Question

integration dx / 2x + 3 =​

Answer 1

$\large \rm\int \frac{dx}{2x + 3} \: \: \: ...........(1)$

Let 2x + 3 = m ...................(a)

Differentiate equation (a),

=> 2.dx = dm

=> dx = dm/2 ...................(b)

Using (a) and (b) in (1),

$= \rm \large \frac{1}{2} \int \frac{dm}{m}$

$= \rm \large\frac{1}{2} ln( |m| )$

Bring 'm' back from equation (a),

$= \rm \large\frac{1}{2} ln( |2x+3| )$