Question

Вычислить интеграл:
∫ dx/3x+5

Answer 1

£dx/(3x+5)

1)t = 3x

dt = 3dx, dx = dt/3

2)1/3£dt/(t+5) = 1/3ln(t+5)+C = 1/3ln(3x+5)+C

Answer 2

$\int \, \dfrac{dx}{3x+5}=\dfrac{1}{3}\int \, \dfrac{d(3x+5)}{3x+5}=ln|3x+5|+C$