Помогите, пожалуйста, найти два интеграла:
1) int cos 2x * cos x dx
2) int ln x^(1/2)/x^(1/2) dx
1) int cos 2x * cos x dx = int (1/2 * (cos (2x + x) + cos (2x - x))) dx =
= 1/2 * int (cos 3x + cos x) dx = 1/2 * (1/3 * sin 3x + sin x) + C =
= 1/6 * sin 3x + 1/2 * sin x + C
2) int ln x^(1/2)/x^(1/2) dx = | x^(1/2) = t, x = t^2, dx = 2 * t dt | =
= int ln t/t * 2 * t dt = 2 * int ln t dt = 2 * t * ln t - 2 * int t d(ln t) =
= 2 * t * ln t - 2 * int t * 1/t dt = 2 * t * ln t - 2 * int dt = 2 * t * ln t - 2 * t + C =
= | t = x^(1/2) | = 2 * x^(1/2) * ln x^(1/2) - 2 * x^(1/2) + C =
= 2 * x^(1/2) * (ln x^(1/2) - 1) + C
Спасибо большое!!
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