Помогите, пожалуйста, вычислить два интеграла:
1) int (0 pi/2) sin x * cos^2 x dx
2) int (e e^2) dx/(x * ln x)

1) int (0 pi/2) sin x * cos^2 x dx = int (0 pi/2) cos^2 x d(-cos x) =
= -int (0 pi/2) cos^2 x d(cos x) = | cos x = t | = -int (1 0) t^2 dt =
= int (0 1) t^2 dt = (1/3 * t^3)_{0}^{1} = 1/3 * 1^3 - 1/3 * 0^3 = 1/3.
2) int (e e^2) dx/(x * ln x) = int (e e^2) 1/ln x d(ln x) = | t = ln x | =
= int (1 2) 1/t dt = (ln |t|)_{1}^{2} = ln 2 - ln 1 = ln 2.

Спасибо.