x)**2+(-20*x* *4+100*x**3-160*x)*exp(x)+30*x**5-240*x**4+520*x**3-320*x**2-150*x-200)*ln (x)+((4*x**2-16*x)*exp(x)**4+(-12*x**4+64*x**3-56*x**2-32*x)*exp(x)**3+(12 *x**6-72*x**5+72*x**4+144*x**3-192*x**2)*exp(x)**2+(-4*x**8+16*x**7+72*x** 6-448*x**5+736*x**4-384*x**3)*exp(x)+8*x**9-88*x**8+368*x**7-736*x**6+704* x**5-256*x**4)*ln(-4+x)**3+((12*x**2-48*x)*exp(x)**4+(-36*x**4+192*x**3-16 8*x**2-96*x)*exp(x)**3+(36*x**6-216*x**5+216*x**4+432*x**3-536*x**2-150*x- 40)*exp(x)**2+(-12*x**8+48*x**7+216*x**6-1344*x**5+2168*x**4-1012*x**3+200 *x**2-480*x)*exp(x)+24*x**9-264*x**8+1104*x**7-2208*x**6+2202*x**5-1408*x* *4+1320*x**3-800*x**2)*ln(-4+x)**2+((12*x**2-48*x)*exp(x)**4+(-36*x**4+192 *x**3-168*x**2-96*x)*exp(x)**3+(36*x**6-216*x**5+216*x**4+432*x**3-496*x** 2-320*x-80)*exp(x)**2+(-12*x**8+48*x**7+216*x**6-1344*x**5+2128*x**4-832*x **3+320*x**2-960*x)*exp(x)+24*x**9-264*x**8+1104*x**7-2208*x**6+2272*x**5- 1968*x**4+2560*x**3-1600*x**2+100*x-400)*ln(-4+x)+(4*x**2-16*x)*exp(x)**4+ (-12*x**4+64*x**3-56*x**2-32*x)*exp(x)**3+(12*x**6-72*x**5+72*x**4+144*x** 3-152*x**2-170*x-40)*exp(x)**2+(-4*x**8+16*x**7+72*x**6-448*x**5+696*x**4- 204*x**3+120*x**2-480*x)*exp(x)+8*x**9-88*x**8+368*x**7-736*x**6+774*x**5- 816*x**4+1240*x**3-800*x**2-100*x-400)/((25*x**2-100*x)*ln(-4+x)**3+(75*x* *2-300*x)*ln(-4+x)**2+(75*x**2-300*x)*ln(-4+x)+25*x**2-100*x),x)
Output:
x**8/25 - 8*x**7/25 + 24*x**6/25 - 32*x**5/25 + 16*x**4/25 + ((15625*log(x - 4)**2 + 31250*log(x - 4) + 15625)*exp(4*x) + (-62500*x**2*log(x - 4)**2 - 125000*x**2*log(x - 4) - 62500*x**2 + 125000*x*log(x - 4)**2 + 250000*x *log(x - 4) + 125000*x)*exp(3*x) + (93750*x**4*log(x - 4)**2 + 187500*x**4 *log(x - 4) + 93750*x**4 - 375000*x**3*log(x - 4)**2 - 750000*x**3*log(x - 4) - 375000*x**3 + 375000*x**2*log(x - 4)**2 + 750000*x**2*log(x - 4) + 3 75000*x**2 + 156250*log(x)*log(x - 4) + 156250*log(x) + 312500*log(x - 4) + 312500)*exp(2*x) + (-62500*x**6*log(x - 4)**2 - 125000*x**6*log(x - 4) - 62500*x**6 + 375000*x**5*log(x - 4)**2 + 750000*x**5*log(x - 4) + 375000* x**5 - 750000*x**4*log(x - 4)**2 - 1500000*x**4*log(x - 4) - 750000*x**4 + 500000*x**3*log(x - 4)**2 + 1000000*x**3*log(x - 4) + 500000*x**3 - 31250 0*x**2*log(x)*log(x - 4) - 312500*x**2*log(x) - 625000*x**2*log(x - 4) - 6 25000*x**2 + 625000*x*log(x)*log(x - 4) + 625000*x*log(x) + 1250000*x*log( x - 4) + 1250000*x)*exp(x))/(390625*log(x - 4)**2 + 781250*log(x - 4) + 39 0625) + (2*x**4*log(x) + 4*x**4 - 8*x**3*log(x) - 16*x**3 + 8*x**2*log(x) + 16*x**2 + (2*x**4*log(x) + 4*x**4 - 8*x**3*log(x) - 16*x**3 + 8*x**2*log (x) + 16*x**2)*log(x - 4) + 5*log(x)**2 + 20*log(x) + 20)/(5*log(x - 4)**2 + 10*log(x - 4) + 5)
Leaf count of result is larger than twice the leaf count of optimal. 400 vs. \(2 (32) = 64\).
Time = 0.16 (sec) , antiderivative size = 400, normalized size of antiderivative = 11.76 \[ \int \frac {-400-100 x-800 x^2+1240 x^3-816 x^4+774 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-40-170 x-152 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-480 x+120 x^2-204 x^3+696 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )+\left (-400+100 x-1600 x^2+2560 x^3-1968 x^4+2272 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-80-320 x-496 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-960 x+320 x^2-832 x^3+2128 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log (-4+x)+\left (-800 x^2+1320 x^3-1408 x^4+2202 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-40-150 x-536 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-480 x+200 x^2-1012 x^3+2168 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log ^2(-4+x)+\left (-256 x^4+704 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-192 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-384 x^3+736 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )\right ) \log ^3(-4+x)+\left (-200-150 x-320 x^2+520 x^3-240 x^4+30 x^5+e^{2 x} \left (-90 x+20 x^2\right )+e^x \left (-160 x+100 x^3-20 x^4\right )+\left (-200+50 x-640 x^2+1080 x^3-520 x^4+70 x^5+e^{2 x} \left (-170 x+40 x^2\right )+e^x \left (-320 x+40 x^2+180 x^3-40 x^4\right )\right ) \log (-4+x)+\left (-320 x^2+560 x^3-280 x^4+40 x^5+e^{2 x} \left (-80 x+20 x^2\right )+e^x \left (-160 x+40 x^2+80 x^3-20 x^4\right )\right ) \log ^2(-4+x)\right ) \log (x)-50 x \log ^2(x)}{-100 x+25 x^2+\left (-300 x+75 x^2\right ) \log (-4+x)+\left (-300 x+75 x^2\right ) \log ^2(-4+x)+\left (-100 x+25 x^2\right ) \log ^3(-4+x)} \, dx=\frac {x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 36 \, x^{4} - 80 \, x^{3} + {\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 16 \, x^{4} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3}\right )} e^{x} + e^{\left (4 \, x\right )}\right )} \log \left (x - 4\right )^{2} + 80 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 2 \, {\left (3 \, x^{4} - 12 \, x^{3} + 12 \, x^{2} + 5 \, \log \left (x\right ) + 10\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3} + 10 \, x^{2} + 5 \, {\left (x^{2} - 2 \, x\right )} \log \left (x\right ) - 20 \, x\right )} e^{x} + 2 \, {\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 26 \, x^{4} - 40 \, x^{3} + 40 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + {\left (6 \, x^{4} - 24 \, x^{3} + 24 \, x^{2} + 5 \, \log \left (x\right ) + 10\right )} e^{\left (2 \, x\right )} - 2 \, {\left (2 \, x^{6} - 12 \, x^{5} + 24 \, x^{4} - 16 \, x^{3} + 10 \, x^{2} + 5 \, {\left (x^{2} - 2 \, x\right )} \log \left (x\right ) - 20 \, x\right )} e^{x} + 5 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2}\right )} \log \left (x\right ) + e^{\left (4 \, x\right )}\right )} \log \left (x - 4\right ) + 10 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2} + 10\right )} \log \left (x\right ) + 25 \, \log \left (x\right )^{2} + e^{\left (4 \, x\right )} + 100}{25 \, {\left (\log \left (x - 4\right )^{2} + 2 \, \log \left (x - 4\right ) + 1\right )}} \] Input:
integrate((-50*x*log(x)^2+(((20*x^2-80*x)*exp(x)^2+(-20*x^4+80*x^3+40*x^2- 160*x)*exp(x)+40*x^5-280*x^4+560*x^3-320*x^2)*log(-4+x)^2+((40*x^2-170*x)* exp(x)^2+(-40*x^4+180*x^3+40*x^2-320*x)*exp(x)+70*x^5-520*x^4+1080*x^3-640 *x^2+50*x-200)*log(-4+x)+(20*x^2-90*x)*exp(x)^2+(-20*x^4+100*x^3-160*x)*ex p(x)+30*x^5-240*x^4+520*x^3-320*x^2-150*x-200)*log(x)+((4*x^2-16*x)*exp(x) ^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-192 *x^2)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+736*x^4-384*x^3)*exp(x)+8*x^9 -88*x^8+368*x^7-736*x^6+704*x^5-256*x^4)*log(-4+x)^3+((12*x^2-48*x)*exp(x) ^4+(-36*x^4+192*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3 -536*x^2-150*x-40)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2168*x^4-1012 *x^3+200*x^2-480*x)*exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2202*x^5-1408* x^4+1320*x^3-800*x^2)*log(-4+x)^2+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3 -168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-496*x^2-320*x-80)* exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2128*x^4-832*x^3+320*x^2-960*x)* exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2272*x^5-1968*x^4+2560*x^3-1600*x^ 2+100*x-400)*log(-4+x)+(4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)* exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-152*x^2-170*x-40)*exp(x)^2+(-4*x^8+ 16*x^7+72*x^6-448*x^5+696*x^4-204*x^3+120*x^2-480*x)*exp(x)+8*x^9-88*x^8+3 68*x^7-736*x^6+774*x^5-816*x^4+1240*x^3-800*x^2-100*x-400)/((25*x^2-100*x) *log(-4+x)^3+(75*x^2-300*x)*log(-4+x)^2+(75*x^2-300*x)*log(-4+x)+25*x^2-10 0*x),x, algorithm="maxima")
Output:
1/25*(x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 36*x^4 - 80*x^3 + (x^8 - 8*x^7 + 24* x^6 - 32*x^5 + 16*x^4 - 4*(x^2 - 2*x)*e^(3*x) + 6*(x^4 - 4*x^3 + 4*x^2)*e^ (2*x) - 4*(x^6 - 6*x^5 + 12*x^4 - 8*x^3)*e^x + e^(4*x))*log(x - 4)^2 + 80* x^2 - 4*(x^2 - 2*x)*e^(3*x) + 2*(3*x^4 - 12*x^3 + 12*x^2 + 5*log(x) + 10)* e^(2*x) - 4*(x^6 - 6*x^5 + 12*x^4 - 8*x^3 + 10*x^2 + 5*(x^2 - 2*x)*log(x) - 20*x)*e^x + 2*(x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 26*x^4 - 40*x^3 + 40*x^2 - 4*(x^2 - 2*x)*e^(3*x) + (6*x^4 - 24*x^3 + 24*x^2 + 5*log(x) + 10)*e^(2*x ) - 2*(2*x^6 - 12*x^5 + 24*x^4 - 16*x^3 + 10*x^2 + 5*(x^2 - 2*x)*log(x) - 20*x)*e^x + 5*(x^4 - 4*x^3 + 4*x^2)*log(x) + e^(4*x))*log(x - 4) + 10*(x^4 - 4*x^3 + 4*x^2 + 10)*log(x) + 25*log(x)^2 + e^(4*x) + 100)/(log(x - 4)^2 + 2*log(x - 4) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 670 vs. \(2 (32) = 64\).
Time = 0.72 (sec) , antiderivative size = 670, normalized size of antiderivative = 19.71 \[ \int \frac {-400-100 x-800 x^2+1240 x^3-816 x^4+774 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-40-170 x-152 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-480 x+120 x^2-204 x^3+696 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )+\left (-400+100 x-1600 x^2+2560 x^3-1968 x^4+2272 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-80-320 x-496 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-960 x+320 x^2-832 x^3+2128 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log (-4+x)+\left (-800 x^2+1320 x^3-1408 x^4+2202 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-40-150 x-536 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-480 x+200 x^2-1012 x^3+2168 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log ^2(-4+x)+\left (-256 x^4+704 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-192 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-384 x^3+736 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )\right ) \log ^3(-4+x)+\left (-200-150 x-320 x^2+520 x^3-240 x^4+30 x^5+e^{2 x} \left (-90 x+20 x^2\right )+e^x \left (-160 x+100 x^3-20 x^4\right )+\left (-200+50 x-640 x^2+1080 x^3-520 x^4+70 x^5+e^{2 x} \left (-170 x+40 x^2\right )+e^x \left (-320 x+40 x^2+180 x^3-40 x^4\right )\right ) \log (-4+x)+\left (-320 x^2+560 x^3-280 x^4+40 x^5+e^{2 x} \left (-80 x+20 x^2\right )+e^x \left (-160 x+40 x^2+80 x^3-20 x^4\right )\right ) \log ^2(-4+x)\right ) \log (x)-50 x \log ^2(x)}{-100 x+25 x^2+\left (-300 x+75 x^2\right ) \log (-4+x)+\left (-300 x+75 x^2\right ) \log ^2(-4+x)+\left (-100 x+25 x^2\right ) \log ^3(-4+x)} \, dx =\text {Too large to display} \] Input:
integrate((-50*x*log(x)^2+(((20*x^2-80*x)*exp(x)^2+(-20*x^4+80*x^3+40*x^2- 160*x)*exp(x)+40*x^5-280*x^4+560*x^3-320*x^2)*log(-4+x)^2+((40*x^2-170*x)* exp(x)^2+(-40*x^4+180*x^3+40*x^2-320*x)*exp(x)+70*x^5-520*x^4+1080*x^3-640 *x^2+50*x-200)*log(-4+x)+(20*x^2-90*x)*exp(x)^2+(-20*x^4+100*x^3-160*x)*ex p(x)+30*x^5-240*x^4+520*x^3-320*x^2-150*x-200)*log(x)+((4*x^2-16*x)*exp(x) ^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-192 *x^2)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+736*x^4-384*x^3)*exp(x)+8*x^9 -88*x^8+368*x^7-736*x^6+704*x^5-256*x^4)*log(-4+x)^3+((12*x^2-48*x)*exp(x) ^4+(-36*x^4+192*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3 -536*x^2-150*x-40)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2168*x^4-1012 *x^3+200*x^2-480*x)*exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2202*x^5-1408* x^4+1320*x^3-800*x^2)*log(-4+x)^2+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3 -168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-496*x^2-320*x-80)* exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2128*x^4-832*x^3+320*x^2-960*x)* exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2272*x^5-1968*x^4+2560*x^3-1600*x^ 2+100*x-400)*log(-4+x)+(4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)* exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-152*x^2-170*x-40)*exp(x)^2+(-4*x^8+ 16*x^7+72*x^6-448*x^5+696*x^4-204*x^3+120*x^2-480*x)*exp(x)+8*x^9-88*x^8+3 68*x^7-736*x^6+774*x^5-816*x^4+1240*x^3-800*x^2-100*x-400)/((25*x^2-100*x) *log(-4+x)^3+(75*x^2-300*x)*log(-4+x)^2+(75*x^2-300*x)*log(-4+x)+25*x^2-10 0*x),x, algorithm="giac")
Output:
1/25*(x^8*log(x - 4)^2 + 2*x^8*log(x - 4) - 8*x^7*log(x - 4)^2 - 4*x^6*e^x *log(x - 4)^2 + x^8 - 16*x^7*log(x - 4) - 8*x^6*e^x*log(x - 4) + 24*x^6*lo g(x - 4)^2 + 24*x^5*e^x*log(x - 4)^2 - 8*x^7 - 4*x^6*e^x + 48*x^6*log(x - 4) + 48*x^5*e^x*log(x - 4) - 32*x^5*log(x - 4)^2 + 6*x^4*e^(2*x)*log(x - 4 )^2 - 48*x^4*e^x*log(x - 4)^2 + 24*x^6 + 24*x^5*e^x - 64*x^5*log(x - 4) + 12*x^4*e^(2*x)*log(x - 4) - 96*x^4*e^x*log(x - 4) + 16*x^4*log(x - 4)^2 - 24*x^3*e^(2*x)*log(x - 4)^2 + 32*x^3*e^x*log(x - 4)^2 + 10*x^4*log(x - 4)* log(x) - 32*x^5 + 6*x^4*e^(2*x) - 48*x^4*e^x + 52*x^4*log(x - 4) - 48*x^3* e^(2*x)*log(x - 4) + 64*x^3*e^x*log(x - 4) - 4*x^2*e^(3*x)*log(x - 4)^2 + 24*x^2*e^(2*x)*log(x - 4)^2 + 10*x^4*log(x) - 40*x^3*log(x - 4)*log(x) - 2 0*x^2*e^x*log(x - 4)*log(x) + 36*x^4 - 24*x^3*e^(2*x) + 32*x^3*e^x - 80*x^ 3*log(x - 4) - 8*x^2*e^(3*x)*log(x - 4) + 48*x^2*e^(2*x)*log(x - 4) - 40*x ^2*e^x*log(x - 4) + 8*x*e^(3*x)*log(x - 4)^2 - 40*x^3*log(x) - 20*x^2*e^x* log(x) + 40*x^2*log(x - 4)*log(x) + 40*x*e^x*log(x - 4)*log(x) - 80*x^3 - 4*x^2*e^(3*x) + 24*x^2*e^(2*x) - 40*x^2*e^x + 80*x^2*log(x - 4) + 16*x*e^( 3*x)*log(x - 4) + 80*x*e^x*log(x - 4) + e^(4*x)*log(x - 4)^2 + 40*x^2*log( x) + 40*x*e^x*log(x) + 10*e^(2*x)*log(x - 4)*log(x) + 80*x^2 + 8*x*e^(3*x) + 80*x*e^x + 2*e^(4*x)*log(x - 4) + 20*e^(2*x)*log(x - 4) + 10*e^(2*x)*lo g(x) + 25*log(x)^2 + e^(4*x) + 20*e^(2*x) + 100*log(x) + 100)/(log(x - 4)^ 2 + 2*log(x - 4) + 1)
Time = 3.91 (sec) , antiderivative size = 1647, normalized size of antiderivative = 48.44 \[ \int \frac {-400-100 x-800 x^2+1240 x^3-816 x^4+774 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-40-170 x-152 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-480 x+120 x^2-204 x^3+696 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )+\left (-400+100 x-1600 x^2+2560 x^3-1968 x^4+2272 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-80-320 x-496 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-960 x+320 x^2-832 x^3+2128 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log (-4+x)+\left (-800 x^2+1320 x^3-1408 x^4+2202 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-40-150 x-536 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-480 x+200 x^2-1012 x^3+2168 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log ^2(-4+x)+\left (-256 x^4+704 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-192 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-384 x^3+736 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )\right ) \log ^3(-4+x)+\left (-200-150 x-320 x^2+520 x^3-240 x^4+30 x^5+e^{2 x} \left (-90 x+20 x^2\right )+e^x \left (-160 x+100 x^3-20 x^4\right )+\left (-200+50 x-640 x^2+1080 x^3-520 x^4+70 x^5+e^{2 x} \left (-170 x+40 x^2\right )+e^x \left (-320 x+40 x^2+180 x^3-40 x^4\right )\right ) \log (-4+x)+\left (-320 x^2+560 x^3-280 x^4+40 x^5+e^{2 x} \left (-80 x+20 x^2\right )+e^x \left (-160 x+40 x^2+80 x^3-20 x^4\right )\right ) \log ^2(-4+x)\right ) \log (x)-50 x \log ^2(x)}{-100 x+25 x^2+\left (-300 x+75 x^2\right ) \log (-4+x)+\left (-300 x+75 x^2\right ) \log ^2(-4+x)+\left (-100 x+25 x^2\right ) \log ^3(-4+x)} \, dx=\text {Too large to display} \] Input:
int((100*x + exp(4*x)*(16*x - 4*x^2) + 50*x*log(x)^2 + log(x - 4)^3*(exp(4 *x)*(16*x - 4*x^2) - exp(2*x)*(144*x^3 - 192*x^2 + 72*x^4 - 72*x^5 + 12*x^ 6) + exp(3*x)*(32*x + 56*x^2 - 64*x^3 + 12*x^4) + 256*x^4 - 704*x^5 + 736* x^6 - 368*x^7 + 88*x^8 - 8*x^9 + exp(x)*(384*x^3 - 736*x^4 + 448*x^5 - 72* x^6 - 16*x^7 + 4*x^8)) + log(x - 4)^2*(exp(4*x)*(48*x - 12*x^2) + exp(3*x) *(96*x + 168*x^2 - 192*x^3 + 36*x^4) + 800*x^2 - 1320*x^3 + 1408*x^4 - 220 2*x^5 + 2208*x^6 - 1104*x^7 + 264*x^8 - 24*x^9 + exp(2*x)*(150*x + 536*x^2 - 432*x^3 - 216*x^4 + 216*x^5 - 36*x^6 + 40) + exp(x)*(480*x - 200*x^2 + 1012*x^3 - 2168*x^4 + 1344*x^5 - 216*x^6 - 48*x^7 + 12*x^8)) + exp(3*x)*(3 2*x + 56*x^2 - 64*x^3 + 12*x^4) + log(x)*(150*x + exp(2*x)*(90*x - 20*x^2) + log(x - 4)^2*(exp(2*x)*(80*x - 20*x^2) + exp(x)*(160*x - 40*x^2 - 80*x^ 3 + 20*x^4) + 320*x^2 - 560*x^3 + 280*x^4 - 40*x^5) + 320*x^2 - 520*x^3 + 240*x^4 - 30*x^5 + log(x - 4)*(exp(2*x)*(170*x - 40*x^2) - 50*x + exp(x)*( 320*x - 40*x^2 - 180*x^3 + 40*x^4) + 640*x^2 - 1080*x^3 + 520*x^4 - 70*x^5 + 200) + exp(x)*(160*x - 100*x^3 + 20*x^4) + 200) + 800*x^2 - 1240*x^3 + 816*x^4 - 774*x^5 + 736*x^6 - 368*x^7 + 88*x^8 - 8*x^9 + exp(2*x)*(170*x + 152*x^2 - 144*x^3 - 72*x^4 + 72*x^5 - 12*x^6 + 40) + log(x - 4)*(exp(4*x) *(48*x - 12*x^2) - 100*x + exp(3*x)*(96*x + 168*x^2 - 192*x^3 + 36*x^4) + 1600*x^2 - 2560*x^3 + 1968*x^4 - 2272*x^5 + 2208*x^6 - 1104*x^7 + 264*x^8 - 24*x^9 + exp(2*x)*(320*x + 496*x^2 - 432*x^3 - 216*x^4 + 216*x^5 - 36*x^ 6 + 80) + exp(x)*(960*x - 320*x^2 + 832*x^3 - 2128*x^4 + 1344*x^5 - 216*x^ 6 - 48*x^7 + 12*x^8) + 400) + exp(x)*(480*x - 120*x^2 + 204*x^3 - 696*x^4 + 448*x^5 - 72*x^6 - 16*x^7 + 4*x^8) + 400)/(100*x + log(x - 4)*(300*x - 7 5*x^2) + log(x - 4)^3*(100*x - 25*x^2) + log(x - 4)^2*(300*x - 75*x^2) - 2 5*x^2),x)
Output:
exp(4*x)/25 - (1552*x)/5 + (448*log(x - 4))/5 + (128*log(x))/5 + exp(3*x)* ((8*x)/25 - (4*x^2)/25) + log(x)*(exp(2*x)*((4*x^2)/5 - (26*x)/5 + 8) + ex p(x)*((28*x^2)/5 - (84*x)/5 + (6*x^3)/5 - (2*x^4)/5 + 16/5) + (4*x + (1088 *x^3)/5 - 560*x^4 + (1836*x^5)/5 - (336*x^6)/5 - 16)/x^2 - ((1632*x^3)/5 - 672*x^4 + 408*x^5 - 72*x^6)/x^2) - ((40*x - 16*exp(2*x) - 80*log(x) + 64* x*exp(2*x) + 32*x^2*exp(x) - 236*x^3*exp(x) + 74*x^4*exp(x) + 12*x^5*exp(x ) - 4*x^6*exp(x) + 123*x^2*log(x) - 512*x^3*log(x) + 500*x^4*log(x) - 172* x^5*log(x) + 19*x^6*log(x) + 63*x^2*exp(2*x) - 52*x^3*exp(2*x) + 8*x^4*exp (2*x) + 64*x*exp(x) + 40*x*log(x) + 443*x^2 - 1472*x^3 + 1324*x^4 - 436*x^ 5 + 47*x^6 + 47*x^2*exp(2*x)*log(x) - 28*x^3*exp(2*x)*log(x) + 4*x^4*exp(2 *x)*log(x) + 32*x^2*exp(x)*log(x) - 92*x^3*exp(x)*log(x) + 22*x^4*exp(x)*l og(x) + 8*x^5*exp(x)*log(x) - 2*x^6*exp(x)*log(x) - 80)/(5*x^2) + (log(x - 4)*(x - 4)*(5*x + 8*exp(2*x) + 20*log(x) - 31*x*exp(2*x) - 36*x^2*exp(x) + 110*x^3*exp(x) - 4*x^4*exp(x) - 8*x^5*exp(x) - 64*x^2*log(x) + 232*x^3*l og(x) - 180*x^4*log(x) + 36*x^5*log(x) - 44*x^2*exp(2*x) + 16*x^3*exp(2*x) - 32*x*exp(x) - 224*x^2 + 660*x^3 - 468*x^4 + 89*x^5 - 26*x^2*exp(2*x)*lo g(x) + 8*x^3*exp(2*x)*log(x) - 20*x^2*exp(x)*log(x) + 40*x^3*exp(x)*log(x) + 2*x^4*exp(x)*log(x) - 4*x^5*exp(x)*log(x) + 20))/(5*x^2) - (2*log(x - 4 )^2*(x - 4)*(8*x*exp(2*x) - 2*exp(2*x) + 12*x^2*exp(x) - 28*x^3*exp(x) + 2 *x^5*exp(x) + 16*x^2*log(x) - 56*x^3*log(x) + 42*x^4*log(x) - 8*x^5*log...
Time = 0.21 (sec) , antiderivative size = 713, normalized size of antiderivative = 20.97 \[ \int \frac {-400-100 x-800 x^2+1240 x^3-816 x^4+774 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-40-170 x-152 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-480 x+120 x^2-204 x^3+696 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )+\left (-400+100 x-1600 x^2+2560 x^3-1968 x^4+2272 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-80-320 x-496 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-960 x+320 x^2-832 x^3+2128 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log (-4+x)+\left (-800 x^2+1320 x^3-1408 x^4+2202 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} \left (-48 x+12 x^2\right )+e^{3 x} \left (-96 x-168 x^2+192 x^3-36 x^4\right )+e^{2 x} \left (-40-150 x-536 x^2+432 x^3+216 x^4-216 x^5+36 x^6\right )+e^x \left (-480 x+200 x^2-1012 x^3+2168 x^4-1344 x^5+216 x^6+48 x^7-12 x^8\right )\right ) \log ^2(-4+x)+\left (-256 x^4+704 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} \left (-16 x+4 x^2\right )+e^{3 x} \left (-32 x-56 x^2+64 x^3-12 x^4\right )+e^{2 x} \left (-192 x^2+144 x^3+72 x^4-72 x^5+12 x^6\right )+e^x \left (-384 x^3+736 x^4-448 x^5+72 x^6+16 x^7-4 x^8\right )\right ) \log ^3(-4+x)+\left (-200-150 x-320 x^2+520 x^3-240 x^4+30 x^5+e^{2 x} \left (-90 x+20 x^2\right )+e^x \left (-160 x+100 x^3-20 x^4\right )+\left (-200+50 x-640 x^2+1080 x^3-520 x^4+70 x^5+e^{2 x} \left (-170 x+40 x^2\right )+e^x \left (-320 x+40 x^2+180 x^3-40 x^4\right )\right ) \log (-4+x)+\left (-320 x^2+560 x^3-280 x^4+40 x^5+e^{2 x} \left (-80 x+20 x^2\right )+e^x \left (-160 x+40 x^2+80 x^3-20 x^4\right )\right ) \log ^2(-4+x)\right ) \log (x)-50 x \log ^2(x)}{-100 x+25 x^2+\left (-300 x+75 x^2\right ) \log (-4+x)+\left (-300 x+75 x^2\right ) \log ^2(-4+x)+\left (-100 x+25 x^2\right ) \log ^3(-4+x)} \, dx =\text {Too large to display} \] Input:
int((-50*x*log(x)^2+(((20*x^2-80*x)*exp(x)^2+(-20*x^4+80*x^3+40*x^2-160*x) *exp(x)+40*x^5-280*x^4+560*x^3-320*x^2)*log(-4+x)^2+((40*x^2-170*x)*exp(x) ^2+(-40*x^4+180*x^3+40*x^2-320*x)*exp(x)+70*x^5-520*x^4+1080*x^3-640*x^2+5 0*x-200)*log(-4+x)+(20*x^2-90*x)*exp(x)^2+(-20*x^4+100*x^3-160*x)*exp(x)+3 0*x^5-240*x^4+520*x^3-320*x^2-150*x-200)*log(x)+((4*x^2-16*x)*exp(x)^4+(-1 2*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-192*x^2)* exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+736*x^4-384*x^3)*exp(x)+8*x^9-88*x^ 8+368*x^7-736*x^6+704*x^5-256*x^4)*log(-4+x)^3+((12*x^2-48*x)*exp(x)^4+(-3 6*x^4+192*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-536*x ^2-150*x-40)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2168*x^4-1012*x^3+2 00*x^2-480*x)*exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2202*x^5-1408*x^4+13 20*x^3-800*x^2)*log(-4+x)^2+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3-168*x ^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-496*x^2-320*x-80)*exp(x) ^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2128*x^4-832*x^3+320*x^2-960*x)*exp(x) +24*x^9-264*x^8+1104*x^7-2208*x^6+2272*x^5-1968*x^4+2560*x^3-1600*x^2+100* x-400)*log(-4+x)+(4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x) ^3+(12*x^6-72*x^5+72*x^4+144*x^3-152*x^2-170*x-40)*exp(x)^2+(-4*x^8+16*x^7 +72*x^6-448*x^5+696*x^4-204*x^3+120*x^2-480*x)*exp(x)+8*x^9-88*x^8+368*x^7 -736*x^6+774*x^5-816*x^4+1240*x^3-800*x^2-100*x-400)/((25*x^2-100*x)*log(- 4+x)^3+(75*x^2-300*x)*log(-4+x)^2+(75*x^2-300*x)*log(-4+x)+25*x^2-100*x),x )
Output:
(e**(4*x)*log(x - 4)**2 + 2*e**(4*x)*log(x - 4) + e**(4*x) - 4*e**(3*x)*lo g(x - 4)**2*x**2 + 8*e**(3*x)*log(x - 4)**2*x - 8*e**(3*x)*log(x - 4)*x**2 + 16*e**(3*x)*log(x - 4)*x - 4*e**(3*x)*x**2 + 8*e**(3*x)*x + 6*e**(2*x)* log(x - 4)**2*x**4 - 24*e**(2*x)*log(x - 4)**2*x**3 + 24*e**(2*x)*log(x - 4)**2*x**2 + 10*e**(2*x)*log(x - 4)*log(x) + 12*e**(2*x)*log(x - 4)*x**4 - 48*e**(2*x)*log(x - 4)*x**3 + 48*e**(2*x)*log(x - 4)*x**2 + 20*e**(2*x)*l og(x - 4) + 10*e**(2*x)*log(x) + 6*e**(2*x)*x**4 - 24*e**(2*x)*x**3 + 24*e **(2*x)*x**2 + 20*e**(2*x) - 4*e**x*log(x - 4)**2*x**6 + 24*e**x*log(x - 4 )**2*x**5 - 48*e**x*log(x - 4)**2*x**4 + 32*e**x*log(x - 4)**2*x**3 - 20*e **x*log(x - 4)*log(x)*x**2 + 40*e**x*log(x - 4)*log(x)*x - 8*e**x*log(x - 4)*x**6 + 48*e**x*log(x - 4)*x**5 - 96*e**x*log(x - 4)*x**4 + 64*e**x*log( x - 4)*x**3 - 40*e**x*log(x - 4)*x**2 + 80*e**x*log(x - 4)*x - 20*e**x*log (x)*x**2 + 40*e**x*log(x)*x - 4*e**x*x**6 + 24*e**x*x**5 - 48*e**x*x**4 + 32*e**x*x**3 - 40*e**x*x**2 + 80*e**x*x + log(x - 4)**2*x**8 - 8*log(x - 4 )**2*x**7 + 24*log(x - 4)**2*x**6 - 32*log(x - 4)**2*x**5 + 16*log(x - 4)* *2*x**4 + 10*log(x - 4)*log(x)*x**4 - 40*log(x - 4)*log(x)*x**3 + 40*log(x - 4)*log(x)*x**2 + 2*log(x - 4)*x**8 - 16*log(x - 4)*x**7 + 48*log(x - 4) *x**6 - 64*log(x - 4)*x**5 + 52*log(x - 4)*x**4 - 80*log(x - 4)*x**3 + 80* log(x - 4)*x**2 + 25*log(x)**2 + 10*log(x)*x**4 - 40*log(x)*x**3 + 40*log( x)*x**2 + 100*log(x) + x**8 - 8*x**7 + 24*x**6 - 32*x**5 + 36*x**4 - 80...