Question

Найти первообразную: 1) ∫ cos(3x-2)dx 2) ∫ 5ax⁴ dx

Answer 1

1) ∫ cos(3x-2)dx = =

d(3x-2) = 3 dx

dx = d(3x-2) / 3

= = ∫ cos(3x-2) d(3x-2) / 3 = 1/3 ∫ cos(3x-2) d(3x-2) = 1/3 sin(3x-2) + C

2) ∫ 5ax⁴ dx = 5a ∫ x⁴ dx = 5a * x^5/5 + C  = a x^5 + C