1. int (-1 1) dx/(x + 2) = int (-1 1) 1/(x + 2) d(x + 2) = | t = x + 2 | = int (1 3) dt/t =
= (ln |t|)_{1}^{3} = ln 3 - ln 1 = ln 3
2. int e^(-x^3) * x^2 dx = int e^(-x^3) d(1/3 * x^3) = 1/3 * int e^(-x^3) d(x^3) =
= | t = x^3 | = 1/3 * int e^(-t) dt = -1/3 * e^(-t) + C = | t = x^3 | =
= -1/3 * e^(-x^3) + C
3. int sin^3 x * cos^2 x dx - подскажите, с чего начать решать этот пример, пожалуйста.

3. int sin^3 х * cos^2 x dx = int sin^2 x * cos^2 x * sin x dx =
= int sin^2 x * cos^2 x d(-cos x) = -int sin^2 x * cos^2 x d(cos x) =
= -int (1 - cos^2 x) * cos^2 x d(cos x) = | t = cos x | =
= -int (1 - t^2) * t^2 dt = -int (t^2 - t^4) dt = -(1/3 * t^3 - 1/5 * t^5) + C =
= 1/5 * t^5 - 1/3 * t^3 + C = | t = cos x | = 1/5 * cos^5 x - 1/3 * cos^3 x + C