Integrand size = 325, antiderivative size = 27 \[ \int \frac {-645248-249920 x+38032 x^2+848 x^3+4 x^4+\left (1290496-147680 x-4512 x^2-24 x^3\right ) \log \left (x^2\right )+\left (4544 x+32 x^2\right ) \log ^2\left (x^2\right )}{6505390336 x+13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+\left (-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5\right ) \log (5)+x \log ^2(5)+\left (-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+\left (645248 x+331712 x^2+4576 x^3+16 x^4\right ) \log (5)\right ) \log \left (x^2\right )+\left (156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+\left (-645248 x-9088 x^2-32 x^3\right ) \log (5)\right ) \log ^2\left (x^2\right )+\left (-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6\right ) \log ^3\left (x^2\right )+\left (104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5\right ) \log ^4\left (x^2\right )} \, dx=\frac {1}{\log (5)-(-142-x)^2 \left (-2-x+4 \log \left (x^2\right )\right )^2} \]
Time = 0.10 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.96 \[ \int \frac {-645248-249920 x+38032 x^2+848 x^3+4 x^4+\left (1290496-147680 x-4512 x^2-24 x^3\right ) \log \left (x^2\right )+\left (4544 x+32 x^2\right ) \log ^2\left (x^2\right )}{6505390336 x+13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+\left (-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5\right ) \log (5)+x \log ^2(5)+\left (-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+\left (645248 x+331712 x^2+4576 x^3+16 x^4\right ) \log (5)\right ) \log \left (x^2\right )+\left (156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+\left (-645248 x-9088 x^2-32 x^3\right ) \log (5)\right ) \log ^2\left (x^2\right )+\left (-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6\right ) \log ^3\left (x^2\right )+\left (104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5\right ) \log ^4\left (x^2\right )} \, dx=-\frac {1}{80656+81792 x+21304 x^2+288 x^3+x^4-\log (5)-8 (2+x) (142+x)^2 \log \left (x^2\right )+16 (142+x)^2 \log ^2\left (x^2\right )} \]
Integrate[(-645248 - 249920*x + 38032*x^2 + 848*x^3 + 4*x^4 + (1290496 - 1 47680*x - 4512*x^2 - 24*x^3)*Log[x^2] + (4544*x + 32*x^2)*Log[x^2]^2)/(650 5390336*x + 13194031104*x^2 + 10126522112*x^3 + 3531451392*x^4 + 501133920 *x^5 + 12434688*x^6 + 125552*x^7 + 576*x^8 + x^9 + (-161312*x - 163584*x^2 - 42608*x^3 - 576*x^4 - 2*x^5)*Log[5] + x*Log[5]^2 + (-52043122688*x - 79 530687488*x^2 - 41246833152*x^3 - 7628194560*x^4 - 194974080*x^5 - 1990464 *x^6 - 9184*x^7 - 16*x^8 + (645248*x + 331712*x^2 + 4576*x^3 + 16*x^4)*Log [5])*Log[x^2] + (156129368064*x + 160527378432*x^2 + 43476810240*x^3 + 114 6178560*x^4 + 11832960*x^5 + 54912*x^6 + 96*x^7 + (-645248*x - 9088*x^2 - 32*x^3)*Log[5])*Log[x^2]^2 + (-208172490752*x - 109950259200*x^2 - 2993950 720*x^3 - 31262720*x^4 - 145920*x^5 - 256*x^6)*Log[x^2]^3 + (104086245376* x + 2932006912*x^2 + 30971904*x^3 + 145408*x^4 + 256*x^5)*Log[x^2]^4),x]
-(80656 + 81792*x + 21304*x^2 + 288*x^3 + x^4 - Log[5] - 8*(2 + x)*(142 + x)^2*Log[x^2] + 16*(142 + x)^2*Log[x^2]^2)^(-1)
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.
| \(\displaystyle \int \frac {4 x^4+848 x^3+38032 x^2+\left (32 x^2+4544 x\right ) \log ^2\left (x^2\right )+\left (-24 x^3-4512 x^2-147680 x+1290496\right ) \log \left (x^2\right )-249920 x-645248}{x^9+576 x^8+125552 x^7+12434688 x^6+501133920 x^5+3531451392 x^4+10126522112 x^3+13194031104 x^2+\left (256 x^5+145408 x^4+30971904 x^3+2932006912 x^2+104086245376 x\right ) \log ^4\left (x^2\right )+\left (-2 x^5-576 x^4-42608 x^3-163584 x^2-161312 x\right ) \log (5)+\left (-256 x^6-145920 x^5-31262720 x^4-2993950720 x^3-109950259200 x^2-208172490752 x\right ) \log ^3\left (x^2\right )+\left (96 x^7+54912 x^6+11832960 x^5+1146178560 x^4+43476810240 x^3+160527378432 x^2+\left (-32 x^3-9088 x^2-645248 x\right ) \log (5)+156129368064 x\right ) \log ^2\left (x^2\right )+\left (-16 x^8-9184 x^7-1990464 x^6-194974080 x^5-7628194560 x^4-41246833152 x^3-79530687488 x^2+\left (16 x^4+4576 x^3+331712 x^2+645248 x\right ) \log (5)-52043122688 x\right ) \log \left (x^2\right )+6505390336 x+x \log ^2(5)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {4 x^4+848 x^3+38032 x^2+\left (32 x^2+4544 x\right ) \log ^2\left (x^2\right )+\left (-24 x^3-4512 x^2-147680 x+1290496\right ) \log \left (x^2\right )-249920 x-645248}{x^9+576 x^8+125552 x^7+12434688 x^6+501133920 x^5+3531451392 x^4+10126522112 x^3+13194031104 x^2+\left (256 x^5+145408 x^4+30971904 x^3+2932006912 x^2+104086245376 x\right ) \log ^4\left (x^2\right )+\left (-2 x^5-576 x^4-42608 x^3-163584 x^2-161312 x\right ) \log (5)+\left (-256 x^6-145920 x^5-31262720 x^4-2993950720 x^3-109950259200 x^2-208172490752 x\right ) \log ^3\left (x^2\right )+\left (96 x^7+54912 x^6+11832960 x^5+1146178560 x^4+43476810240 x^3+160527378432 x^2+\left (-32 x^3-9088 x^2-645248 x\right ) \log (5)+156129368064 x\right ) \log ^2\left (x^2\right )+\left (-16 x^8-9184 x^7-1990464 x^6-194974080 x^5-7628194560 x^4-41246833152 x^3-79530687488 x^2+\left (16 x^4+4576 x^3+331712 x^2+645248 x\right ) \log (5)-52043122688 x\right ) \log \left (x^2\right )+x \left (6505390336+\log ^2(5)\right )}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 (x+142) \left (x^3+70 x^2+8 x \log ^2\left (x^2\right )+\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )-432 x-1136\right )}{x \left (x^4+288 x^3+21304 x^2+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+81792 x+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-2 \left (-3 x^2-138 x+1136\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )-\log (5)+80656\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-2 \left (-3 x^2-138 x+1136\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )-\log (5)+80656\right )^2}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-2 \left (-3 x^2-138 x+1136\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(x+142) \left (-x^3-70 x^2-8 \log ^2\left (x^2\right ) x+432 x-\left (-6 x^2-276 x+2272\right ) \log \left (x^2\right )+1136\right )}{x \left (x^4+288 x^3+21304 x^2+81792 x+16 (x+142)^2 \log ^2\left (x^2\right )-8 (x+2) (x+142)^2 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {-x^5+4 \log \left (x^2\right ) x^4-420 x^4+1672 \log \left (x^2\right ) x^3-57920 x^3+228336 \log \left (x^2\right ) x^2-2493520 x^2+9517408 \log \left (x^2\right ) x+18147600 \left (1-\frac {\log (5)}{18147600}\right ) x-91625216 \log \left (x^2\right )+45812608}{2 x (x+142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )^2}+\frac {1}{2 (-x-142) \left (x^4-8 \log \left (x^2\right ) x^3+288 x^3+16 \log ^2\left (x^2\right ) x^2-2288 \log \left (x^2\right ) x^2+21304 x^2+4544 \log ^2\left (x^2\right ) x-165856 \log \left (x^2\right ) x+81792 x+322624 \log ^2\left (x^2\right )-322624 \log \left (x^2\right )+80656 \left (1-\frac {\log (5)}{80656}\right )\right )}\right )dx\) |
Int[(-645248 - 249920*x + 38032*x^2 + 848*x^3 + 4*x^4 + (1290496 - 147680* x - 4512*x^2 - 24*x^3)*Log[x^2] + (4544*x + 32*x^2)*Log[x^2]^2)/(650539033 6*x + 13194031104*x^2 + 10126522112*x^3 + 3531451392*x^4 + 501133920*x^5 + 12434688*x^6 + 125552*x^7 + 576*x^8 + x^9 + (-161312*x - 163584*x^2 - 426 08*x^3 - 576*x^4 - 2*x^5)*Log[5] + x*Log[5]^2 + (-52043122688*x - 79530687 488*x^2 - 41246833152*x^3 - 7628194560*x^4 - 194974080*x^5 - 1990464*x^6 - 9184*x^7 - 16*x^8 + (645248*x + 331712*x^2 + 4576*x^3 + 16*x^4)*Log[5])*L og[x^2] + (156129368064*x + 160527378432*x^2 + 43476810240*x^3 + 114617856 0*x^4 + 11832960*x^5 + 54912*x^6 + 96*x^7 + (-645248*x - 9088*x^2 - 32*x^3 )*Log[5])*Log[x^2]^2 + (-208172490752*x - 109950259200*x^2 - 2993950720*x^ 3 - 31262720*x^4 - 145920*x^5 - 256*x^6)*Log[x^2]^3 + (104086245376*x + 29 32006912*x^2 + 30971904*x^3 + 145408*x^4 + 256*x^5)*Log[x^2]^4),x]
3.20.49.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
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. \(83\) vs. \(2(27)=54\).
Time = 0.66 (sec) , antiderivative size = 84, normalized size of antiderivative = 3.11
| method | result | size |
| risch | \(\frac {1}{-16 x^{2} \ln \left (x^{2}\right )^{2}+8 x^{3} \ln \left (x^{2}\right )-x^{4}-4544 x \ln \left (x^{2}\right )^{2}+2288 x^{2} \ln \left (x^{2}\right )-288 x^{3}-322624 \ln \left (x^{2}\right )^{2}+165856 x \ln \left (x^{2}\right )-21304 x^{2}+\ln \left (5\right )+322624 \ln \left (x^{2}\right )-81792 x -80656}\) | \(84\) |
| parallelrisch | \(\frac {1}{-16 x^{2} \ln \left (x^{2}\right )^{2}+8 x^{3} \ln \left (x^{2}\right )-x^{4}-4544 x \ln \left (x^{2}\right )^{2}+2288 x^{2} \ln \left (x^{2}\right )-288 x^{3}-322624 \ln \left (x^{2}\right )^{2}+165856 x \ln \left (x^{2}\right )-21304 x^{2}+\ln \left (5\right )+322624 \ln \left (x^{2}\right )-81792 x -80656}\) | \(84\) |
int(((32*x^2+4544*x)*ln(x^2)^2+(-24*x^3-4512*x^2-147680*x+1290496)*ln(x^2) +4*x^4+848*x^3+38032*x^2-249920*x-645248)/((256*x^5+145408*x^4+30971904*x^ 3+2932006912*x^2+104086245376*x)*ln(x^2)^4+(-256*x^6-145920*x^5-31262720*x ^4-2993950720*x^3-109950259200*x^2-208172490752*x)*ln(x^2)^3+((-32*x^3-908 8*x^2-645248*x)*ln(5)+96*x^7+54912*x^6+11832960*x^5+1146178560*x^4+4347681 0240*x^3+160527378432*x^2+156129368064*x)*ln(x^2)^2+((16*x^4+4576*x^3+3317 12*x^2+645248*x)*ln(5)-16*x^8-9184*x^7-1990464*x^6-194974080*x^5-762819456 0*x^4-41246833152*x^3-79530687488*x^2-52043122688*x)*ln(x^2)+x*ln(5)^2+(-2 *x^5-576*x^4-42608*x^3-163584*x^2-161312*x)*ln(5)+x^9+576*x^8+125552*x^7+1 2434688*x^6+501133920*x^5+3531451392*x^4+10126522112*x^3+13194031104*x^2+6 505390336*x),x,method=_RETURNVERBOSE)
1/(-16*x^2*ln(x^2)^2+8*x^3*ln(x^2)-x^4-4544*x*ln(x^2)^2+2288*x^2*ln(x^2)-2 88*x^3-322624*ln(x^2)^2+165856*x*ln(x^2)-21304*x^2+ln(5)+322624*ln(x^2)-81 792*x-80656)
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (26) = 52\).
Time = 0.26 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.26 \[ \int \frac {-645248-249920 x+38032 x^2+848 x^3+4 x^4+\left (1290496-147680 x-4512 x^2-24 x^3\right ) \log \left (x^2\right )+\left (4544 x+32 x^2\right ) \log ^2\left (x^2\right )}{6505390336 x+13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+\left (-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5\right ) \log (5)+x \log ^2(5)+\left (-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+\left (645248 x+331712 x^2+4576 x^3+16 x^4\right ) \log (5)\right ) \log \left (x^2\right )+\left (156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+\left (-645248 x-9088 x^2-32 x^3\right ) \log (5)\right ) \log ^2\left (x^2\right )+\left (-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6\right ) \log ^3\left (x^2\right )+\left (104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5\right ) \log ^4\left (x^2\right )} \, dx=-\frac {1}{x^{4} + 288 \, x^{3} + 16 \, {\left (x^{2} + 284 \, x + 20164\right )} \log \left (x^{2}\right )^{2} + 21304 \, x^{2} - 8 \, {\left (x^{3} + 286 \, x^{2} + 20732 \, x + 40328\right )} \log \left (x^{2}\right ) + 81792 \, x - \log \left (5\right ) + 80656} \]
integrate(((32*x^2+4544*x)*log(x^2)^2+(-24*x^3-4512*x^2-147680*x+1290496)* log(x^2)+4*x^4+848*x^3+38032*x^2-249920*x-645248)/((256*x^5+145408*x^4+309 71904*x^3+2932006912*x^2+104086245376*x)*log(x^2)^4+(-256*x^6-145920*x^5-3 1262720*x^4-2993950720*x^3-109950259200*x^2-208172490752*x)*log(x^2)^3+((- 32*x^3-9088*x^2-645248*x)*log(5)+96*x^7+54912*x^6+11832960*x^5+1146178560* x^4+43476810240*x^3+160527378432*x^2+156129368064*x)*log(x^2)^2+((16*x^4+4 576*x^3+331712*x^2+645248*x)*log(5)-16*x^8-9184*x^7-1990464*x^6-194974080* x^5-7628194560*x^4-41246833152*x^3-79530687488*x^2-52043122688*x)*log(x^2) +x*log(5)^2+(-2*x^5-576*x^4-42608*x^3-163584*x^2-161312*x)*log(5)+x^9+576* x^8+125552*x^7+12434688*x^6+501133920*x^5+3531451392*x^4+10126522112*x^3+1 3194031104*x^2+6505390336*x),x, algorithm=\
-1/(x^4 + 288*x^3 + 16*(x^2 + 284*x + 20164)*log(x^2)^2 + 21304*x^2 - 8*(x ^3 + 286*x^2 + 20732*x + 40328)*log(x^2) + 81792*x - log(5) + 80656)
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (22) = 44\).
Time = 0.41 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.33 \[ \int \frac {-645248-249920 x+38032 x^2+848 x^3+4 x^4+\left (1290496-147680 x-4512 x^2-24 x^3\right ) \log \left (x^2\right )+\left (4544 x+32 x^2\right ) \log ^2\left (x^2\right )}{6505390336 x+13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+\left (-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5\right ) \log (5)+x \log ^2(5)+\left (-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+\left (645248 x+331712 x^2+4576 x^3+16 x^4\right ) \log (5)\right ) \log \left (x^2\right )+\left (156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+\left (-645248 x-9088 x^2-32 x^3\right ) \log (5)\right ) \log ^2\left (x^2\right )+\left (-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6\right ) \log ^3\left (x^2\right )+\left (104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5\right ) \log ^4\left (x^2\right )} \, dx=- \frac {1}{x^{4} + 288 x^{3} + 21304 x^{2} + 81792 x + \left (16 x^{2} + 4544 x + 322624\right ) \log {\left (x^{2} \right )}^{2} + \left (- 8 x^{3} - 2288 x^{2} - 165856 x - 322624\right ) \log {\left (x^{2} \right )} - \log {\left (5 \right )} + 80656} \]
integrate(((32*x**2+4544*x)*ln(x**2)**2+(-24*x**3-4512*x**2-147680*x+12904 96)*ln(x**2)+4*x**4+848*x**3+38032*x**2-249920*x-645248)/((256*x**5+145408 *x**4+30971904*x**3+2932006912*x**2+104086245376*x)*ln(x**2)**4+(-256*x**6 -145920*x**5-31262720*x**4-2993950720*x**3-109950259200*x**2-208172490752* x)*ln(x**2)**3+((-32*x**3-9088*x**2-645248*x)*ln(5)+96*x**7+54912*x**6+118 32960*x**5+1146178560*x**4+43476810240*x**3+160527378432*x**2+156129368064 *x)*ln(x**2)**2+((16*x**4+4576*x**3+331712*x**2+645248*x)*ln(5)-16*x**8-91 84*x**7-1990464*x**6-194974080*x**5-7628194560*x**4-41246833152*x**3-79530 687488*x**2-52043122688*x)*ln(x**2)+x*ln(5)**2+(-2*x**5-576*x**4-42608*x** 3-163584*x**2-161312*x)*ln(5)+x**9+576*x**8+125552*x**7+12434688*x**6+5011 33920*x**5+3531451392*x**4+10126522112*x**3+13194031104*x**2+6505390336*x) ,x)
-1/(x**4 + 288*x**3 + 21304*x**2 + 81792*x + (16*x**2 + 4544*x + 322624)*l og(x**2)**2 + (-8*x**3 - 2288*x**2 - 165856*x - 322624)*log(x**2) - log(5) + 80656)
Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (26) = 52\).
Time = 0.35 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.11 \[ \int \frac {-645248-249920 x+38032 x^2+848 x^3+4 x^4+\left (1290496-147680 x-4512 x^2-24 x^3\right ) \log \left (x^2\right )+\left (4544 x+32 x^2\right ) \log ^2\left (x^2\right )}{6505390336 x+13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+\left (-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5\right ) \log (5)+x \log ^2(5)+\left (-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+\left (645248 x+331712 x^2+4576 x^3+16 x^4\right ) \log (5)\right ) \log \left (x^2\right )+\left (156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+\left (-645248 x-9088 x^2-32 x^3\right ) \log (5)\right ) \log ^2\left (x^2\right )+\left (-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6\right ) \log ^3\left (x^2\right )+\left (104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5\right ) \log ^4\left (x^2\right )} \, dx=-\frac {1}{x^{4} + 288 \, x^{3} + 64 \, {\left (x^{2} + 284 \, x + 20164\right )} \log \left (x\right )^{2} + 21304 \, x^{2} - 16 \, {\left (x^{3} + 286 \, x^{2} + 20732 \, x + 40328\right )} \log \left (x\right ) + 81792 \, x - \log \left (5\right ) + 80656} \]
integrate(((32*x^2+4544*x)*log(x^2)^2+(-24*x^3-4512*x^2-147680*x+1290496)* log(x^2)+4*x^4+848*x^3+38032*x^2-249920*x-645248)/((256*x^5+145408*x^4+309 71904*x^3+2932006912*x^2+104086245376*x)*log(x^2)^4+(-256*x^6-145920*x^5-3 1262720*x^4-2993950720*x^3-109950259200*x^2-208172490752*x)*log(x^2)^3+((- 32*x^3-9088*x^2-645248*x)*log(5)+96*x^7+54912*x^6+11832960*x^5+1146178560* x^4+43476810240*x^3+160527378432*x^2+156129368064*x)*log(x^2)^2+((16*x^4+4 576*x^3+331712*x^2+645248*x)*log(5)-16*x^8-9184*x^7-1990464*x^6-194974080* x^5-7628194560*x^4-41246833152*x^3-79530687488*x^2-52043122688*x)*log(x^2) +x*log(5)^2+(-2*x^5-576*x^4-42608*x^3-163584*x^2-161312*x)*log(5)+x^9+576* x^8+125552*x^7+12434688*x^6+501133920*x^5+3531451392*x^4+10126522112*x^3+1 3194031104*x^2+6505390336*x),x, algorithm=\
-1/(x^4 + 288*x^3 + 64*(x^2 + 284*x + 20164)*log(x)^2 + 21304*x^2 - 16*(x^ 3 + 286*x^2 + 20732*x + 40328)*log(x) + 81792*x - log(5) + 80656)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (26) = 52\).
Time = 0.65 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.15 \[ \int \frac {-645248-249920 x+38032 x^2+848 x^3+4 x^4+\left (1290496-147680 x-4512 x^2-24 x^3\right ) \log \left (x^2\right )+\left (4544 x+32 x^2\right ) \log ^2\left (x^2\right )}{6505390336 x+13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+\left (-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5\right ) \log (5)+x \log ^2(5)+\left (-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+\left (645248 x+331712 x^2+4576 x^3+16 x^4\right ) \log (5)\right ) \log \left (x^2\right )+\left (156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+\left (-645248 x-9088 x^2-32 x^3\right ) \log (5)\right ) \log ^2\left (x^2\right )+\left (-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6\right ) \log ^3\left (x^2\right )+\left (104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5\right ) \log ^4\left (x^2\right )} \, dx=-\frac {1}{x^{4} - 8 \, x^{3} \log \left (x^{2}\right ) + 16 \, x^{2} \log \left (x^{2}\right )^{2} + 288 \, x^{3} - 2288 \, x^{2} \log \left (x^{2}\right ) + 4544 \, x \log \left (x^{2}\right )^{2} + 21304 \, x^{2} - 165856 \, x \log \left (x^{2}\right ) + 322624 \, \log \left (x^{2}\right )^{2} + 81792 \, x - \log \left (5\right ) - 322624 \, \log \left (x^{2}\right ) + 80656} \]
integrate(((32*x^2+4544*x)*log(x^2)^2+(-24*x^3-4512*x^2-147680*x+1290496)* log(x^2)+4*x^4+848*x^3+38032*x^2-249920*x-645248)/((256*x^5+145408*x^4+309 71904*x^3+2932006912*x^2+104086245376*x)*log(x^2)^4+(-256*x^6-145920*x^5-3 1262720*x^4-2993950720*x^3-109950259200*x^2-208172490752*x)*log(x^2)^3+((- 32*x^3-9088*x^2-645248*x)*log(5)+96*x^7+54912*x^6+11832960*x^5+1146178560* x^4+43476810240*x^3+160527378432*x^2+156129368064*x)*log(x^2)^2+((16*x^4+4 576*x^3+331712*x^2+645248*x)*log(5)-16*x^8-9184*x^7-1990464*x^6-194974080* x^5-7628194560*x^4-41246833152*x^3-79530687488*x^2-52043122688*x)*log(x^2) +x*log(5)^2+(-2*x^5-576*x^4-42608*x^3-163584*x^2-161312*x)*log(5)+x^9+576* x^8+125552*x^7+12434688*x^6+501133920*x^5+3531451392*x^4+10126522112*x^3+1 3194031104*x^2+6505390336*x),x, algorithm=\
-1/(x^4 - 8*x^3*log(x^2) + 16*x^2*log(x^2)^2 + 288*x^3 - 2288*x^2*log(x^2) + 4544*x*log(x^2)^2 + 21304*x^2 - 165856*x*log(x^2) + 322624*log(x^2)^2 + 81792*x - log(5) - 322624*log(x^2) + 80656)
Timed out. \[ \int \frac {-645248-249920 x+38032 x^2+848 x^3+4 x^4+\left (1290496-147680 x-4512 x^2-24 x^3\right ) \log \left (x^2\right )+\left (4544 x+32 x^2\right ) \log ^2\left (x^2\right )}{6505390336 x+13194031104 x^2+10126522112 x^3+3531451392 x^4+501133920 x^5+12434688 x^6+125552 x^7+576 x^8+x^9+\left (-161312 x-163584 x^2-42608 x^3-576 x^4-2 x^5\right ) \log (5)+x \log ^2(5)+\left (-52043122688 x-79530687488 x^2-41246833152 x^3-7628194560 x^4-194974080 x^5-1990464 x^6-9184 x^7-16 x^8+\left (645248 x+331712 x^2+4576 x^3+16 x^4\right ) \log (5)\right ) \log \left (x^2\right )+\left (156129368064 x+160527378432 x^2+43476810240 x^3+1146178560 x^4+11832960 x^5+54912 x^6+96 x^7+\left (-645248 x-9088 x^2-32 x^3\right ) \log (5)\right ) \log ^2\left (x^2\right )+\left (-208172490752 x-109950259200 x^2-2993950720 x^3-31262720 x^4-145920 x^5-256 x^6\right ) \log ^3\left (x^2\right )+\left (104086245376 x+2932006912 x^2+30971904 x^3+145408 x^4+256 x^5\right ) \log ^4\left (x^2\right )} \, dx=\int \frac {{\ln \left (x^2\right )}^2\,\left (32\,x^2+4544\,x\right )-\ln \left (x^2\right )\,\left (24\,x^3+4512\,x^2+147680\,x-1290496\right )-249920\,x+38032\,x^2+848\,x^3+4\,x^4-645248}{6505390336\,x+{\ln \left (x^2\right )}^4\,\left (256\,x^5+145408\,x^4+30971904\,x^3+2932006912\,x^2+104086245376\,x\right )-\ln \left (x^2\right )\,\left (52043122688\,x-\ln \left (5\right )\,\left (16\,x^4+4576\,x^3+331712\,x^2+645248\,x\right )+79530687488\,x^2+41246833152\,x^3+7628194560\,x^4+194974080\,x^5+1990464\,x^6+9184\,x^7+16\,x^8\right )-{\ln \left (x^2\right )}^3\,\left (256\,x^6+145920\,x^5+31262720\,x^4+2993950720\,x^3+109950259200\,x^2+208172490752\,x\right )+{\ln \left (x^2\right )}^2\,\left (156129368064\,x-\ln \left (5\right )\,\left (32\,x^3+9088\,x^2+645248\,x\right )+160527378432\,x^2+43476810240\,x^3+1146178560\,x^4+11832960\,x^5+54912\,x^6+96\,x^7\right )+x\,{\ln \left (5\right )}^2+13194031104\,x^2+10126522112\,x^3+3531451392\,x^4+501133920\,x^5+12434688\,x^6+125552\,x^7+576\,x^8+x^9-\ln \left (5\right )\,\left (2\,x^5+576\,x^4+42608\,x^3+163584\,x^2+161312\,x\right )} \,d x \]
int((log(x^2)^2*(4544*x + 32*x^2) - log(x^2)*(147680*x + 4512*x^2 + 24*x^3 - 1290496) - 249920*x + 38032*x^2 + 848*x^3 + 4*x^4 - 645248)/(6505390336 *x + log(x^2)^4*(104086245376*x + 2932006912*x^2 + 30971904*x^3 + 145408*x ^4 + 256*x^5) - log(x^2)*(52043122688*x - log(5)*(645248*x + 331712*x^2 + 4576*x^3 + 16*x^4) + 79530687488*x^2 + 41246833152*x^3 + 7628194560*x^4 + 194974080*x^5 + 1990464*x^6 + 9184*x^7 + 16*x^8) - log(x^2)^3*(20817249075 2*x + 109950259200*x^2 + 2993950720*x^3 + 31262720*x^4 + 145920*x^5 + 256* x^6) + log(x^2)^2*(156129368064*x - log(5)*(645248*x + 9088*x^2 + 32*x^3) + 160527378432*x^2 + 43476810240*x^3 + 1146178560*x^4 + 11832960*x^5 + 549 12*x^6 + 96*x^7) + x*log(5)^2 + 13194031104*x^2 + 10126522112*x^3 + 353145 1392*x^4 + 501133920*x^5 + 12434688*x^6 + 125552*x^7 + 576*x^8 + x^9 - log (5)*(161312*x + 163584*x^2 + 42608*x^3 + 576*x^4 + 2*x^5)),x)
int((log(x^2)^2*(4544*x + 32*x^2) - log(x^2)*(147680*x + 4512*x^2 + 24*x^3 - 1290496) - 249920*x + 38032*x^2 + 848*x^3 + 4*x^4 - 645248)/(6505390336 *x + log(x^2)^4*(104086245376*x + 2932006912*x^2 + 30971904*x^3 + 145408*x ^4 + 256*x^5) - log(x^2)*(52043122688*x - log(5)*(645248*x + 331712*x^2 + 4576*x^3 + 16*x^4) + 79530687488*x^2 + 41246833152*x^3 + 7628194560*x^4 + 194974080*x^5 + 1990464*x^6 + 9184*x^7 + 16*x^8) - log(x^2)^3*(20817249075 2*x + 109950259200*x^2 + 2993950720*x^3 + 31262720*x^4 + 145920*x^5 + 256* x^6) + log(x^2)^2*(156129368064*x - log(5)*(645248*x + 9088*x^2 + 32*x^3) + 160527378432*x^2 + 43476810240*x^3 + 1146178560*x^4 + 11832960*x^5 + 549 12*x^6 + 96*x^7) + x*log(5)^2 + 13194031104*x^2 + 10126522112*x^3 + 353145 1392*x^4 + 501133920*x^5 + 12434688*x^6 + 125552*x^7 + 576*x^8 + x^9 - log (5)*(161312*x + 163584*x^2 + 42608*x^3 + 576*x^4 + 2*x^5)), x)