Separate the intervals of monotonicity for the following functions.
`f(x) = sin x + cos x, x in (0, 2pi)`

Separate the intervals of monotonicity for the following functions. f(x) = x^(2) e^(-x)

Separate the intervals of monotonicity for the following functions. f(x) = 3 cos^(4) x + 10 cos^(3) x + 6 cos^(2) x - 3, x in [0, pi]

Separate the intervals of monotonicity for the following functions. f(x) = -2x^(3) - 9x^(2) - 12x + 1

Separate the intervals of monotonicity for the following functions. f(x) = (log_(e)x)^(2) + (log_(e)x)

Integrate the following functions sqrt(sin2x) cos2x

Find the interval of monotonicity of the function f(x) = |x - 1| //x^(2) .

Integrate the following functions: (cos2x+2 sin^2 x)/cos^2x

Discuss the extremum of f(x) = sin x (1 + cos x), x in (0, pi//2) .

Integrate the following functions: (sin^3x + cos^3x)/(sin^2x cos^2x)