Помогите, пожалуйста, найти интеграл
int (sin x - cos x) dx/(cos x + sin x)^3
int (sin x - cos x) dx/(cos x + sin x)^3 =
= | t = cos x + sin x; dt = (-sin x + cos x) dx => (sin x - cos x) dx = -dt | =
= -int dt/t^3 = -int t^(-3) dt = -1/(-3 + 1) * t^(-3 + 1) + C =
= 1/2 * t^(-2) + C = 1/2 * 1/t^2 + C = | t = sin x + cos x | =
= 1/2 * 1/(sin x + cos x)^2 + C =
= 1/2 * 1/(sin^2 x + 2 * sin x * cos x + cos^2 x) + C = 1/2 * 1/(1 + sin (2 * x)) + C
Спасибо!
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