Дано
$$frac{11}{sqrt{6}} log{left (frac{2 x – 2 sqrt{6} – 8}{2 x + -8 + 2 sqrt{6}} right )} + frac{3}{2} log{left (x^{2} – 8 x + 10 right )}$$
Подстановка условия
$$frac{11}{sqrt{6}} log{left (frac{2 x – 2 sqrt{6} – 8}{2 x + -8 + 2 sqrt{6}} right )} + frac{3}{2} log{left (x^{2} – 8 x + 10 right )}$$
(11*log((2*(3) – 2*sqrt(6) – 8)/(-8 + 2*sqrt(6) + 2*(3))))/sqrt(6) + (3*log((3)^2 – 8*(3) + 10))/2
$$frac{11}{sqrt{6}} log{left (frac{2 (3) – 2 sqrt{6} – 8}{2 (3) + -8 + 2 sqrt{6}} right )} + frac{3}{2} log{left ((3)^{2} – 8 (3) + 10 right )}$$
(11*log((2*3 – 2*sqrt(6) – 8)/(-8 + 2*sqrt(6) + 2*3)))/sqrt(6) + (3*log(3^2 – 8*3 + 10))/2
$$frac{3}{2} log{left (- 24 + 3^{2} + 10 right )} + frac{11}{sqrt{6}} log{left (frac{-8 + – 2 sqrt{6} + 2 cdot 3}{-8 + 2 sqrt{6} + 2 cdot 3} right )}$$
3*log(5)/2 + sqrt(6)*(11*log(-(-2 – 2*sqrt(6))/(-2 + 2*sqrt(6))) + 11*pi*i)/6 + 3*pi*i/2
$$frac{3}{2} log{left (5 right )} + frac{3 pi}{2} i + frac{sqrt{6}}{6} left(11 log{left (- frac{- 2 sqrt{6} – 2}{-2 + 2 sqrt{6}} right )} + 11 i piright)$$
Степени
$$frac{11 sqrt{6}}{6} log{left (frac{2 x – 8 – 2 sqrt{6}}{2 x – 8 + 2 sqrt{6}} right )} + frac{3}{2} log{left (x^{2} – 8 x + 10 right )}$$
Численный ответ
1.5*log(x^2 – 8*x + 10) + 4.49073119510249*log((2*x – 2*sqrt(6) – 8)/(-8 + 2*sqrt(6) + 2*x))
Рациональный знаменатель
$$frac{1}{6} left(9 log{left (x^{2} – 8 x + 10 right )} + 11 sqrt{6} log{left (frac{2 x}{2 x – 8 + 2 sqrt{6}} – frac{8}{2 x – 8 + 2 sqrt{6}} – frac{2 sqrt{6}}{2 x – 8 + 2 sqrt{6}} right )}right)$$
Объединение рациональных выражений
$$frac{1}{6} left(11 sqrt{6} log{left (frac{x – 4 – sqrt{6}}{x – 4 + sqrt{6}} right )} + 9 log{left (x left(x – 8right) + 10 right )}right)$$
Общее упрощение
/ ___
___ |-4 + x – / 6 |
11*/ 6 *log|————–|
/ 2 | ___|
3*log10 + x – 8*x/ -4 + x + / 6 /
——————– + —————————-
2 6
$$frac{11 sqrt{6}}{6} log{left (frac{x – 4 – sqrt{6}}{x – 4 + sqrt{6}} right )} + frac{3}{2} log{left (x^{2} – 8 x + 10 right )}$$
Соберем выражение
$$frac{sqrt{6}}{12} left(log{left (frac{left(x – 4 – sqrt{6}right)^{22}}{left(x – 4 + sqrt{6}right)^{22}} right )} + sqrt{6} log{left (left(x^{2} – 8 x + 10right)^{3} right )}right)$$
Общий знаменатель
/ ___
___ | 4 x / 6 |
11*/ 6 *log|- ————– + ————– – ————–|
/ 2 | ___ ___ ___|
3*log10 + x – 8*x/ -4 + x + / 6 -4 + x + / 6 -4 + x + / 6 /
——————– + —————————————————————-
2 6
$$frac{3}{2} log{left (x^{2} – 8 x + 10 right )} + frac{11 sqrt{6}}{6} log{left (frac{x}{x – 4 + sqrt{6}} – frac{4}{x – 4 + sqrt{6}} – frac{sqrt{6}}{x – 4 + sqrt{6}} right )}$$
Комбинаторика
/ ___
/ 2 ___ | 8 2*/ 6 2*x |
9*log10 + x – 8*x/ + 11*/ 6 *log|- —————— – —————— + ——————|
| ___ ___ ___|
-8 + 2*x + 2*/ 6 -8 + 2*x + 2*/ 6 -8 + 2*x + 2*/ 6 /
—————————————————————————————————
6
$$frac{1}{6} left(9 log{left (x^{2} – 8 x + 10 right )} + 11 sqrt{6} log{left (frac{2 x}{2 x – 8 + 2 sqrt{6}} – frac{8}{2 x – 8 + 2 sqrt{6}} – frac{2 sqrt{6}}{2 x – 8 + 2 sqrt{6}} right )}right)$$
Раскрыть выражение
/ 2 ___ / / ___ / ___
3*log10 + x – 8*x/ / 6 * – 11*log -8 + 2*x + 2*/ 6 / + 11*log -8 – 2*/ 6 + 2*x//
——————– + —————————————————————–
2 6
$$frac{sqrt{6}}{6} left(11 log{left (2 x – 8 – 2 sqrt{6} right )} – 11 log{left (2 x – 8 + 2 sqrt{6} right )}right) + frac{3}{2} log{left (x^{2} – 8 x + 10 right )}$$
