Integrand size = 183, antiderivative size = 31 \[ \int \frac {-1090000-336000 x+313600 x^2+\left (2360000+336000 x-627200 x^2\right ) \log (x)+\left (-1605000-84000 x+470400 x^2\right ) \log ^2(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (-38125+19600 x^2\right ) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+\left (-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4\right ) \log (x)+\left (177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4\right ) \log ^2(x)+\left (-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4\right ) \log ^3(x)+\left (2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4\right ) \log ^4(x)} \, dx=3-\frac {x}{-3+x+16 \left (\frac {2}{5} (-5+x)+x+\frac {3}{-2+\log (x)}\right )^2} \] Output:
3-x/(4*(7/5*x-2+3/(ln(x)-2))*(28/5*x-8+12/(ln(x)-2))+x-3)
Time = 0.06 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.71 \[ \int \frac {-1090000-336000 x+313600 x^2+\left (2360000+336000 x-627200 x^2\right ) \log (x)+\left (-1605000-84000 x+470400 x^2\right ) \log ^2(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (-38125+19600 x^2\right ) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+\left (-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4\right ) \log (x)+\left (177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4\right ) \log ^2(x)+\left (-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4\right ) \log ^3(x)+\left (2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4\right ) \log ^4(x)} \, dx=-\frac {25 x (-2+\log (x))^2}{4 \left (4825-3895 x+784 x^2\right )-4 \left (2725-3055 x+784 x^2\right ) \log (x)+\left (1525-2215 x+784 x^2\right ) \log ^2(x)} \] Input:
Integrate[(-1090000 - 336000*x + 313600*x^2 + (2360000 + 336000*x - 627200 *x^2)*Log[x] + (-1605000 - 84000*x + 470400*x^2)*Log[x]^2 + (425000 - 1568 00*x^2)*Log[x]^3 + (-38125 + 19600*x^2)*Log[x]^4)/(372490000 - 601388000*x + 363786000*x^2 - 97717760*x^3 + 9834496*x^4 + (-420740000 + 811336000*x - 570189600*x^2 + 174361600*x^3 - 19668992*x^4)*Log[x] + (177675000 - 3994 14000*x + 326539800*x^2 - 114965760*x^3 + 14751744*x^4)*Log[x]^2 + (-33245 000 + 85558000*x - 80790600*x^2 + 33053440*x^3 - 4917248*x^4)*Log[x]^3 + ( 2325625 - 6755750*x + 7297425*x^2 - 3473120*x^3 + 614656*x^4)*Log[x]^4),x]
Output:
(-25*x*(-2 + Log[x])^2)/(4*(4825 - 3895*x + 784*x^2) - 4*(2725 - 3055*x + 784*x^2)*Log[x] + (1525 - 2215*x + 784*x^2)*Log[x]^2)
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {313600 x^2+\left (19600 x^2-38125\right ) \log ^4(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (470400 x^2-84000 x-1605000\right ) \log ^2(x)+\left (-627200 x^2+336000 x+2360000\right ) \log (x)-336000 x-1090000}{9834496 x^4-97717760 x^3+363786000 x^2+\left (614656 x^4-3473120 x^3+7297425 x^2-6755750 x+2325625\right ) \log ^4(x)+\left (-4917248 x^4+33053440 x^3-80790600 x^2+85558000 x-33245000\right ) \log ^3(x)+\left (14751744 x^4-114965760 x^3+326539800 x^2-399414000 x+177675000\right ) \log ^2(x)+\left (-19668992 x^4+174361600 x^3-570189600 x^2+811336000 x-420740000\right ) \log (x)-601388000 x+372490000} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {25 (2-\log (x)) \left (-8 \left (-784 x^2+840 x+2725\right )-\left (\left (784 x^2-1525\right ) \log ^3(x)\right )+6 \left (784 x^2-2325\right ) \log ^2(x)-12 \left (784 x^2-280 x-3025\right ) \log (x)\right )}{\left (4 \left (784 x^2-3895 x+4825\right )+\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 25 \int -\frac {(2-\log (x)) \left (-\left (\left (1525-784 x^2\right ) \log ^3(x)\right )+6 \left (2325-784 x^2\right ) \log ^2(x)-12 \left (-784 x^2+280 x+3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (-\left (\left (1525-784 x^2\right ) \log ^3(x)\right )+6 \left (2325-784 x^2\right ) \log ^2(x)-12 \left (-784 x^2+280 x+3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -25 \int \frac {(2-\log (x)) \left (\left (784 x^2-1525\right ) \log ^3(x)-6 \left (784 x^2-2325\right ) \log ^2(x)+12 \left (784 x^2-280 x-3025\right ) \log (x)+8 \left (-784 x^2+840 x+2725\right )\right )}{\left (\left (784 x^2-2215 x+1525\right ) \log ^2(x)-4 \left (784 x^2-3055 x+2725\right ) \log (x)+4 \left (784 x^2-3895 x+4825\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -25 \int \left (\frac {1525-784 x^2}{\left (784 x^2-2215 x+1525\right )^2}+\frac {240 \left (17210368 \log (x) x^5-25815552 x^5-85503040 \log (x) x^4+100869440 x^4+138924800 \log (x) x^3-52362450 x^3-51368000 \log (x) x^2-255971625 x^2-65117500 \log (x) x+408068750 x+46512500 \log (x)-174421875\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )}-\frac {7200 \left (481890304 \log (x) x^6-963780608 x^6-5147744000 \log (x) x^5+11328110080 x^5+20649756400 \log (x) x^4-50822290400 x^4-41160897625 \log (x) x^3+112506061250 x^3+43080930625 \log (x) x^2-129206776250 x^2-21902271875 \log (x) x+71064418750 x+3895421875 \log (x)-13372343750\right )}{\left (784 x^2-2215 x+1525\right )^3 \left (784 \log ^2(x) x^2-3136 \log (x) x^2+3136 x^2-2215 \log ^2(x) x+12220 \log (x) x-15580 x+1525 \log ^2(x)-10900 \log (x)+19300\right )^2}\right )dx\) |
Input:
Int[(-1090000 - 336000*x + 313600*x^2 + (2360000 + 336000*x - 627200*x^2)* Log[x] + (-1605000 - 84000*x + 470400*x^2)*Log[x]^2 + (425000 - 156800*x^2 )*Log[x]^3 + (-38125 + 19600*x^2)*Log[x]^4)/(372490000 - 601388000*x + 363 786000*x^2 - 97717760*x^3 + 9834496*x^4 + (-420740000 + 811336000*x - 5701 89600*x^2 + 174361600*x^3 - 19668992*x^4)*Log[x] + (177675000 - 399414000* x + 326539800*x^2 - 114965760*x^3 + 14751744*x^4)*Log[x]^2 + (-33245000 + 85558000*x - 80790600*x^2 + 33053440*x^3 - 4917248*x^4)*Log[x]^3 + (232562 5 - 6755750*x + 7297425*x^2 - 3473120*x^3 + 614656*x^4)*Log[x]^4),x]
Output:
$Aborted
Time = 3.07 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.19
| method | result | size |
| norman | \(\frac {-100 x -25 x \ln \left (x \right )^{2}+100 x \ln \left (x \right )}{784 x^{2} \ln \left (x \right )^{2}-2215 x \ln \left (x \right )^{2}-3136 x^{2} \ln \left (x \right )+1525 \ln \left (x \right )^{2}+12220 x \ln \left (x \right )+3136 x^{2}-10900 \ln \left (x \right )-15580 x +19300}\) | \(68\) |
| default | \(\frac {-100 x -25 x \ln \left (x \right )^{2}+100 x \ln \left (x \right )}{784 x^{2} \ln \left (x \right )^{2}-2215 x \ln \left (x \right )^{2}-3136 x^{2} \ln \left (x \right )+1525 \ln \left (x \right )^{2}+12220 x \ln \left (x \right )+3136 x^{2}-10900 \ln \left (x \right )-15580 x +19300}\) | \(69\) |
| parallelrisch | \(\frac {-78400 x +78400 x \ln \left (x \right )-19600 x \ln \left (x \right )^{2}}{614656 x^{2} \ln \left (x \right )^{2}-1736560 x \ln \left (x \right )^{2}-2458624 x^{2} \ln \left (x \right )+1195600 \ln \left (x \right )^{2}+9580480 x \ln \left (x \right )+2458624 x^{2}-8545600 \ln \left (x \right )-12214720 x +15131200}\) | \(69\) |
| risch | \(-\frac {25 x}{784 x^{2}-2215 x +1525}+\frac {6000 x \left (14 x \ln \left (x \right )-28 x -20 \ln \left (x \right )+55\right )}{\left (784 x^{2}-2215 x +1525\right ) \left (784 x^{2} \ln \left (x \right )^{2}-2215 x \ln \left (x \right )^{2}-3136 x^{2} \ln \left (x \right )+1525 \ln \left (x \right )^{2}+12220 x \ln \left (x \right )+3136 x^{2}-10900 \ln \left (x \right )-15580 x +19300\right )}\) | \(96\) |
Input:
int(((19600*x^2-38125)*ln(x)^4+(-156800*x^2+425000)*ln(x)^3+(470400*x^2-84 000*x-1605000)*ln(x)^2+(-627200*x^2+336000*x+2360000)*ln(x)+313600*x^2-336 000*x-1090000)/((614656*x^4-3473120*x^3+7297425*x^2-6755750*x+2325625)*ln( x)^4+(-4917248*x^4+33053440*x^3-80790600*x^2+85558000*x-33245000)*ln(x)^3+ (14751744*x^4-114965760*x^3+326539800*x^2-399414000*x+177675000)*ln(x)^2+( -19668992*x^4+174361600*x^3-570189600*x^2+811336000*x-420740000)*ln(x)+983 4496*x^4-97717760*x^3+363786000*x^2-601388000*x+372490000),x,method=_RETUR NVERBOSE)
Output:
(-100*x-25*x*ln(x)^2+100*x*ln(x))/(784*x^2*ln(x)^2-2215*x*ln(x)^2-3136*x^2 *ln(x)+1525*ln(x)^2+12220*x*ln(x)+3136*x^2-10900*ln(x)-15580*x+19300)
Time = 0.10 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.87 \[ \int \frac {-1090000-336000 x+313600 x^2+\left (2360000+336000 x-627200 x^2\right ) \log (x)+\left (-1605000-84000 x+470400 x^2\right ) \log ^2(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (-38125+19600 x^2\right ) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+\left (-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4\right ) \log (x)+\left (177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4\right ) \log ^2(x)+\left (-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4\right ) \log ^3(x)+\left (2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4\right ) \log ^4(x)} \, dx=-\frac {25 \, {\left (x \log \left (x\right )^{2} - 4 \, x \log \left (x\right ) + 4 \, x\right )}}{{\left (784 \, x^{2} - 2215 \, x + 1525\right )} \log \left (x\right )^{2} + 3136 \, x^{2} - 4 \, {\left (784 \, x^{2} - 3055 \, x + 2725\right )} \log \left (x\right ) - 15580 \, x + 19300} \] Input:
integrate(((19600*x^2-38125)*log(x)^4+(-156800*x^2+425000)*log(x)^3+(47040 0*x^2-84000*x-1605000)*log(x)^2+(-627200*x^2+336000*x+2360000)*log(x)+3136 00*x^2-336000*x-1090000)/((614656*x^4-3473120*x^3+7297425*x^2-6755750*x+23 25625)*log(x)^4+(-4917248*x^4+33053440*x^3-80790600*x^2+85558000*x-3324500 0)*log(x)^3+(14751744*x^4-114965760*x^3+326539800*x^2-399414000*x+17767500 0)*log(x)^2+(-19668992*x^4+174361600*x^3-570189600*x^2+811336000*x-4207400 00)*log(x)+9834496*x^4-97717760*x^3+363786000*x^2-601388000*x+372490000),x , algorithm="fricas")
Output:
-25*(x*log(x)^2 - 4*x*log(x) + 4*x)/((784*x^2 - 2215*x + 1525)*log(x)^2 + 3136*x^2 - 4*(784*x^2 - 3055*x + 2725)*log(x) - 15580*x + 19300)
Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (20) = 40\).
Time = 0.40 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.29 \[ \int \frac {-1090000-336000 x+313600 x^2+\left (2360000+336000 x-627200 x^2\right ) \log (x)+\left (-1605000-84000 x+470400 x^2\right ) \log ^2(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (-38125+19600 x^2\right ) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+\left (-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4\right ) \log (x)+\left (177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4\right ) \log ^2(x)+\left (-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4\right ) \log ^3(x)+\left (2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4\right ) \log ^4(x)} \, dx=- \frac {25 x}{784 x^{2} - 2215 x + 1525} + \frac {- 168000 x^{2} + 330000 x + \left (84000 x^{2} - 120000 x\right ) \log {\left (x \right )}}{2458624 x^{4} - 19160960 x^{3} + 54423300 x^{2} - 66509000 x + \left (- 2458624 x^{4} + 16526720 x^{3} - 40395300 x^{2} + 42779000 x - 16622500\right ) \log {\left (x \right )} + \left (614656 x^{4} - 3473120 x^{3} + 7297425 x^{2} - 6755750 x + 2325625\right ) \log {\left (x \right )}^{2} + 29432500} \] Input:
integrate(((19600*x**2-38125)*ln(x)**4+(-156800*x**2+425000)*ln(x)**3+(470 400*x**2-84000*x-1605000)*ln(x)**2+(-627200*x**2+336000*x+2360000)*ln(x)+3 13600*x**2-336000*x-1090000)/((614656*x**4-3473120*x**3+7297425*x**2-67557 50*x+2325625)*ln(x)**4+(-4917248*x**4+33053440*x**3-80790600*x**2+85558000 *x-33245000)*ln(x)**3+(14751744*x**4-114965760*x**3+326539800*x**2-3994140 00*x+177675000)*ln(x)**2+(-19668992*x**4+174361600*x**3-570189600*x**2+811 336000*x-420740000)*ln(x)+9834496*x**4-97717760*x**3+363786000*x**2-601388 000*x+372490000),x)
Output:
-25*x/(784*x**2 - 2215*x + 1525) + (-168000*x**2 + 330000*x + (84000*x**2 - 120000*x)*log(x))/(2458624*x**4 - 19160960*x**3 + 54423300*x**2 - 665090 00*x + (-2458624*x**4 + 16526720*x**3 - 40395300*x**2 + 42779000*x - 16622 500)*log(x) + (614656*x**4 - 3473120*x**3 + 7297425*x**2 - 6755750*x + 232 5625)*log(x)**2 + 29432500)
Time = 0.10 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.87 \[ \int \frac {-1090000-336000 x+313600 x^2+\left (2360000+336000 x-627200 x^2\right ) \log (x)+\left (-1605000-84000 x+470400 x^2\right ) \log ^2(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (-38125+19600 x^2\right ) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+\left (-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4\right ) \log (x)+\left (177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4\right ) \log ^2(x)+\left (-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4\right ) \log ^3(x)+\left (2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4\right ) \log ^4(x)} \, dx=-\frac {25 \, {\left (x \log \left (x\right )^{2} - 4 \, x \log \left (x\right ) + 4 \, x\right )}}{{\left (784 \, x^{2} - 2215 \, x + 1525\right )} \log \left (x\right )^{2} + 3136 \, x^{2} - 4 \, {\left (784 \, x^{2} - 3055 \, x + 2725\right )} \log \left (x\right ) - 15580 \, x + 19300} \] Input:
integrate(((19600*x^2-38125)*log(x)^4+(-156800*x^2+425000)*log(x)^3+(47040 0*x^2-84000*x-1605000)*log(x)^2+(-627200*x^2+336000*x+2360000)*log(x)+3136 00*x^2-336000*x-1090000)/((614656*x^4-3473120*x^3+7297425*x^2-6755750*x+23 25625)*log(x)^4+(-4917248*x^4+33053440*x^3-80790600*x^2+85558000*x-3324500 0)*log(x)^3+(14751744*x^4-114965760*x^3+326539800*x^2-399414000*x+17767500 0)*log(x)^2+(-19668992*x^4+174361600*x^3-570189600*x^2+811336000*x-4207400 00)*log(x)+9834496*x^4-97717760*x^3+363786000*x^2-601388000*x+372490000),x , algorithm="maxima")
Output:
-25*(x*log(x)^2 - 4*x*log(x) + 4*x)/((784*x^2 - 2215*x + 1525)*log(x)^2 + 3136*x^2 - 4*(784*x^2 - 3055*x + 2725)*log(x) - 15580*x + 19300)
Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (29) = 58\).
Time = 0.35 (sec) , antiderivative size = 131, normalized size of antiderivative = 4.23 \[ \int \frac {-1090000-336000 x+313600 x^2+\left (2360000+336000 x-627200 x^2\right ) \log (x)+\left (-1605000-84000 x+470400 x^2\right ) \log ^2(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (-38125+19600 x^2\right ) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+\left (-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4\right ) \log (x)+\left (177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4\right ) \log ^2(x)+\left (-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4\right ) \log ^3(x)+\left (2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4\right ) \log ^4(x)} \, dx=\frac {6000 \, {\left (14 \, x^{2} \log \left (x\right ) - 28 \, x^{2} - 20 \, x \log \left (x\right ) + 55 \, x\right )}}{614656 \, x^{4} \log \left (x\right )^{2} - 2458624 \, x^{4} \log \left (x\right ) - 3473120 \, x^{3} \log \left (x\right )^{2} + 2458624 \, x^{4} + 16526720 \, x^{3} \log \left (x\right ) + 7297425 \, x^{2} \log \left (x\right )^{2} - 19160960 \, x^{3} - 40395300 \, x^{2} \log \left (x\right ) - 6755750 \, x \log \left (x\right )^{2} + 54423300 \, x^{2} + 42779000 \, x \log \left (x\right ) + 2325625 \, \log \left (x\right )^{2} - 66509000 \, x - 16622500 \, \log \left (x\right ) + 29432500} - \frac {25 \, x}{784 \, x^{2} - 2215 \, x + 1525} \] Input:
integrate(((19600*x^2-38125)*log(x)^4+(-156800*x^2+425000)*log(x)^3+(47040 0*x^2-84000*x-1605000)*log(x)^2+(-627200*x^2+336000*x+2360000)*log(x)+3136 00*x^2-336000*x-1090000)/((614656*x^4-3473120*x^3+7297425*x^2-6755750*x+23 25625)*log(x)^4+(-4917248*x^4+33053440*x^3-80790600*x^2+85558000*x-3324500 0)*log(x)^3+(14751744*x^4-114965760*x^3+326539800*x^2-399414000*x+17767500 0)*log(x)^2+(-19668992*x^4+174361600*x^3-570189600*x^2+811336000*x-4207400 00)*log(x)+9834496*x^4-97717760*x^3+363786000*x^2-601388000*x+372490000),x , algorithm="giac")
Output:
6000*(14*x^2*log(x) - 28*x^2 - 20*x*log(x) + 55*x)/(614656*x^4*log(x)^2 - 2458624*x^4*log(x) - 3473120*x^3*log(x)^2 + 2458624*x^4 + 16526720*x^3*log (x) + 7297425*x^2*log(x)^2 - 19160960*x^3 - 40395300*x^2*log(x) - 6755750* x*log(x)^2 + 54423300*x^2 + 42779000*x*log(x) + 2325625*log(x)^2 - 6650900 0*x - 16622500*log(x) + 29432500) - 25*x/(784*x^2 - 2215*x + 1525)
Timed out. \[ \int \frac {-1090000-336000 x+313600 x^2+\left (2360000+336000 x-627200 x^2\right ) \log (x)+\left (-1605000-84000 x+470400 x^2\right ) \log ^2(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (-38125+19600 x^2\right ) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+\left (-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4\right ) \log (x)+\left (177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4\right ) \log ^2(x)+\left (-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4\right ) \log ^3(x)+\left (2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4\right ) \log ^4(x)} \, dx=\int -\frac {336000\,x+{\ln \left (x\right )}^2\,\left (-470400\,x^2+84000\,x+1605000\right )-{\ln \left (x\right )}^4\,\left (19600\,x^2-38125\right )+{\ln \left (x\right )}^3\,\left (156800\,x^2-425000\right )-\ln \left (x\right )\,\left (-627200\,x^2+336000\,x+2360000\right )-313600\,x^2+1090000}{{\ln \left (x\right )}^4\,\left (614656\,x^4-3473120\,x^3+7297425\,x^2-6755750\,x+2325625\right )-601388000\,x-{\ln \left (x\right )}^3\,\left (4917248\,x^4-33053440\,x^3+80790600\,x^2-85558000\,x+33245000\right )-\ln \left (x\right )\,\left (19668992\,x^4-174361600\,x^3+570189600\,x^2-811336000\,x+420740000\right )+{\ln \left (x\right )}^2\,\left (14751744\,x^4-114965760\,x^3+326539800\,x^2-399414000\,x+177675000\right )+363786000\,x^2-97717760\,x^3+9834496\,x^4+372490000} \,d x \] Input:
int(-(336000*x + log(x)^2*(84000*x - 470400*x^2 + 1605000) - log(x)^4*(196 00*x^2 - 38125) + log(x)^3*(156800*x^2 - 425000) - log(x)*(336000*x - 6272 00*x^2 + 2360000) - 313600*x^2 + 1090000)/(log(x)^4*(7297425*x^2 - 6755750 *x - 3473120*x^3 + 614656*x^4 + 2325625) - 601388000*x - log(x)^3*(8079060 0*x^2 - 85558000*x - 33053440*x^3 + 4917248*x^4 + 33245000) - log(x)*(5701 89600*x^2 - 811336000*x - 174361600*x^3 + 19668992*x^4 + 420740000) + log( x)^2*(326539800*x^2 - 399414000*x - 114965760*x^3 + 14751744*x^4 + 1776750 00) + 363786000*x^2 - 97717760*x^3 + 9834496*x^4 + 372490000),x)
Output:
int(-(336000*x + log(x)^2*(84000*x - 470400*x^2 + 1605000) - log(x)^4*(196 00*x^2 - 38125) + log(x)^3*(156800*x^2 - 425000) - log(x)*(336000*x - 6272 00*x^2 + 2360000) - 313600*x^2 + 1090000)/(log(x)^4*(7297425*x^2 - 6755750 *x - 3473120*x^3 + 614656*x^4 + 2325625) - 601388000*x - log(x)^3*(8079060 0*x^2 - 85558000*x - 33053440*x^3 + 4917248*x^4 + 33245000) - log(x)*(5701 89600*x^2 - 811336000*x - 174361600*x^3 + 19668992*x^4 + 420740000) + log( x)^2*(326539800*x^2 - 399414000*x - 114965760*x^3 + 14751744*x^4 + 1776750 00) + 363786000*x^2 - 97717760*x^3 + 9834496*x^4 + 372490000), x)
\[ \int \frac {-1090000-336000 x+313600 x^2+\left (2360000+336000 x-627200 x^2\right ) \log (x)+\left (-1605000-84000 x+470400 x^2\right ) \log ^2(x)+\left (425000-156800 x^2\right ) \log ^3(x)+\left (-38125+19600 x^2\right ) \log ^4(x)}{372490000-601388000 x+363786000 x^2-97717760 x^3+9834496 x^4+\left (-420740000+811336000 x-570189600 x^2+174361600 x^3-19668992 x^4\right ) \log (x)+\left (177675000-399414000 x+326539800 x^2-114965760 x^3+14751744 x^4\right ) \log ^2(x)+\left (-33245000+85558000 x-80790600 x^2+33053440 x^3-4917248 x^4\right ) \log ^3(x)+\left (2325625-6755750 x+7297425 x^2-3473120 x^3+614656 x^4\right ) \log ^4(x)} \, dx=\text {too large to display} \] Input:
int(((19600*x^2-38125)*log(x)^4+(-156800*x^2+425000)*log(x)^3+(470400*x^2- 84000*x-1605000)*log(x)^2+(-627200*x^2+336000*x+2360000)*log(x)+313600*x^2 -336000*x-1090000)/((614656*x^4-3473120*x^3+7297425*x^2-6755750*x+2325625) *log(x)^4+(-4917248*x^4+33053440*x^3-80790600*x^2+85558000*x-33245000)*log (x)^3+(14751744*x^4-114965760*x^3+326539800*x^2-399414000*x+177675000)*log (x)^2+(-19668992*x^4+174361600*x^3-570189600*x^2+811336000*x-420740000)*lo g(x)+9834496*x^4-97717760*x^3+363786000*x^2-601388000*x+372490000),x)
Output:
25*( - 1525*int(log(x)**4/(614656*log(x)**4*x**4 - 3473120*log(x)**4*x**3 + 7297425*log(x)**4*x**2 - 6755750*log(x)**4*x + 2325625*log(x)**4 - 49172 48*log(x)**3*x**4 + 33053440*log(x)**3*x**3 - 80790600*log(x)**3*x**2 + 85 558000*log(x)**3*x - 33245000*log(x)**3 + 14751744*log(x)**2*x**4 - 114965 760*log(x)**2*x**3 + 326539800*log(x)**2*x**2 - 399414000*log(x)**2*x + 17 7675000*log(x)**2 - 19668992*log(x)*x**4 + 174361600*log(x)*x**3 - 5701896 00*log(x)*x**2 + 811336000*log(x)*x - 420740000*log(x) + 9834496*x**4 - 97 717760*x**3 + 363786000*x**2 - 601388000*x + 372490000),x) + 17000*int(log (x)**3/(614656*log(x)**4*x**4 - 3473120*log(x)**4*x**3 + 7297425*log(x)**4 *x**2 - 6755750*log(x)**4*x + 2325625*log(x)**4 - 4917248*log(x)**3*x**4 + 33053440*log(x)**3*x**3 - 80790600*log(x)**3*x**2 + 85558000*log(x)**3*x - 33245000*log(x)**3 + 14751744*log(x)**2*x**4 - 114965760*log(x)**2*x**3 + 326539800*log(x)**2*x**2 - 399414000*log(x)**2*x + 177675000*log(x)**2 - 19668992*log(x)*x**4 + 174361600*log(x)*x**3 - 570189600*log(x)*x**2 + 81 1336000*log(x)*x - 420740000*log(x) + 9834496*x**4 - 97717760*x**3 + 36378 6000*x**2 - 601388000*x + 372490000),x) - 64200*int(log(x)**2/(614656*log( x)**4*x**4 - 3473120*log(x)**4*x**3 + 7297425*log(x)**4*x**2 - 6755750*log (x)**4*x + 2325625*log(x)**4 - 4917248*log(x)**3*x**4 + 33053440*log(x)**3 *x**3 - 80790600*log(x)**3*x**2 + 85558000*log(x)**3*x - 33245000*log(x)** 3 + 14751744*log(x)**2*x**4 - 114965760*log(x)**2*x**3 + 326539800*log(...