Answer to Question #174621 in Calculus for Phyroe

Question

Evaluate the integral of 3dx/(5x+1)

Answer 1

$\int \dfrac{3\,dx}{5x+1} = \Big| y = 5x+1, \; dy = (5x+1)'dx, \; dy = 5dx, \; dx = \dfrac15dy \Big| =\\= \dfrac35\int \dfrac{dy}{y} = \dfrac35 \ln | y| + C = \dfrac35 \ln |5x+1| + C,$

where C is an arbitrary constant.