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