Question:
$\int \frac{2 x+3}{x^{2}+3 x} d x=\log \left|x^{2}+3 x\right|+C$
Solution:
L.H.S. $=\int \frac{2 x+3}{x^{2}+3 x} d x$
Putting, $\quad x^{2}+3 x=t$
So, $\quad(2 x+3) d x=d t$
$\Rightarrow \quad \int \frac{d t}{t}=\log |t| \Rightarrow \log \left|x^{2}+3 x\right|+\mathrm{C}=$ R.H.S.
L.H.S. $=$ R.H.S
- Hence proved.
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