Question:
Evaluate the following integrals:
$\int \frac{\operatorname{cosec}^{2} x}{1+\cot x} d x$
Solution:
Assume $1+\cot x=t$
$\mathrm{d}(1+\cot x)=\mathrm{dt}$
$\Rightarrow \operatorname{cosec}^{2} x=d t$
Put $t$ and $d t$ in given equation we get
$\Rightarrow \int \frac{d t}{t}$
$=\ln |t|+c$
But $t=1+\cot x$
$=\ln |1+\cot x|+c$
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