log((2*cos(x)-2^(3/2))*1/(2^(3/2)+2*cos(x)))*1/(2^(3/2)) если x=4 (упростите выражение)

$$frac{1}{2^{frac{3}{2}}} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2^{frac{3}{2}}} right )}$$

$$frac{1}{2^{frac{3}{2}}} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2^{frac{3}{2}}} right )}$$

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

$$frac{sqrt{2}}{4} left(log{left (- frac{- 2 sqrt{2} + 2 cos{left (4 right )}}{2 cos{left (4 right )} + 2 sqrt{2}} right )} + i piright)$$

$$frac{sqrt{2}}{4} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2 sqrt{2}} right )}$$

0.353553390593274*log((2*cos(x) – 2^(3/2))/(2^(3/2) + 2*cos(x)))

$$frac{sqrt{2}}{4} log{left (frac{1}{cos^{2}{left (x right )} – 2} left(cos^{2}{left (x right )} – 2 sqrt{2} cos{left (x right )} + 2right) right )}$$

$$frac{sqrt{2}}{4} log{left (frac{cos{left (x right )} – sqrt{2}}{cos{left (x right )} + sqrt{2}} right )}$$

/ ___
___ |- / 2 + cos(x)|
/ 2 *log|—————-|
| ___ |
/ 2 + cos(x) /
—————————
4

$$frac{sqrt{2}}{4} log{left (frac{cos{left (x right )} – sqrt{2}}{cos{left (x right )} + sqrt{2}} right )}$$

$$frac{sqrt{2}}{4} log{left (frac{2 cos{left (x right )} – 2 sqrt{2}}{2 cos{left (x right )} + 2^{frac{3}{2}}} right )}$$

/ ___
___ |- 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

$$frac{sqrt{2}}{4} log{left (frac{cos{left (2 x right )}}{4 sqrt{2} cos{left (x right )} + cos{left (2 x right )} + 5} – frac{3}{4 sqrt{2} cos{left (x right )} + cos{left (2 x right )} + 5} right )}$$

/ ___
___ | cos(x) / 2 |
/ 2 *log|————– – ————–|
| ___ ___ |
/ 2 + cos(x) / 2 + cos(x)/
——————————————
4

$$frac{sqrt{2}}{4} log{left (frac{cos{left (x right )}}{cos{left (x right )} + sqrt{2}} – frac{sqrt{2}}{cos{left (x right )} + sqrt{2}} right )}$$

/ ___
___ |- / 2 + cos(x)|
/ 2 *log|—————-|
| ___ |
/ 2 + cos(x) /
—————————
4

$$frac{sqrt{2}}{4} log{left (frac{cos{left (x right )} – sqrt{2}}{cos{left (x right )} + sqrt{2}} right )}$$

/ ___
___ | 2*/ 2 2*cos(x) |
/ 2 *log|- —————— + ——————|
| ___ ___ |
2*/ 2 + 2*cos(x) 2*/ 2 + 2*cos(x)/
—————————————————-
4

$$frac{sqrt{2}}{4} log{left (frac{2 cos{left (x right )}}{2 cos{left (x right )} + 2 sqrt{2}} – frac{2 sqrt{2}}{2 cos{left (x right )} + 2 sqrt{2}} right )}$$

/ ___
___ |- 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

$$frac{sqrt{2}}{4} left(log{left (2 cos{left (x right )} – 2 sqrt{2} right )} – log{left (2 cos{left (x right )} + 2 sqrt{2} right )}right)$$