Дано
$$frac{296740963 x}{1000000000} + – frac{443777778 x – 480703815}{2000000000 x^{2} + – 4000000000 x + 2000000000} + frac{1}{1000000000} left(-1 cdot 444444111 log{left (x – 1 right )}right)$$
Подстановка условия
$$frac{296740963 x}{1000000000} + – frac{443777778 x – 480703815}{2000000000 x^{2} + – 4000000000 x + 2000000000} + frac{1}{1000000000} left(-1 cdot 444444111 log{left (x – 1 right )}right)$$
(-444444111*log((-1/3) – 1))/1000000000 – (443777778*(-1/3) – 480703815)/(2000000000 – 4000000000*(-1/3) + 2000000000*(-1/3)^2) + (296740963*(-1/3))/1000000000
$$frac{296740963 (-1/3)}{1000000000} + – frac{443777778 (-1/3) – 480703815}{2000000000 (-1/3)^{2} + – 4000000000 (-1/3) + 2000000000} + frac{1}{1000000000} left(-1 cdot 444444111 log{left ((-1/3) – 1 right )}right)$$
(-444444111*log(-1/3 – 1))/1000000000 – (443777778*(-1)/3 – 480703815)/(2000000000 – 4000000000*(-1)/3 + 2000000000*(-1/3)^2) + (296740963*(-1)/3)/1000000000
$$frac{- frac{296740963}{3}}{1000000000} 1 + – frac{-480703815 + frac{-443777778}{3}}{2000000000 left(- frac{1}{3}right)^{2} + – frac{-4000000000}{3} + 2000000000} + frac{1}{1000000000} left(-1 cdot 444444111 log{left (-1 – frac{1}{3} right )}right)$$
7477292191/96000000000 – 444444111*log(4)/1000000000 + 444444111*log(3)/1000000000 – 444444111*pi*i/1000000000
$$- frac{444444111}{1000000000} log{left (4 right )} + frac{7477292191}{96000000000} + frac{444444111}{1000000000} log{left (3 right )} – frac{444444111 pi}{1000000000} i$$
Степени
$$frac{296740963 x}{1000000000} – frac{443777778 x – 480703815}{2000000000 x^{2} – 4000000000 x + 2000000000} – frac{444444111}{1000000000} log{left (x – 1 right )}$$
444444111*log(-1 + x) 296740963*x 480703815 – 443777778*x
– ——————— + ———– + —————————————–
1000000000 1000000000 2
2000000000 – 4000000000*x + 2000000000*x
$$frac{296740963 x}{1000000000} + frac{- 443777778 x + 480703815}{2000000000 x^{2} – 4000000000 x + 2000000000} – frac{444444111}{1000000000} log{left (x – 1 right )}$$
Численный ответ
0.296740963*x – 0.444444111*log(x – 1) – (-480703815.0 + 443777778.0*x)/(2000000000.0 + 2000000000.0*x^2 – 4000000000.0*x)
Рациональный знаменатель
$$frac{1}{2000000000 x^{2} – 4000000000 x + 2000000000} left(593481926 x^{3} – 888888222 x^{2} log{left (x – 1 right )} – 1186963852 x^{2} + 1777776444 x log{left (x – 1 right )} + 149704148 x – 888888222 log{left (x – 1 right )} + 480703815right)$$
Объединение рациональных выражений
$$frac{1}{2000000000 x^{2} – 4000000000 x + 2000000000} left(593481926 x left(x^{2} – 2 x + 1right) – 443777778 x – 888888222 left(x^{2} – 2 x + 1right) log{left (x – 1 right )} + 480703815right)$$
Общее упрощение
/ 2
480703815 – 443777778*x + 889778*(-999*log(-1 + x) + 667*x)*1 + x – 2*x/
————————————————————————–
/ 2
2000000000*1 + x – 2*x/
$$frac{1}{2000000000 x^{2} – 4000000000 x + 2000000000} left(- 443777778 x + 889778 left(667 x – 999 log{left (x – 1 right )}right) left(x^{2} – 2 x + 1right) + 480703815right)$$
Соберем выражение
$$frac{296740963 x}{1000000000} – frac{443777778 x – 480703815}{2000000000 x^{2} + – 4000000000 x + 2000000000} + frac{1}{1000000000} left(-1 cdot 444444111 log{left (x – 1 right )}right)$$
444444111*log(-1 + x) 296740963*x 480703815 – 443777778*x
– ——————— + ———– + —————————————–
1000000000 1000000000 2
2000000000 – 4000000000*x + 2000000000*x
$$frac{296740963 x}{1000000000} + frac{- 443777778 x + 480703815}{2000000000 x^{2} – 4000000000 x + 2000000000} – frac{444444111}{1000000000} log{left (x – 1 right )}$$
Общий знаменатель
444444111*log(-1 + x) 296740963*x -480703815 + 443777778*x
– ——————— + ———– – —————————————–
1000000000 1000000000 2
2000000000 – 4000000000*x + 2000000000*x
$$frac{296740963 x}{1000000000} – frac{443777778 x – 480703815}{2000000000 x^{2} – 4000000000 x + 2000000000} – frac{444444111}{1000000000} log{left (x – 1 right )}$$
Комбинаторика
2 3 2
480703815 – 1186963852*x – 888888222*log(-1 + x) + 149704148*x + 593481926*x – 888888222*x *log(-1 + x) + 1777776444*x*log(-1 + x)
————————————————————————————————————————————
2
2000000000*(-1 + x)
$$frac{1}{2000000000 left(x – 1right)^{2}} left(593481926 x^{3} – 888888222 x^{2} log{left (x – 1 right )} – 1186963852 x^{2} + 1777776444 x log{left (x – 1 right )} + 149704148 x – 888888222 log{left (x – 1 right )} + 480703815right)$$
Раскрыть выражение
444444111*log(-1 + x) 296740963*x 480703815 – 443777778*x
– ——————— + ———– + —————————————–
1000000000 1000000000 2
2000000000 – 4000000000*x + 2000000000*x
$$frac{296740963 x}{1000000000} + frac{- 443777778 x + 480703815}{2000000000 x^{2} – 4000000000 x + 2000000000} – frac{444444111}{1000000000} log{left (x – 1 right )}$$
