Дано
$$frac{1}{2^{frac{3}{2}}} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2^{frac{3}{2}}} right )}$$
Подстановка условия
$$frac{1}{2^{frac{3}{2}}} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2^{frac{3}{2}}} right )}$$
log((2*cos((4)) – 2^(3/2))/(2^(3/2) + 2*cos((4))))/2^(3/2)
$$frac{1}{2^{frac{3}{2}}} log{left (frac{2 cos{left ((4) right )} – 2 sqrt{2}}{2 cos{left ((4) right )} + 2^{frac{3}{2}}} right )}$$
log((2*cos(4) – 2^(3/2))/(2^(3/2) + 2*cos(4)))/2^(3/2)
$$frac{1}{2^{frac{3}{2}}} log{left (frac{- 2 sqrt{2} + 2 cos{left (4 right )}}{2 cos{left (4 right )} + 2^{frac{3}{2}}} right )}$$
sqrt(2)*(pi*i + log(-(-2*sqrt(2) + 2*cos(4))/(2*sqrt(2) + 2*cos(4))))/4
$$frac{sqrt{2}}{4} left(log{left (- frac{- 2 sqrt{2} + 2 cos{left (4 right )}}{2 cos{left (4 right )} + 2 sqrt{2}} right )} + i piright)$$
Степени
$$frac{sqrt{2}}{4} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2 sqrt{2}} right )}$$
Численный ответ
0.353553390593274*log((2*cos(x) – 2^(3/2))/(2^(3/2) + 2*cos(x)))
Рациональный знаменатель
$$frac{sqrt{2}}{4} log{left (frac{1}{cos^{2}{left (x right )} – 2} left(cos^{2}{left (x right )} – 2 sqrt{2} cos{left (x right )} + 2right) right )}$$
Объединение рациональных выражений
$$frac{sqrt{2}}{4} log{left (frac{cos{left (x right )} – sqrt{2}}{cos{left (x right )} + sqrt{2}} right )}$$
Общее упрощение
/ ___
___ |- / 2 + cos(x)|
/ 2 *log|—————-|
| ___ |
/ 2 + cos(x) /
—————————
4
$$frac{sqrt{2}}{4} log{left (frac{cos{left (x right )} – sqrt{2}}{cos{left (x right )} + sqrt{2}} right )}$$
Соберем выражение
$$frac{sqrt{2}}{4} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2^{frac{3}{2}}} right )}$$
/ ___
___ |- 2*/ 2 + 2*cos(x)|
/ 2 *log|——————–|
| ___ |
2*/ 2 + 2*cos(x) /
——————————-
4
$$frac{sqrt{2}}{4} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2 sqrt{2}} right )}$$
___ / 3 cos(2*x)
/ 2 *log|- —————————– + —————————–|
| ___ ___ |
5 + 4*/ 2 *cos(x) + cos(2*x) 5 + 4*/ 2 *cos(x) + cos(2*x)/
————————————————————————–
4
$$frac{sqrt{2}}{4} log{left (frac{cos{left (2 x right )}}{4 sqrt{2} cos{left (x right )} + cos{left (2 x right )} + 5} – frac{3}{4 sqrt{2} cos{left (x right )} + cos{left (2 x right )} + 5} right )}$$
Общий знаменатель
/ ___
___ | cos(x) / 2 |
/ 2 *log|————– – ————–|
| ___ ___ |
/ 2 + cos(x) / 2 + cos(x)/
——————————————
4
$$frac{sqrt{2}}{4} log{left (frac{cos{left (x right )}}{cos{left (x right )} + sqrt{2}} – frac{sqrt{2}}{cos{left (x right )} + sqrt{2}} right )}$$
Тригонометрическая часть
/ ___
___ |- / 2 + cos(x)|
/ 2 *log|—————-|
| ___ |
/ 2 + cos(x) /
—————————
4
$$frac{sqrt{2}}{4} log{left (frac{cos{left (x right )} – sqrt{2}}{cos{left (x right )} + sqrt{2}} right )}$$
Комбинаторика
/ ___
___ | 2*/ 2 2*cos(x) |
/ 2 *log|- —————— + ——————|
| ___ ___ |
2*/ 2 + 2*cos(x) 2*/ 2 + 2*cos(x)/
—————————————————-
4
$$frac{sqrt{2}}{4} log{left (frac{2 cos{left (x right )}}{2 cos{left (x right )} + 2 sqrt{2}} – frac{2 sqrt{2}}{2 cos{left (x right )} + 2 sqrt{2}} right )}$$
Раскрыть выражение
/ ___
___ |- 2*/ 2 + 2*cos(x)|
/ 2 *log|——————–|
| ___ |
2*/ 2 + 2*cos(x) /
——————————-
4
$$frac{sqrt{2}}{4} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2 sqrt{2}} right )}$$
___ / / ___ / ___
/ 2 * – log2*/ 2 + 2*cos(x)/ + log – 2*/ 2 + 2*cos(x)//
————————————————————-
4
$$frac{sqrt{2}}{4} left(log{left (2 cos{left (x right )} – 2 sqrt{2} right )} – log{left (2 cos{left (x right )} + 2 sqrt{2} right )}right)$$
