Integrand size = 538, antiderivative size = 31 \[ \int \frac {e^{-\frac {3025+6065 x+2856 x^2+58 x^3-174 x^4-3 x^5+9 x^6+x^7+\left (660+852 x+144 x^2-60 x^3-12 x^4\right ) \log (4)+\left (-74-106 x-24 x^2+10 x^3+2 x^4\right ) \log ^2(4)+(-12-12 x) \log ^3(4)+(1+x) \log ^4(4)}{3025+1760 x-184 x^2-238 x^3-16 x^4+8 x^5+x^6+\left (660+192 x-48 x^2-12 x^3\right ) \log (4)+\left (-74-32 x+8 x^2+2 x^3\right ) \log ^2(4)-12 \log ^3(4)+\log ^4(4)}} \left (-166375+91575 x+259580 x^2+126599 x^3+21533 x^4+3943 x^5+2515 x^6+625 x^7+17 x^8-11 x^9-x^{10}+\left (-54450+30450 x+50352 x^2+9612 x^3-2076 x^4-282 x^5+126 x^6+18 x^7\right ) \log (4)+\left (3135-863 x-6232 x^2-1926 x^3+238 x^4+47 x^5-21 x^6-3 x^7\right ) \log ^2(4)+\left (1764-1188 x-720 x^2+108 x^3+36 x^4\right ) \log ^3(4)+\left (-57+9 x+60 x^2-9 x^3-3 x^4\right ) \log ^4(4)+(-18+18 x) \log ^5(4)+(1-x) \log ^6(4)\right )}{-166375-145200 x-5940 x^2+26099 x^3+5712 x^4-1320 x^5-485 x^6+12 x^8+x^9+\left (-54450-31680 x+3312 x^2+4284 x^3+288 x^4-144 x^5-18 x^6\right ) \log (4)+\left (3135+3552 x-120 x^2-606 x^3-48 x^4+24 x^5+3 x^6\right ) \log ^2(4)+\left (1764+576 x-144 x^2-36 x^3\right ) \log ^3(4)+\left (-57-48 x+12 x^2+3 x^3\right ) \log ^4(4)-18 \log ^5(4)+\log ^6(4)} \, dx=e^{-1-x-\frac {5 x}{\left (-4+x+\frac {(3-\log (4))^2}{(4+x)^2}\right )^2}} x \]
Leaf count is larger than twice the leaf count of optimal. \(109\) vs. \(2(31)=62\).
Time = 0.43 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.52 \[ \int \frac {e^{-\frac {3025+6065 x+2856 x^2+58 x^3-174 x^4-3 x^5+9 x^6+x^7+\left (660+852 x+144 x^2-60 x^3-12 x^4\right ) \log (4)+\left (-74-106 x-24 x^2+10 x^3+2 x^4\right ) \log ^2(4)+(-12-12 x) \log ^3(4)+(1+x) \log ^4(4)}{3025+1760 x-184 x^2-238 x^3-16 x^4+8 x^5+x^6+\left (660+192 x-48 x^2-12 x^3\right ) \log (4)+\left (-74-32 x+8 x^2+2 x^3\right ) \log ^2(4)-12 \log ^3(4)+\log ^4(4)}} \left (-166375+91575 x+259580 x^2+126599 x^3+21533 x^4+3943 x^5+2515 x^6+625 x^7+17 x^8-11 x^9-x^{10}+\left (-54450+30450 x+50352 x^2+9612 x^3-2076 x^4-282 x^5+126 x^6+18 x^7\right ) \log (4)+\left (3135-863 x-6232 x^2-1926 x^3+238 x^4+47 x^5-21 x^6-3 x^7\right ) \log ^2(4)+\left (1764-1188 x-720 x^2+108 x^3+36 x^4\right ) \log ^3(4)+\left (-57+9 x+60 x^2-9 x^3-3 x^4\right ) \log ^4(4)+(-18+18 x) \log ^5(4)+(1-x) \log ^6(4)\right )}{-166375-145200 x-5940 x^2+26099 x^3+5712 x^4-1320 x^5-485 x^6+12 x^8+x^9+\left (-54450-31680 x+3312 x^2+4284 x^3+288 x^4-144 x^5-18 x^6\right ) \log (4)+\left (3135+3552 x-120 x^2-606 x^3-48 x^4+24 x^5+3 x^6\right ) \log ^2(4)+\left (1764+576 x-144 x^2-36 x^3\right ) \log ^3(4)+\left (-57-48 x+12 x^2+3 x^3\right ) \log ^4(4)-18 \log ^5(4)+\log ^6(4)} \, dx=e^{-1-x-\frac {5 \left (64+12 x+x^2\right )}{-55-16 x+4 x^2+x^3-6 \log (4)+\log ^2(4)}+\frac {5 \left (x^2 \left (-247-6 \log (4)+\log ^2(4)\right )+64 \left (-55-6 \log (4)+\log ^2(4)\right )+4 x \left (-485-18 \log (4)+3 \log ^2(4)\right )\right )}{\left (-55-16 x+4 x^2+x^3-6 \log (4)+\log ^2(4)\right )^2}} x \]
Integrate[(-166375 + 91575*x + 259580*x^2 + 126599*x^3 + 21533*x^4 + 3943* x^5 + 2515*x^6 + 625*x^7 + 17*x^8 - 11*x^9 - x^10 + (-54450 + 30450*x + 50 352*x^2 + 9612*x^3 - 2076*x^4 - 282*x^5 + 126*x^6 + 18*x^7)*Log[4] + (3135 - 863*x - 6232*x^2 - 1926*x^3 + 238*x^4 + 47*x^5 - 21*x^6 - 3*x^7)*Log[4] ^2 + (1764 - 1188*x - 720*x^2 + 108*x^3 + 36*x^4)*Log[4]^3 + (-57 + 9*x + 60*x^2 - 9*x^3 - 3*x^4)*Log[4]^4 + (-18 + 18*x)*Log[4]^5 + (1 - x)*Log[4]^ 6)/(E^((3025 + 6065*x + 2856*x^2 + 58*x^3 - 174*x^4 - 3*x^5 + 9*x^6 + x^7 + (660 + 852*x + 144*x^2 - 60*x^3 - 12*x^4)*Log[4] + (-74 - 106*x - 24*x^2 + 10*x^3 + 2*x^4)*Log[4]^2 + (-12 - 12*x)*Log[4]^3 + (1 + x)*Log[4]^4)/(3 025 + 1760*x - 184*x^2 - 238*x^3 - 16*x^4 + 8*x^5 + x^6 + (660 + 192*x - 4 8*x^2 - 12*x^3)*Log[4] + (-74 - 32*x + 8*x^2 + 2*x^3)*Log[4]^2 - 12*Log[4] ^3 + Log[4]^4))*(-166375 - 145200*x - 5940*x^2 + 26099*x^3 + 5712*x^4 - 13 20*x^5 - 485*x^6 + 12*x^8 + x^9 + (-54450 - 31680*x + 3312*x^2 + 4284*x^3 + 288*x^4 - 144*x^5 - 18*x^6)*Log[4] + (3135 + 3552*x - 120*x^2 - 606*x^3 - 48*x^4 + 24*x^5 + 3*x^6)*Log[4]^2 + (1764 + 576*x - 144*x^2 - 36*x^3)*Lo g[4]^3 + (-57 - 48*x + 12*x^2 + 3*x^3)*Log[4]^4 - 18*Log[4]^5 + Log[4]^6)) ,x]
E^(-1 - x - (5*(64 + 12*x + x^2))/(-55 - 16*x + 4*x^2 + x^3 - 6*Log[4] + L og[4]^2) + (5*(x^2*(-247 - 6*Log[4] + Log[4]^2) + 64*(-55 - 6*Log[4] + Log [4]^2) + 4*x*(-485 - 18*Log[4] + 3*Log[4]^2)))/(-55 - 16*x + 4*x^2 + x^3 - 6*Log[4] + Log[4]^2)^2)*x
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (-x^{10}-11 x^9+17 x^8+625 x^7+2515 x^6+3943 x^5+21533 x^4+126599 x^3+259580 x^2+\left (-3 x^4-9 x^3+60 x^2+9 x-57\right ) \log ^4(4)+\left (36 x^4+108 x^3-720 x^2-1188 x+1764\right ) \log ^3(4)+\left (-3 x^7-21 x^6+47 x^5+238 x^4-1926 x^3-6232 x^2-863 x+3135\right ) \log ^2(4)+\left (18 x^7+126 x^6-282 x^5-2076 x^4+9612 x^3+50352 x^2+30450 x-54450\right ) \log (4)+91575 x+(1-x) \log ^6(4)+(18 x-18) \log ^5(4)-166375\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5-174 x^4+58 x^3+2856 x^2+\left (2 x^4+10 x^3-24 x^2-106 x-74\right ) \log ^2(4)+\left (-12 x^4-60 x^3+144 x^2+852 x+660\right ) \log (4)+6065 x+(x+1) \log ^4(4)+(-12 x-12) \log ^3(4)+3025}{x^6+8 x^5-16 x^4-238 x^3-184 x^2+\left (2 x^3+8 x^2-32 x-74\right ) \log ^2(4)+\left (-12 x^3-48 x^2+192 x+660\right ) \log (4)+1760 x+3025+\log ^4(4)-12 \log ^3(4)}\right )}{x^9+12 x^8-485 x^6-1320 x^5+5712 x^4+26099 x^3-5940 x^2+\left (3 x^3+12 x^2-48 x-57\right ) \log ^4(4)+\left (-36 x^3-144 x^2+576 x+1764\right ) \log ^3(4)+\left (3 x^6+24 x^5-48 x^4-606 x^3-120 x^2+3552 x+3135\right ) \log ^2(4)+\left (-18 x^6-144 x^5+288 x^4+4284 x^3+3312 x^2-31680 x-54450\right ) \log (4)-145200 x-166375+\log ^6(4)-18 \log ^5(4)} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \frac {\left (-x^{10}-11 x^9+17 x^8+625 x^7+2515 x^6+3943 x^5+21533 x^4+126599 x^3+259580 x^2+\left (-3 x^4-9 x^3+60 x^2+9 x-57\right ) \log ^4(4)+\left (36 x^4+108 x^3-720 x^2-1188 x+1764\right ) \log ^3(4)+\left (-3 x^7-21 x^6+47 x^5+238 x^4-1926 x^3-6232 x^2-863 x+3135\right ) \log ^2(4)+\left (18 x^7+126 x^6-282 x^5-2076 x^4+9612 x^3+50352 x^2+30450 x-54450\right ) \log (4)+91575 x+(1-x) \log ^6(4)+(18 x-18) \log ^5(4)-166375\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5-174 x^4+58 x^3+2856 x^2+\left (2 x^4+10 x^3-24 x^2-106 x-74\right ) \log ^2(4)+\left (-12 x^4-60 x^3+144 x^2+852 x+660\right ) \log (4)+6065 x+(x+1) \log ^4(4)+(-12 x-12) \log ^3(4)+3025}{x^6+8 x^5-16 x^4-238 x^3-184 x^2+\left (2 x^3+8 x^2-32 x-74\right ) \log ^2(4)+\left (-12 x^3-48 x^2+192 x+660\right ) \log (4)+1760 x+3025+\log ^4(4)-12 \log ^3(4)}\right )}{\left (x^3+4 x^2-16 x-55+\log ^2(4)-6 \log (4)\right )^3}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (x^{10}+11 x^9-17 x^8-625 x^7-2515 x^6-3943 x^5-21533 x^4-126599 x^3-259580 x^2-\left (-3 x^4-9 x^3+60 x^2+9 x-57\right ) \log ^4(4)-\left (36 x^4+108 x^3-720 x^2-1188 x+1764\right ) \log ^3(4)-\left (-3 x^7-21 x^6+47 x^5+238 x^4-1926 x^3-6232 x^2-863 x+3135\right ) \log ^2(4)-\left (18 x^7+126 x^6-282 x^5-2076 x^4+9612 x^3+50352 x^2+30450 x-54450\right ) \log (4)-91575 x-(18 x-18) \left (1-\frac {\log (2)}{9}\right ) \log ^5(4)+166375\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5-174 x^4+58 x^3+2856 x^2+\left (2 x^4+10 x^3-24 x^2-106 x-74\right ) \log ^2(4)+\left (-12 x^4-60 x^3+144 x^2+852 x+660\right ) \log (4)+6065 x+(-12 x-12) \left (1-\frac {\log (2)}{6}\right ) \log ^3(4)+3025}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-e^{-\frac {x^7+9 x^6-3 x^5-174 x^4+58 x^3+2856 x^2+6065 x+(-12 x-12) \left (1-\frac {\log (2)}{6}\right ) \log ^3(4)+\left (2 x^4+10 x^3-24 x^2-106 x-74\right ) \log ^2(4)+\left (-12 x^4-60 x^3+144 x^2+852 x+660\right ) \log (4)+3025}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+e^{-\frac {x^7+9 x^6-3 x^5-174 x^4+58 x^3+2856 x^2+6065 x+(-12 x-12) \left (1-\frac {\log (2)}{6}\right ) \log ^3(4)+\left (2 x^4+10 x^3-24 x^2-106 x-74\right ) \log ^2(4)+\left (-12 x^4-60 x^3+144 x^2+852 x+660\right ) \log (4)+3025}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5 e^{-\frac {x^7+9 x^6-3 x^5-174 x^4+58 x^3+2856 x^2+6065 x+(-12 x-12) \left (1-\frac {\log (2)}{6}\right ) \log ^3(4)+\left (2 x^4+10 x^3-24 x^2-106 x-74\right ) \log ^2(4)+\left (-12 x^4-60 x^3+144 x^2+852 x+660\right ) \log (4)+3025}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {10 e^{-\frac {x^7+9 x^6-3 x^5-174 x^4+58 x^3+2856 x^2+6065 x+(-12 x-12) \left (1-\frac {\log (2)}{6}\right ) \log ^3(4)+\left (2 x^4+10 x^3-24 x^2-106 x-74\right ) \log ^2(4)+\left (-12 x^4-60 x^3+144 x^2+852 x+660\right ) \log (4)+3025}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5 e^{-\frac {x^7+9 x^6-3 x^5-174 x^4+58 x^3+2856 x^2+6065 x+(-12 x-12) \left (1-\frac {\log (2)}{6}\right ) \log ^3(4)+\left (2 x^4+10 x^3-24 x^2-106 x-74\right ) \log ^2(4)+\left (-12 x^4-60 x^3+144 x^2+852 x+660\right ) \log (4)+3025}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4^{\frac {12 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-4^{\frac {12 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+4^{\frac {12 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 4^{\frac {12 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 4^{\frac {12 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} x+2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (\left (1217+42 \log (4)-7 \log ^2(4)\right ) x^2+12 \left (961+42 \log (4)-7 \log ^2(4)\right ) x+64 \left (623+54 \log (4)-9 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^2}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}+1} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-\left ((19-\log (4)) (13+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right ) x^2\right )-32 \left (13873+1620 \log (4)-234 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x-64 (11-\log (4)) (5+\log (4)) \left (229+18 \log (4)-3 \log ^2(4)\right )\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}+\frac {5\ 2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} e^{-\frac {x^7+9 x^6-3 x^5+2 \left (-87+\log ^2(4)\right ) x^4+2 \left (29+5 \log ^2(4)\right ) x^3-24 \left (-119+\log ^2(4)\right ) x^2+\left (6065-106 \log ^2(4)-12 \log ^3(4)+\log ^4(4)\right ) x+3025 \left (1+\frac {2 \log ^2(4) (-37+(-6+\log (2)) \log (4))}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (-x^2-20 x-192\right )}{-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {24 \left (x^4+5 x^3-12 x^2-71 x-55\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}} \left (x^{10}+11 x^9-17 x^8-x^7 \left (625-3 \log ^2(4)+18 \log (4)\right )-x^6 \left (2515-21 \log ^2(4)+126 \log (4)\right )-x^5 \left (3943+47 \log ^2(4)-282 \log (4)\right )-x^4 \left (21533-3 \log ^4(4)+36 \log ^3(4)+238 \log ^2(4)-2076 \log (4)\right )-x^3 \left (126599-9 \log ^4(4)+108 \log ^3(4)-1926 \log ^2(4)+9612 \log (4)\right )-4 x^2 \left (64895+15 \log ^4(4)-180 \log ^3(4)-1558 \log ^2(4)+12588 \log (4)\right )-x \left (91575-\log ^6(4)+18 \log ^5(4)+9 \log ^4(4)-1188 \log ^3(4)-863 \log ^2(4)+30450 \log (4)\right )-\left (-55+\log ^2(4)-6 \log (4)\right )^3\right ) \exp \left (-\frac {x^7+9 x^6-3 x^5+2 x^4 \left (\log ^2(4)-87\right )+2 x^3 \left (29+5 \log ^2(4)\right )-24 x^2 \left (\log ^2(4)-119\right )+x \left (6065+\log ^4(4)-12 \log ^3(4)-106 \log ^2(4)\right )+3025 \left (1+\frac {2 \log ^2(4) ((\log (2)-6) \log (4)-37)}{3025}\right )}{\left (x^3+4 x^2-16 x-(11-\log (4)) (5+\log (4))\right )^2}\right )}{\left (-x^3-4 x^2+16 x+(11-\log (4)) (5+\log (4))\right )^3}dx\) |
Int[(-166375 + 91575*x + 259580*x^2 + 126599*x^3 + 21533*x^4 + 3943*x^5 + 2515*x^6 + 625*x^7 + 17*x^8 - 11*x^9 - x^10 + (-54450 + 30450*x + 50352*x^ 2 + 9612*x^3 - 2076*x^4 - 282*x^5 + 126*x^6 + 18*x^7)*Log[4] + (3135 - 863 *x - 6232*x^2 - 1926*x^3 + 238*x^4 + 47*x^5 - 21*x^6 - 3*x^7)*Log[4]^2 + ( 1764 - 1188*x - 720*x^2 + 108*x^3 + 36*x^4)*Log[4]^3 + (-57 + 9*x + 60*x^2 - 9*x^3 - 3*x^4)*Log[4]^4 + (-18 + 18*x)*Log[4]^5 + (1 - x)*Log[4]^6)/(E^ ((3025 + 6065*x + 2856*x^2 + 58*x^3 - 174*x^4 - 3*x^5 + 9*x^6 + x^7 + (660 + 852*x + 144*x^2 - 60*x^3 - 12*x^4)*Log[4] + (-74 - 106*x - 24*x^2 + 10* x^3 + 2*x^4)*Log[4]^2 + (-12 - 12*x)*Log[4]^3 + (1 + x)*Log[4]^4)/(3025 + 1760*x - 184*x^2 - 238*x^3 - 16*x^4 + 8*x^5 + x^6 + (660 + 192*x - 48*x^2 - 12*x^3)*Log[4] + (-74 - 32*x + 8*x^2 + 2*x^3)*Log[4]^2 - 12*Log[4]^3 + L og[4]^4))*(-166375 - 145200*x - 5940*x^2 + 26099*x^3 + 5712*x^4 - 1320*x^5 - 485*x^6 + 12*x^8 + x^9 + (-54450 - 31680*x + 3312*x^2 + 4284*x^3 + 288* x^4 - 144*x^5 - 18*x^6)*Log[4] + (3135 + 3552*x - 120*x^2 - 606*x^3 - 48*x ^4 + 24*x^5 + 3*x^6)*Log[4]^2 + (1764 + 576*x - 144*x^2 - 36*x^3)*Log[4]^3 + (-57 - 48*x + 12*x^2 + 3*x^3)*Log[4]^4 - 18*Log[4]^5 + Log[4]^6)),x]
3.29.97.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(231\) vs. \(2(30)=60\).
Time = 0.05 (sec) , antiderivative size = 232, normalized size of antiderivative = 7.48
\[x \,{\mathrm e}^{-\frac {x^{7}+8 x^{4} \ln \left (2\right )^{2}+9 x^{6}+16 x \ln \left (2\right )^{4}+40 x^{3} \ln \left (2\right )^{2}-24 x^{4} \ln \left (2\right )-3 x^{5}+16 \ln \left (2\right )^{4}-96 x \ln \left (2\right )^{3}-96 x^{2} \ln \left (2\right )^{2}-120 x^{3} \ln \left (2\right )-174 x^{4}-96 \ln \left (2\right )^{3}-424 x \ln \left (2\right )^{2}+288 x^{2} \ln \left (2\right )+58 x^{3}-296 \ln \left (2\right )^{2}+1704 x \ln \left (2\right )+2856 x^{2}+1320 \ln \left (2\right )+6065 x +3025}{x^{6}+8 x^{3} \ln \left (2\right )^{2}+8 x^{5}+16 \ln \left (2\right )^{4}+32 x^{2} \ln \left (2\right )^{2}-24 x^{3} \ln \left (2\right )-16 x^{4}-96 \ln \left (2\right )^{3}-128 x \ln \left (2\right )^{2}-96 x^{2} \ln \left (2\right )-238 x^{3}-296 \ln \left (2\right )^{2}+384 x \ln \left (2\right )-184 x^{2}+1320 \ln \left (2\right )+1760 x +3025}}\]
int((64*(1-x)*ln(2)^6+32*(18*x-18)*ln(2)^5+16*(-3*x^4-9*x^3+60*x^2+9*x-57) *ln(2)^4+8*(36*x^4+108*x^3-720*x^2-1188*x+1764)*ln(2)^3+4*(-3*x^7-21*x^6+4 7*x^5+238*x^4-1926*x^3-6232*x^2-863*x+3135)*ln(2)^2+2*(18*x^7+126*x^6-282* x^5-2076*x^4+9612*x^3+50352*x^2+30450*x-54450)*ln(2)-x^10-11*x^9+17*x^8+62 5*x^7+2515*x^6+3943*x^5+21533*x^4+126599*x^3+259580*x^2+91575*x-166375)/(6 4*ln(2)^6-576*ln(2)^5+16*(3*x^3+12*x^2-48*x-57)*ln(2)^4+8*(-36*x^3-144*x^2 +576*x+1764)*ln(2)^3+4*(3*x^6+24*x^5-48*x^4-606*x^3-120*x^2+3552*x+3135)*l n(2)^2+2*(-18*x^6-144*x^5+288*x^4+4284*x^3+3312*x^2-31680*x-54450)*ln(2)+x ^9+12*x^8-485*x^6-1320*x^5+5712*x^4+26099*x^3-5940*x^2-145200*x-166375)/ex p((16*(1+x)*ln(2)^4+8*(-12*x-12)*ln(2)^3+4*(2*x^4+10*x^3-24*x^2-106*x-74)* ln(2)^2+2*(-12*x^4-60*x^3+144*x^2+852*x+660)*ln(2)+x^7+9*x^6-3*x^5-174*x^4 +58*x^3+2856*x^2+6065*x+3025)/(16*ln(2)^4-96*ln(2)^3+4*(2*x^3+8*x^2-32*x-7 4)*ln(2)^2+2*(-12*x^3-48*x^2+192*x+660)*ln(2)+x^6+8*x^5-16*x^4-238*x^3-184 *x^2+1760*x+3025)),x)
x/exp((x^7+8*x^4*ln(2)^2+9*x^6+16*x*ln(2)^4+40*x^3*ln(2)^2-24*x^4*ln(2)-3* x^5+16*ln(2)^4-96*x*ln(2)^3-96*x^2*ln(2)^2-120*x^3*ln(2)-174*x^4-96*ln(2)^ 3-424*x*ln(2)^2+288*x^2*ln(2)+58*x^3-296*ln(2)^2+1704*x*ln(2)+2856*x^2+132 0*ln(2)+6065*x+3025)/(x^6+8*x^3*ln(2)^2+8*x^5+16*ln(2)^4+32*x^2*ln(2)^2-24 *x^3*ln(2)-16*x^4-96*ln(2)^3-128*x*ln(2)^2-96*x^2*ln(2)-238*x^3-296*ln(2)^ 2+384*x*ln(2)-184*x^2+1320*ln(2)+1760*x+3025))
Leaf count of result is larger than twice the leaf count of optimal. 180 vs. \(2 (30) = 60\).
Time = 0.31 (sec) , antiderivative size = 180, normalized size of antiderivative = 5.81 \[ \int \frac {e^{-\frac {3025+6065 x+2856 x^2+58 x^3-174 x^4-3 x^5+9 x^6+x^7+\left (660+852 x+144 x^2-60 x^3-12 x^4\right ) \log (4)+\left (-74-106 x-24 x^2+10 x^3+2 x^4\right ) \log ^2(4)+(-12-12 x) \log ^3(4)+(1+x) \log ^4(4)}{3025+1760 x-184 x^2-238 x^3-16 x^4+8 x^5+x^6+\left (660+192 x-48 x^2-12 x^3\right ) \log (4)+\left (-74-32 x+8 x^2+2 x^3\right ) \log ^2(4)-12 \log ^3(4)+\log ^4(4)}} \left (-166375+91575 x+259580 x^2+126599 x^3+21533 x^4+3943 x^5+2515 x^6+625 x^7+17 x^8-11 x^9-x^{10}+\left (-54450+30450 x+50352 x^2+9612 x^3-2076 x^4-282 x^5+126 x^6+18 x^7\right ) \log (4)+\left (3135-863 x-6232 x^2-1926 x^3+238 x^4+47 x^5-21 x^6-3 x^7\right ) \log ^2(4)+\left (1764-1188 x-720 x^2+108 x^3+36 x^4\right ) \log ^3(4)+\left (-57+9 x+60 x^2-9 x^3-3 x^4\right ) \log ^4(4)+(-18+18 x) \log ^5(4)+(1-x) \log ^6(4)\right )}{-166375-145200 x-5940 x^2+26099 x^3+5712 x^4-1320 x^5-485 x^6+12 x^8+x^9+\left (-54450-31680 x+3312 x^2+4284 x^3+288 x^4-144 x^5-18 x^6\right ) \log (4)+\left (3135+3552 x-120 x^2-606 x^3-48 x^4+24 x^5+3 x^6\right ) \log ^2(4)+\left (1764+576 x-144 x^2-36 x^3\right ) \log ^3(4)+\left (-57-48 x+12 x^2+3 x^3\right ) \log ^4(4)-18 \log ^5(4)+\log ^6(4)} \, dx=x e^{\left (-\frac {x^{7} + 9 \, x^{6} - 3 \, x^{5} + 16 \, {\left (x + 1\right )} \log \left (2\right )^{4} - 174 \, x^{4} - 96 \, {\left (x + 1\right )} \log \left (2\right )^{3} + 58 \, x^{3} + 8 \, {\left (x^{4} + 5 \, x^{3} - 12 \, x^{2} - 53 \, x - 37\right )} \log \left (2\right )^{2} + 2856 \, x^{2} - 24 \, {\left (x^{4} + 5 \, x^{3} - 12 \, x^{2} - 71 \, x - 55\right )} \log \left (2\right ) + 6065 \, x + 3025}{x^{6} + 8 \, x^{5} - 16 \, x^{4} + 16 \, \log \left (2\right )^{4} - 238 \, x^{3} + 8 \, {\left (x^{3} + 4 \, x^{2} - 16 \, x - 37\right )} \log \left (2\right )^{2} - 96 \, \log \left (2\right )^{3} - 184 \, x^{2} - 24 \, {\left (x^{3} + 4 \, x^{2} - 16 \, x - 55\right )} \log \left (2\right ) + 1760 \, x + 3025}\right )} \]
integrate((64*(1-x)*log(2)^6+32*(18*x-18)*log(2)^5+16*(-3*x^4-9*x^3+60*x^2 +9*x-57)*log(2)^4+8*(36*x^4+108*x^3-720*x^2-1188*x+1764)*log(2)^3+4*(-3*x^ 7-21*x^6+47*x^5+238*x^4-1926*x^3-6232*x^2-863*x+3135)*log(2)^2+2*(18*x^7+1 26*x^6-282*x^5-2076*x^4+9612*x^3+50352*x^2+30450*x-54450)*log(2)-x^10-11*x ^9+17*x^8+625*x^7+2515*x^6+3943*x^5+21533*x^4+126599*x^3+259580*x^2+91575* x-166375)/(64*log(2)^6-576*log(2)^5+16*(3*x^3+12*x^2-48*x-57)*log(2)^4+8*( -36*x^3-144*x^2+576*x+1764)*log(2)^3+4*(3*x^6+24*x^5-48*x^4-606*x^3-120*x^ 2+3552*x+3135)*log(2)^2+2*(-18*x^6-144*x^5+288*x^4+4284*x^3+3312*x^2-31680 *x-54450)*log(2)+x^9+12*x^8-485*x^6-1320*x^5+5712*x^4+26099*x^3-5940*x^2-1 45200*x-166375)/exp((16*(1+x)*log(2)^4+8*(-12*x-12)*log(2)^3+4*(2*x^4+10*x ^3-24*x^2-106*x-74)*log(2)^2+2*(-12*x^4-60*x^3+144*x^2+852*x+660)*log(2)+x ^7+9*x^6-3*x^5-174*x^4+58*x^3+2856*x^2+6065*x+3025)/(16*log(2)^4-96*log(2) ^3+4*(2*x^3+8*x^2-32*x-74)*log(2)^2+2*(-12*x^3-48*x^2+192*x+660)*log(2)+x^ 6+8*x^5-16*x^4-238*x^3-184*x^2+1760*x+3025)),x, algorithm=\
x*e^(-(x^7 + 9*x^6 - 3*x^5 + 16*(x + 1)*log(2)^4 - 174*x^4 - 96*(x + 1)*lo g(2)^3 + 58*x^3 + 8*(x^4 + 5*x^3 - 12*x^2 - 53*x - 37)*log(2)^2 + 2856*x^2 - 24*(x^4 + 5*x^3 - 12*x^2 - 71*x - 55)*log(2) + 6065*x + 3025)/(x^6 + 8* x^5 - 16*x^4 + 16*log(2)^4 - 238*x^3 + 8*(x^3 + 4*x^2 - 16*x - 37)*log(2)^ 2 - 96*log(2)^3 - 184*x^2 - 24*(x^3 + 4*x^2 - 16*x - 55)*log(2) + 1760*x + 3025))
Timed out. \[ \int \frac {e^{-\frac {3025+6065 x+2856 x^2+58 x^3-174 x^4-3 x^5+9 x^6+x^7+\left (660+852 x+144 x^2-60 x^3-12 x^4\right ) \log (4)+\left (-74-106 x-24 x^2+10 x^3+2 x^4\right ) \log ^2(4)+(-12-12 x) \log ^3(4)+(1+x) \log ^4(4)}{3025+1760 x-184 x^2-238 x^3-16 x^4+8 x^5+x^6+\left (660+192 x-48 x^2-12 x^3\right ) \log (4)+\left (-74-32 x+8 x^2+2 x^3\right ) \log ^2(4)-12 \log ^3(4)+\log ^4(4)}} \left (-166375+91575 x+259580 x^2+126599 x^3+21533 x^4+3943 x^5+2515 x^6+625 x^7+17 x^8-11 x^9-x^{10}+\left (-54450+30450 x+50352 x^2+9612 x^3-2076 x^4-282 x^5+126 x^6+18 x^7\right ) \log (4)+\left (3135-863 x-6232 x^2-1926 x^3+238 x^4+47 x^5-21 x^6-3 x^7\right ) \log ^2(4)+\left (1764-1188 x-720 x^2+108 x^3+36 x^4\right ) \log ^3(4)+\left (-57+9 x+60 x^2-9 x^3-3 x^4\right ) \log ^4(4)+(-18+18 x) \log ^5(4)+(1-x) \log ^6(4)\right )}{-166375-145200 x-5940 x^2+26099 x^3+5712 x^4-1320 x^5-485 x^6+12 x^8+x^9+\left (-54450-31680 x+3312 x^2+4284 x^3+288 x^4-144 x^5-18 x^6\right ) \log (4)+\left (3135+3552 x-120 x^2-606 x^3-48 x^4+24 x^5+3 x^6\right ) \log ^2(4)+\left (1764+576 x-144 x^2-36 x^3\right ) \log ^3(4)+\left (-57-48 x+12 x^2+3 x^3\right ) \log ^4(4)-18 \log ^5(4)+\log ^6(4)} \, dx=\text {Timed out} \]
integrate((64*(1-x)*ln(2)**6+32*(18*x-18)*ln(2)**5+16*(-3*x**4-9*x**3+60*x **2+9*x-57)*ln(2)**4+8*(36*x**4+108*x**3-720*x**2-1188*x+1764)*ln(2)**3+4* (-3*x**7-21*x**6+47*x**5+238*x**4-1926*x**3-6232*x**2-863*x+3135)*ln(2)**2 +2*(18*x**7+126*x**6-282*x**5-2076*x**4+9612*x**3+50352*x**2+30450*x-54450 )*ln(2)-x**10-11*x**9+17*x**8+625*x**7+2515*x**6+3943*x**5+21533*x**4+1265 99*x**3+259580*x**2+91575*x-166375)/(64*ln(2)**6-576*ln(2)**5+16*(3*x**3+1 2*x**2-48*x-57)*ln(2)**4+8*(-36*x**3-144*x**2+576*x+1764)*ln(2)**3+4*(3*x* *6+24*x**5-48*x**4-606*x**3-120*x**2+3552*x+3135)*ln(2)**2+2*(-18*x**6-144 *x**5+288*x**4+4284*x**3+3312*x**2-31680*x-54450)*ln(2)+x**9+12*x**8-485*x **6-1320*x**5+5712*x**4+26099*x**3-5940*x**2-145200*x-166375)/exp((16*(1+x )*ln(2)**4+8*(-12*x-12)*ln(2)**3+4*(2*x**4+10*x**3-24*x**2-106*x-74)*ln(2) **2+2*(-12*x**4-60*x**3+144*x**2+852*x+660)*ln(2)+x**7+9*x**6-3*x**5-174*x **4+58*x**3+2856*x**2+6065*x+3025)/(16*ln(2)**4-96*ln(2)**3+4*(2*x**3+8*x* *2-32*x-74)*ln(2)**2+2*(-12*x**3-48*x**2+192*x+660)*ln(2)+x**6+8*x**5-16*x **4-238*x**3-184*x**2+1760*x+3025)),x)
Leaf count of result is larger than twice the leaf count of optimal. 933 vs. \(2 (30) = 60\).
Time = 7.19 (sec) , antiderivative size = 933, normalized size of antiderivative = 30.10 \[ \int \frac {e^{-\frac {3025+6065 x+2856 x^2+58 x^3-174 x^4-3 x^5+9 x^6+x^7+\left (660+852 x+144 x^2-60 x^3-12 x^4\right ) \log (4)+\left (-74-106 x-24 x^2+10 x^3+2 x^4\right ) \log ^2(4)+(-12-12 x) \log ^3(4)+(1+x) \log ^4(4)}{3025+1760 x-184 x^2-238 x^3-16 x^4+8 x^5+x^6+\left (660+192 x-48 x^2-12 x^3\right ) \log (4)+\left (-74-32 x+8 x^2+2 x^3\right ) \log ^2(4)-12 \log ^3(4)+\log ^4(4)}} \left (-166375+91575 x+259580 x^2+126599 x^3+21533 x^4+3943 x^5+2515 x^6+625 x^7+17 x^8-11 x^9-x^{10}+\left (-54450+30450 x+50352 x^2+9612 x^3-2076 x^4-282 x^5+126 x^6+18 x^7\right ) \log (4)+\left (3135-863 x-6232 x^2-1926 x^3+238 x^4+47 x^5-21 x^6-3 x^7\right ) \log ^2(4)+\left (1764-1188 x-720 x^2+108 x^3+36 x^4\right ) \log ^3(4)+\left (-57+9 x+60 x^2-9 x^3-3 x^4\right ) \log ^4(4)+(-18+18 x) \log ^5(4)+(1-x) \log ^6(4)\right )}{-166375-145200 x-5940 x^2+26099 x^3+5712 x^4-1320 x^5-485 x^6+12 x^8+x^9+\left (-54450-31680 x+3312 x^2+4284 x^3+288 x^4-144 x^5-18 x^6\right ) \log (4)+\left (3135+3552 x-120 x^2-606 x^3-48 x^4+24 x^5+3 x^6\right ) \log ^2(4)+\left (1764+576 x-144 x^2-36 x^3\right ) \log ^3(4)+\left (-57-48 x+12 x^2+3 x^3\right ) \log ^4(4)-18 \log ^5(4)+\log ^6(4)} \, dx=\text {Too large to display} \]
integrate((64*(1-x)*log(2)^6+32*(18*x-18)*log(2)^5+16*(-3*x^4-9*x^3+60*x^2 +9*x-57)*log(2)^4+8*(36*x^4+108*x^3-720*x^2-1188*x+1764)*log(2)^3+4*(-3*x^ 7-21*x^6+47*x^5+238*x^4-1926*x^3-6232*x^2-863*x+3135)*log(2)^2+2*(18*x^7+1 26*x^6-282*x^5-2076*x^4+9612*x^3+50352*x^2+30450*x-54450)*log(2)-x^10-11*x ^9+17*x^8+625*x^7+2515*x^6+3943*x^5+21533*x^4+126599*x^3+259580*x^2+91575* x-166375)/(64*log(2)^6-576*log(2)^5+16*(3*x^3+12*x^2-48*x-57)*log(2)^4+8*( -36*x^3-144*x^2+576*x+1764)*log(2)^3+4*(3*x^6+24*x^5-48*x^4-606*x^3-120*x^ 2+3552*x+3135)*log(2)^2+2*(-18*x^6-144*x^5+288*x^4+4284*x^3+3312*x^2-31680 *x-54450)*log(2)+x^9+12*x^8-485*x^6-1320*x^5+5712*x^4+26099*x^3-5940*x^2-1 45200*x-166375)/exp((16*(1+x)*log(2)^4+8*(-12*x-12)*log(2)^3+4*(2*x^4+10*x ^3-24*x^2-106*x-74)*log(2)^2+2*(-12*x^4-60*x^3+144*x^2+852*x+660)*log(2)+x ^7+9*x^6-3*x^5-174*x^4+58*x^3+2856*x^2+6065*x+3025)/(16*log(2)^4-96*log(2) ^3+4*(2*x^3+8*x^2-32*x-74)*log(2)^2+2*(-12*x^3-48*x^2+192*x+660)*log(2)+x^ 6+8*x^5-16*x^4-238*x^3-184*x^2+1760*x+3025)),x, algorithm=\
x*e^(20*x^2*log(2)^2/(x^6 + 8*x^5 + 2*(4*log(2)^2 - 12*log(2) - 119)*x^3 - 16*x^4 + 16*log(2)^4 + 8*(4*log(2)^2 - 12*log(2) - 23)*x^2 - 96*log(2)^3 - 32*(4*log(2)^2 - 12*log(2) - 55)*x - 296*log(2)^2 + 1320*log(2) + 3025) - 60*x^2*log(2)/(x^6 + 8*x^5 + 2*(4*log(2)^2 - 12*log(2) - 119)*x^3 - 16*x ^4 + 16*log(2)^4 + 8*(4*log(2)^2 - 12*log(2) - 23)*x^2 - 96*log(2)^3 - 32* (4*log(2)^2 - 12*log(2) - 55)*x - 296*log(2)^2 + 1320*log(2) + 3025) + 240 *x*log(2)^2/(x^6 + 8*x^5 + 2*(4*log(2)^2 - 12*log(2) - 119)*x^3 - 16*x^4 + 16*log(2)^4 + 8*(4*log(2)^2 - 12*log(2) - 23)*x^2 - 96*log(2)^3 - 32*(4*l og(2)^2 - 12*log(2) - 55)*x - 296*log(2)^2 + 1320*log(2) + 3025) - x - 123 5*x^2/(x^6 + 8*x^5 + 2*(4*log(2)^2 - 12*log(2) - 119)*x^3 - 16*x^4 + 16*lo g(2)^4 + 8*(4*log(2)^2 - 12*log(2) - 23)*x^2 - 96*log(2)^3 - 32*(4*log(2)^ 2 - 12*log(2) - 55)*x - 296*log(2)^2 + 1320*log(2) + 3025) - 5*x^2/(x^3 + 4*x^2 + 4*log(2)^2 - 16*x - 12*log(2) - 55) - 720*x*log(2)/(x^6 + 8*x^5 + 2*(4*log(2)^2 - 12*log(2) - 119)*x^3 - 16*x^4 + 16*log(2)^4 + 8*(4*log(2)^ 2 - 12*log(2) - 23)*x^2 - 96*log(2)^3 - 32*(4*log(2)^2 - 12*log(2) - 55)*x - 296*log(2)^2 + 1320*log(2) + 3025) + 1280*log(2)^2/(x^6 + 8*x^5 + 2*(4* log(2)^2 - 12*log(2) - 119)*x^3 - 16*x^4 + 16*log(2)^4 + 8*(4*log(2)^2 - 1 2*log(2) - 23)*x^2 - 96*log(2)^3 - 32*(4*log(2)^2 - 12*log(2) - 55)*x - 29 6*log(2)^2 + 1320*log(2) + 3025) - 9700*x/(x^6 + 8*x^5 + 2*(4*log(2)^2 - 1 2*log(2) - 119)*x^3 - 16*x^4 + 16*log(2)^4 + 8*(4*log(2)^2 - 12*log(2) ...
Leaf count of result is larger than twice the leaf count of optimal. 209 vs. \(2 (30) = 60\).
Time = 14.46 (sec) , antiderivative size = 209, normalized size of antiderivative = 6.74 \[ \int \frac {e^{-\frac {3025+6065 x+2856 x^2+58 x^3-174 x^4-3 x^5+9 x^6+x^7+\left (660+852 x+144 x^2-60 x^3-12 x^4\right ) \log (4)+\left (-74-106 x-24 x^2+10 x^3+2 x^4\right ) \log ^2(4)+(-12-12 x) \log ^3(4)+(1+x) \log ^4(4)}{3025+1760 x-184 x^2-238 x^3-16 x^4+8 x^5+x^6+\left (660+192 x-48 x^2-12 x^3\right ) \log (4)+\left (-74-32 x+8 x^2+2 x^3\right ) \log ^2(4)-12 \log ^3(4)+\log ^4(4)}} \left (-166375+91575 x+259580 x^2+126599 x^3+21533 x^4+3943 x^5+2515 x^6+625 x^7+17 x^8-11 x^9-x^{10}+\left (-54450+30450 x+50352 x^2+9612 x^3-2076 x^4-282 x^5+126 x^6+18 x^7\right ) \log (4)+\left (3135-863 x-6232 x^2-1926 x^3+238 x^4+47 x^5-21 x^6-3 x^7\right ) \log ^2(4)+\left (1764-1188 x-720 x^2+108 x^3+36 x^4\right ) \log ^3(4)+\left (-57+9 x+60 x^2-9 x^3-3 x^4\right ) \log ^4(4)+(-18+18 x) \log ^5(4)+(1-x) \log ^6(4)\right )}{-166375-145200 x-5940 x^2+26099 x^3+5712 x^4-1320 x^5-485 x^6+12 x^8+x^9+\left (-54450-31680 x+3312 x^2+4284 x^3+288 x^4-144 x^5-18 x^6\right ) \log (4)+\left (3135+3552 x-120 x^2-606 x^3-48 x^4+24 x^5+3 x^6\right ) \log ^2(4)+\left (1764+576 x-144 x^2-36 x^3\right ) \log ^3(4)+\left (-57-48 x+12 x^2+3 x^3\right ) \log ^4(4)-18 \log ^5(4)+\log ^6(4)} \, dx=x e^{\left (-\frac {x^{7} + 8 \, x^{6} + 8 \, x^{4} \log \left (2\right )^{2} - 11 \, x^{5} - 24 \, x^{4} \log \left (2\right ) + 32 \, x^{3} \log \left (2\right )^{2} + 16 \, x \log \left (2\right )^{4} - 158 \, x^{4} - 96 \, x^{3} \log \left (2\right ) - 128 \, x^{2} \log \left (2\right )^{2} - 96 \, x \log \left (2\right )^{3} + 296 \, x^{3} + 384 \, x^{2} \log \left (2\right ) - 296 \, x \log \left (2\right )^{2} + 3040 \, x^{2} + 1320 \, x \log \left (2\right ) + 4305 \, x}{x^{6} + 8 \, x^{5} + 8 \, x^{3} \log \left (2\right )^{2} - 16 \, x^{4} - 24 \, x^{3} \log \left (2\right ) + 32 \, x^{2} \log \left (2\right )^{2} + 16 \, \log \left (2\right )^{4} - 238 \, x^{3} - 96 \, x^{2} \log \left (2\right ) - 128 \, x \log \left (2\right )^{2} - 96 \, \log \left (2\right )^{3} - 184 \, x^{2} + 384 \, x \log \left (2\right ) - 296 \, \log \left (2\right )^{2} + 1760 \, x + 1320 \, \log \left (2\right ) + 3025} - 1\right )} \]
integrate((64*(1-x)*log(2)^6+32*(18*x-18)*log(2)^5+16*(-3*x^4-9*x^3+60*x^2 +9*x-57)*log(2)^4+8*(36*x^4+108*x^3-720*x^2-1188*x+1764)*log(2)^3+4*(-3*x^ 7-21*x^6+47*x^5+238*x^4-1926*x^3-6232*x^2-863*x+3135)*log(2)^2+2*(18*x^7+1 26*x^6-282*x^5-2076*x^4+9612*x^3+50352*x^2+30450*x-54450)*log(2)-x^10-11*x ^9+17*x^8+625*x^7+2515*x^6+3943*x^5+21533*x^4+126599*x^3+259580*x^2+91575* x-166375)/(64*log(2)^6-576*log(2)^5+16*(3*x^3+12*x^2-48*x-57)*log(2)^4+8*( -36*x^3-144*x^2+576*x+1764)*log(2)^3+4*(3*x^6+24*x^5-48*x^4-606*x^3-120*x^ 2+3552*x+3135)*log(2)^2+2*(-18*x^6-144*x^5+288*x^4+4284*x^3+3312*x^2-31680 *x-54450)*log(2)+x^9+12*x^8-485*x^6-1320*x^5+5712*x^4+26099*x^3-5940*x^2-1 45200*x-166375)/exp((16*(1+x)*log(2)^4+8*(-12*x-12)*log(2)^3+4*(2*x^4+10*x ^3-24*x^2-106*x-74)*log(2)^2+2*(-12*x^4-60*x^3+144*x^2+852*x+660)*log(2)+x ^7+9*x^6-3*x^5-174*x^4+58*x^3+2856*x^2+6065*x+3025)/(16*log(2)^4-96*log(2) ^3+4*(2*x^3+8*x^2-32*x-74)*log(2)^2+2*(-12*x^3-48*x^2+192*x+660)*log(2)+x^ 6+8*x^5-16*x^4-238*x^3-184*x^2+1760*x+3025)),x, algorithm=\
x*e^(-(x^7 + 8*x^6 + 8*x^4*log(2)^2 - 11*x^5 - 24*x^4*log(2) + 32*x^3*log( 2)^2 + 16*x*log(2)^4 - 158*x^4 - 96*x^3*log(2) - 128*x^2*log(2)^2 - 96*x*l og(2)^3 + 296*x^3 + 384*x^2*log(2) - 296*x*log(2)^2 + 3040*x^2 + 1320*x*lo g(2) + 4305*x)/(x^6 + 8*x^5 + 8*x^3*log(2)^2 - 16*x^4 - 24*x^3*log(2) + 32 *x^2*log(2)^2 + 16*log(2)^4 - 238*x^3 - 96*x^2*log(2) - 128*x*log(2)^2 - 9 6*log(2)^3 - 184*x^2 + 384*x*log(2) - 296*log(2)^2 + 1760*x + 1320*log(2) + 3025) - 1)
Timed out. \[ \int \frac {e^{-\frac {3025+6065 x+2856 x^2+58 x^3-174 x^4-3 x^5+9 x^6+x^7+\left (660+852 x+144 x^2-60 x^3-12 x^4\right ) \log (4)+\left (-74-106 x-24 x^2+10 x^3+2 x^4\right ) \log ^2(4)+(-12-12 x) \log ^3(4)+(1+x) \log ^4(4)}{3025+1760 x-184 x^2-238 x^3-16 x^4+8 x^5+x^6+\left (660+192 x-48 x^2-12 x^3\right ) \log (4)+\left (-74-32 x+8 x^2+2 x^3\right ) \log ^2(4)-12 \log ^3(4)+\log ^4(4)}} \left (-166375+91575 x+259580 x^2+126599 x^3+21533 x^4+3943 x^5+2515 x^6+625 x^7+17 x^8-11 x^9-x^{10}+\left (-54450+30450 x+50352 x^2+9612 x^3-2076 x^4-282 x^5+126 x^6+18 x^7\right ) \log (4)+\left (3135-863 x-6232 x^2-1926 x^3+238 x^4+47 x^5-21 x^6-3 x^7\right ) \log ^2(4)+\left (1764-1188 x-720 x^2+108 x^3+36 x^4\right ) \log ^3(4)+\left (-57+9 x+60 x^2-9 x^3-3 x^4\right ) \log ^4(4)+(-18+18 x) \log ^5(4)+(1-x) \log ^6(4)\right )}{-166375-145200 x-5940 x^2+26099 x^3+5712 x^4-1320 x^5-485 x^6+12 x^8+x^9+\left (-54450-31680 x+3312 x^2+4284 x^3+288 x^4-144 x^5-18 x^6\right ) \log (4)+\left (3135+3552 x-120 x^2-606 x^3-48 x^4+24 x^5+3 x^6\right ) \log ^2(4)+\left (1764+576 x-144 x^2-36 x^3\right ) \log ^3(4)+\left (-57-48 x+12 x^2+3 x^3\right ) \log ^4(4)-18 \log ^5(4)+\log ^6(4)} \, dx=\text {Hanged} \]
int(-(exp(-(6065*x + 16*log(2)^4*(x + 1) - 4*log(2)^2*(106*x + 24*x^2 - 10 *x^3 - 2*x^4 + 74) - 8*log(2)^3*(12*x + 12) + 2*log(2)*(852*x + 144*x^2 - 60*x^3 - 12*x^4 + 660) + 2856*x^2 + 58*x^3 - 174*x^4 - 3*x^5 + 9*x^6 + x^7 + 3025)/(1760*x + 2*log(2)*(192*x - 48*x^2 - 12*x^3 + 660) - 96*log(2)^3 + 16*log(2)^4 - 4*log(2)^2*(32*x - 8*x^2 - 2*x^3 + 74) - 184*x^2 - 238*x^3 - 16*x^4 + 8*x^5 + x^6 + 3025))*(91575*x - 64*log(2)^6*(x - 1) - 16*log(2 )^4*(9*x^3 - 60*x^2 - 9*x + 3*x^4 + 57) + 8*log(2)^3*(108*x^3 - 720*x^2 - 1188*x + 36*x^4 + 1764) + 2*log(2)*(30450*x + 50352*x^2 + 9612*x^3 - 2076* x^4 - 282*x^5 + 126*x^6 + 18*x^7 - 54450) + 32*log(2)^5*(18*x - 18) - 4*lo g(2)^2*(863*x + 6232*x^2 + 1926*x^3 - 238*x^4 - 47*x^5 + 21*x^6 + 3*x^7 - 3135) + 259580*x^2 + 126599*x^3 + 21533*x^4 + 3943*x^5 + 2515*x^6 + 625*x^ 7 + 17*x^8 - 11*x^9 - x^10 - 166375))/(145200*x + 2*log(2)*(31680*x - 3312 *x^2 - 4284*x^3 - 288*x^4 + 144*x^5 + 18*x^6 + 54450) - 4*log(2)^2*(3552*x - 120*x^2 - 606*x^3 - 48*x^4 + 24*x^5 + 3*x^6 + 3135) + 576*log(2)^5 - 64 *log(2)^6 + 16*log(2)^4*(48*x - 12*x^2 - 3*x^3 + 57) - 8*log(2)^3*(576*x - 144*x^2 - 36*x^3 + 1764) + 5940*x^2 - 26099*x^3 - 5712*x^4 + 1320*x^5 + 4 85*x^6 - 12*x^8 - x^9 + 166375),x)