Дано
$$frac{1}{4 sqrt{23}} log{left (frac{2 x – 4 sqrt{23} + 20}{2 x + 4 sqrt{23} + 20} right )}$$
Подстановка условия
$$frac{1}{4 sqrt{23}} log{left (frac{2 x – 4 sqrt{23} + 20}{2 x + 4 sqrt{23} + 20} right )}$$
log((2*(1) – 4*sqrt(23) + 20)/(20 + 4*sqrt(23) + 2*(1)))/(4*sqrt(23))
$$frac{1}{4 sqrt{23}} log{left (frac{2 (1) – 4 sqrt{23} + 20}{2 (1) + 4 sqrt{23} + 20} right )}$$
log((2 – 4*sqrt(23) + 20)/(20 + 4*sqrt(23) + 2))/(4*sqrt(23))
$$frac{1}{4 sqrt{23}} log{left (frac{- 4 sqrt{23} + 2 + 20}{2 + 4 sqrt{23} + 20} right )}$$
sqrt(23)*log((22 – 4*sqrt(23))/(22 + 4*sqrt(23)))/92
$$frac{sqrt{23}}{92} log{left (frac{- 4 sqrt{23} + 22}{4 sqrt{23} + 22} right )}$$
Степени
$$frac{sqrt{23}}{92} log{left (frac{2 x – 4 sqrt{23} + 20}{2 x + 4 sqrt{23} + 20} right )}$$
Численный ответ
0.0521286035142687*log((2*x – 4*sqrt(23) + 20)/(20 + 4*sqrt(23) + 2*x))
Рациональный знаменатель
$$frac{sqrt{23}}{92} log{left (frac{2 x – 4 sqrt{23} + 20}{2 x + 4 sqrt{23} + 20} right )}$$
Объединение рациональных выражений
$$frac{sqrt{23}}{92} log{left (frac{x – 2 sqrt{23} + 10}{x + 2 sqrt{23} + 10} right )}$$
Общее упрощение
/ ____
____ |10 + x – 2*/ 23 |
/ 23 *log|—————–|
| ____|
10 + x + 2*/ 23 /
—————————–
92
$$frac{sqrt{23}}{92} log{left (frac{x – 2 sqrt{23} + 10}{x + 2 sqrt{23} + 10} right )}$$
Соберем выражение
$$frac{sqrt{23}}{92} log{left (frac{x – 2 sqrt{23} + 10}{x + 2 sqrt{23} + 10} right )}$$
/ ____
____ |2*x – 4*/ 23 + 20|
/ 23 *log|——————-|
| ____ |
20 + 4*/ 23 + 2*x/
——————————-
92
$$frac{sqrt{23}}{92} log{left (frac{2 x – 4 sqrt{23} + 20}{2 x + 4 sqrt{23} + 20} right )}$$
Общий знаменатель
/ ____
____ | 10 x 2*/ 23 |
/ 23 *log|—————– + —————– – —————–|
| ____ ____ ____|
10 + x + 2*/ 23 10 + x + 2*/ 23 10 + x + 2*/ 23 /
———————————————————————
92
$$frac{sqrt{23}}{92} log{left (frac{x}{x + 2 sqrt{23} + 10} – frac{2 sqrt{23}}{x + 2 sqrt{23} + 10} + frac{10}{x + 2 sqrt{23} + 10} right )}$$
Комбинаторика
/ ____
____ | 20 4*/ 23 2*x |
/ 23 *log|——————- – ——————- + ——————-|
| ____ ____ ____|
20 + 2*x + 4*/ 23 20 + 2*x + 4*/ 23 20 + 2*x + 4*/ 23 /
—————————————————————————
92
$$frac{sqrt{23}}{92} log{left (frac{2 x}{2 x + 4 sqrt{23} + 20} – frac{4 sqrt{23}}{2 x + 4 sqrt{23} + 20} + frac{20}{2 x + 4 sqrt{23} + 20} right )}$$
Раскрыть выражение
/ ____
____ |2*x – 4*/ 23 + 20|
/ 23 *log|——————-|
| ____ |
20 + 4*/ 23 + 2*x/
——————————-
92
$$frac{sqrt{23}}{92} log{left (frac{2 x – 4 sqrt{23} + 20}{2 x + 4 sqrt{23} + 20} right )}$$
____ / / ____ / ____
/ 23 * – log20 + 2*x + 4*/ 23 / + log20 – 4*/ 23 + 2*x//
————————————————————–
92
$$frac{sqrt{23}}{92} left(log{left (2 x – 4 sqrt{23} + 20 right )} – log{left (2 x + 4 sqrt{23} + 20 right )}right)$$
