Question

Integrate the following w.r.t $x:\frac{1}{2x+3}$

• A. ln |2x + 3| + c
• B. $\frac{ln|2x+3|}{2}+c$
• C. $\frac{ln(2x+3)}{2x+3}+c$
• D. None of these

Answer 1

The correct option is B

$\frac{ln|2x+3|}{2}+c$

Let $u=2x+3$

$\Rightarrow \frac{du}{dx}=2$

$\Rightarrow dx=\frac{du}{2}$

$I=\int ydx=\int \frac{dx}{2x+3}=\int \frac{1}{u}\times \frac{du}{2}$

= $\frac{1}{2}\int \frac{du}{u}$

= $\frac{1}{2}lnu+c$

= $\frac{1}{2}ln|2x+3|+c$