4. Найдите: a) ∫√2x-3 dx;

a) ∫√(2x-3) dx

Пусть u = 2x - 3, тогда du = 2 dx, и dx = (1/2) du

Интеграл примет вид:

∫√u (1/2) du = (1/2) ∫u^(1/2) du = (1/2) * (u^(3/2) / (3/2)) + C = (1/2) * (2/3) u^(3/2) + C = (1/3) u^(3/2) + C

Подставим u = 2x - 3 обратно:

(1/3) (2x - 3)^(3/2) + C

Ответ: (1/3)(2x-3)^(3/2) + C