Question

integrate x/(2x+3)

Answer 1

\[\int\frac{x}{2x+3}~dx\]
Substitute: \(u=2x+3~~\iff~~x=\dfrac{u-3}{2}\), so \(\dfrac{1}{2}du=dx\).
\[\frac{1}{2}\int\frac{\frac{u-3}{2}}{u}~du=\frac{1}{4}\int\frac{u-3}{u}~du=\cdots\]