Question:
$\int \frac{(1+\cos x)}{x+\sin x} d x$
Solution:
$I=\int \frac{1+\cos x}{x+\sin x} d x$
Putting, $x+\sin x=t \Rightarrow(1+\cos x) d x=d t$
So, $I=\int \frac{d t}{t}=\log |t|=\log |x+\sin x|+C$
Therefore,
$\mathrm{I}=\log |t|=\log |x+\sin x|+\mathrm{C}$
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