|-2x^(2)+1+e^(x)+sin x|=|2x^(2)-1|+e^(x)+|sin x|

Number of solutions to the equation |2e^(sin x) - 3 - e^(2 sin x)|= | e^(sin x) - e^(2 sinx) - 1| i n [0, 2 pi] is

(2+sin 2x)/(1+cos 2x) e^(x)

(2+sin 2x)/(1+cos 2x) e^(x)

e ^ (x) sin x tan x + e ^ (x) sin x + e ^ (x) sin x sec ^ (2) x

If y=sin x+e^(x), then (d^(2)x)/(dy^(2))= (a) (-sin x+e^(x))^(-1)(b)(sin x-e^(x))/((cos x+e^(x))^(2))(c)(sin x-e^(x))/((cos x+e^(x))^(3))(d)(sin x+e^(x))/((cos x+e^(x))^(3))

int((2x+1)e^(2x))/(sin^(2)(xe^(2x)))dx

int (sin x * e ^ (cos x) - (sin x + cos x) e ^ (sin x + cos x)) / (e ^ (2sin x) -2e ^ (sin x) +1) dx

Delta (x) = det [[sin2x, e ^ (x) sin x + x cos x, sin x + x ^ (2) cos xcos x + sin x, e ^ (x) + x, 1 + x ^ ( 2) e ^ (x) cos x, e ^ (2) x, e ^ (x)]]

Delta (x) = det [[sin2x, e ^ (x) sin x + x cos x, sin x + x ^ (2) cos xcos x + sin x, e ^ (x) + x, 1 + x ^ ( 2) e ^ (x) cos x, e ^ (2) x, e ^ (x)]]

e^(x)((2+ sin 2x)/(1 + cos 2 x ))