Дано
$$frac{1}{2 sqrt{22}} log{left (frac{6 x – 2 sqrt{22} + 8}{6 x + 8 + 2 sqrt{22}} right )}$$
Подстановка условия
$$frac{1}{2 sqrt{22}} log{left (frac{6 x – 2 sqrt{22} + 8}{6 x + 8 + 2 sqrt{22}} right )}$$
log((6*(-3/2) – 2*sqrt(22) + 8)/(8 + 2*sqrt(22) + 6*(-3/2)))/(2*sqrt(22))
$$frac{1}{2 sqrt{22}} log{left (frac{6 (-3/2) – 2 sqrt{22} + 8}{6 (-3/2) + 8 + 2 sqrt{22}} right )}$$
log((6*(-3)/2 – 2*sqrt(22) + 8)/(8 + 2*sqrt(22) + 6*(-3)/2))/(2*sqrt(22))
$$frac{1}{2 sqrt{22}} log{left (frac{- 2 sqrt{22} + frac{-18}{2} + 8}{frac{-18}{2} + 8 + 2 sqrt{22}} right )}$$
sqrt(22)*(pi*i + log(-(-1 – 2*sqrt(22))/(-1 + 2*sqrt(22))))/44
$$frac{sqrt{22}}{44} left(log{left (- frac{- 2 sqrt{22} – 1}{-1 + 2 sqrt{22}} right )} + i piright)$$
Степени
$$frac{sqrt{22}}{44} log{left (frac{6 x – 2 sqrt{22} + 8}{6 x + 8 + 2 sqrt{22}} right )}$$
Численный ответ
0.106600358177805*log((6*x – 2*sqrt(22) + 8)/(8 + 2*sqrt(22) + 6*x))
Рациональный знаменатель
$$frac{sqrt{22}}{44} log{left (frac{6 x – 2 sqrt{22} + 8}{6 x + 8 + 2 sqrt{22}} right )}$$
Объединение рациональных выражений
$$frac{sqrt{22}}{44} log{left (frac{3 x – sqrt{22} + 4}{3 x + 4 + sqrt{22}} right )}$$
Общее упрощение
/ ____
____ |4 – / 22 + 3*x|
/ 22 *log|—————-|
| ____ |
4 + / 22 + 3*x/
—————————-
44
$$frac{sqrt{22}}{44} log{left (frac{3 x – sqrt{22} + 4}{3 x + 4 + sqrt{22}} right )}$$
Соберем выражение
$$frac{sqrt{22}}{44} log{left (frac{6 x – 2 sqrt{22} + 8}{6 x + 8 + 2 sqrt{22}} right )}$$
/ ____
____ |4 – / 22 + 3*x|
/ 22 *log|—————-|
| ____ |
4 + / 22 + 3*x/
—————————-
44
$$frac{sqrt{22}}{44} log{left (frac{3 x – sqrt{22} + 4}{3 x + 4 + sqrt{22}} right )}$$
Общий знаменатель
/ ____
____ | 4 / 22 3*x |
/ 22 *log|—————- – —————- + —————-|
| ____ ____ ____ |
4 + / 22 + 3*x 4 + / 22 + 3*x 4 + / 22 + 3*x/
——————————————————————
44
$$frac{sqrt{22}}{44} log{left (frac{3 x}{3 x + 4 + sqrt{22}} – frac{sqrt{22}}{3 x + 4 + sqrt{22}} + frac{4}{3 x + 4 + sqrt{22}} right )}$$
Комбинаторика
/ ____
____ | 8 2*/ 22 6*x |
/ 22 *log|—————— – —————— + ——————|
| ____ ____ ____ |
8 + 2*/ 22 + 6*x 8 + 2*/ 22 + 6*x 8 + 2*/ 22 + 6*x/
————————————————————————
44
$$frac{sqrt{22}}{44} log{left (frac{6 x}{6 x + 8 + 2 sqrt{22}} – frac{2 sqrt{22}}{6 x + 8 + 2 sqrt{22}} + frac{8}{6 x + 8 + 2 sqrt{22}} right )}$$
Раскрыть выражение
/ ____
____ |6*x – 2*/ 22 + 8|
/ 22 *log|——————|
| ____ |
8 + 2*/ 22 + 6*x/
——————————
44
$$frac{sqrt{22}}{44} log{left (frac{6 x – 2 sqrt{22} + 8}{6 x + 8 + 2 sqrt{22}} right )}$$
____ / / ____ / ____
/ 22 * – log8 + 2*/ 22 + 6*x/ + log8 – 2*/ 22 + 6*x//
————————————————————
44
$$frac{sqrt{22}}{44} left(- log{left (6 x + 8 + 2 sqrt{22} right )} + log{left (6 x – 2 sqrt{22} + 8 right )}right)$$
