2*(9*log(sqrt(x+6)+3)*1/5-4*log(sqrt(x+6)-2)*1/5+(-2*sqrt(x+6)+x+6)*1/2) если x=-3/2 (упростите выражение)

$$2 left(- frac{4}{5} log{left (sqrt{x + 6} – 2 right )} + frac{9}{5} log{left (sqrt{x + 6} + 3 right )} + frac{1}{2} left(x – 2 sqrt{x + 6} + 6right)right)$$

$$2 left(- frac{4}{5} log{left (sqrt{x + 6} – 2 right )} + frac{9}{5} log{left (sqrt{x + 6} + 3 right )} + frac{1}{2} left(x – 2 sqrt{x + 6} + 6right)right)$$

2*((9*log(sqrt((-3/2) + 6) + 3))/5 – 4*log(sqrt((-3/2) + 6) – 2)/5 + (-2*sqrt((-3/2) + 6) + (-3/2) + 6)/2)

$$2 left(- frac{4}{5} log{left (sqrt{(-3/2) + 6} – 2 right )} + frac{9}{5} log{left (sqrt{(-3/2) + 6} + 3 right )} + frac{1}{2} left((-3/2) – 2 sqrt{(-3/2) + 6} + 6right)right)$$

2*((9*log(sqrt(-3/2 + 6) + 3))/5 – 4*log(sqrt(-3/2 + 6) – 2)/5 + (-2*sqrt(-3/2 + 6) – 3/2 + 6)/2)

$$2 left(frac{1}{2} left(- 2 sqrt{- frac{3}{2} + 6} – frac{3}{2} + 6right) + – frac{4}{5} log{left (-2 + sqrt{- frac{3}{2} + 6} right )} + frac{9}{5} log{left (sqrt{- frac{3}{2} + 6} + 3 right )}right)$$

9/2 – 3*sqrt(2) – 8*log(-2 + 3*sqrt(2)/2)/5 + 18*log(3 + 3*sqrt(2)/2)/5

$$- 3 sqrt{2} – frac{8}{5} log{left (-2 + frac{3 sqrt{2}}{2} right )} + frac{9}{2} + frac{18}{5} log{left (frac{3 sqrt{2}}{2} + 3 right )}$$

$$x – 2 sqrt{x + 6} – frac{8}{5} log{left (sqrt{x + 6} – 2 right )} + frac{18}{5} log{left (sqrt{x + 6} + 3 right )} + 6$$

6.0 + 1.0*x + 3.6*log(sqrt(x + 6) + 3) – 2.0*(6.0 + x)^0.5 – 1.6*log(sqrt(x + 6) – 2)

$$frac{1}{5} left(5 x – 10 sqrt{x + 6} – 8 log{left (sqrt{x + 6} – 2 right )} + 18 log{left (sqrt{x + 6} + 3 right )} + 30right)$$

$$frac{1}{5} left(5 x – 10 sqrt{x + 6} – 8 log{left (sqrt{x + 6} – 2 right )} + 18 log{left (sqrt{x + 6} + 3 right )} + 30right)$$

/ _______ / _______
_______ 8*log -2 + / 6 + x / 18*log3 + / 6 + x /
6 + x – 2*/ 6 + x – ——————— + ———————
5 5

$$x – 2 sqrt{x + 6} – frac{8}{5} log{left (sqrt{x + 6} – 2 right )} + frac{18}{5} log{left (sqrt{x + 6} + 3 right )} + 6$$

$$frac{1}{2} left(2 left(x – 2 sqrt{x + 6}right) + 12right) – frac{8}{5} log{left (sqrt{x + 6} – 2 right )} + frac{18}{5} log{left (sqrt{x + 6} + 3 right )}$$

/ 8
|/ _______ |
| -2 + / 6 + x / |
log|—————–|
| 18|
|/ _______ |
_______ 3 + / 6 + x / /
6 + x – 2*/ 6 + x – ———————-
5

$$x – 2 sqrt{x + 6} – frac{1}{5} log{left (frac{left(sqrt{x + 6} – 2right)^{8}}{left(sqrt{x + 6} + 3right)^{18}} right )} + 6$$

/ _______ / _______
_______ 8*log -2 + / 6 + x / 18*log3 + / 6 + x /
6 + x – 2*/ 6 + x – ——————— + ———————
5 5

$$x – 2 sqrt{x + 6} – frac{8}{5} log{left (sqrt{x + 6} – 2 right )} + frac{18}{5} log{left (sqrt{x + 6} + 3 right )} + 6$$

_______ / _______ / _______
30 – 10*/ 6 + x – 8*log -2 + / 6 + x / + 5*x + 18*log3 + / 6 + x /
———————————————————————–
5

$$frac{1}{5} left(5 x – 10 sqrt{x + 6} – 8 log{left (sqrt{x + 6} – 2 right )} + 18 log{left (sqrt{x + 6} + 3 right )} + 30right)$$

/ _______ / _______
_______ 8*log -2 + / 6 + x / 18*log3 + / 6 + x /
6 + x – 2*/ 6 + x – ——————— + ———————
5 5

$$x – 2 sqrt{x + 6} – frac{8}{5} log{left (sqrt{x + 6} – 2 right )} + frac{18}{5} log{left (sqrt{x + 6} + 3 right )} + 6$$