Question:
Write a value of $\int \frac{\sin \mathrm{x}}{\cos ^{3} \mathrm{x}} \mathrm{dx}$
Solution:
Let, $\cos x=t$
Differentiating both sides with respect to $\mathrm{x}$
$\frac{d t}{d x}=-\sin x$
$\Rightarrow-d t=\sin x d x$
$y=\int \frac{-1}{t^{3}} d t$
Use formula $\int \frac{1}{t^{n}} d t=\frac{t^{-n+1}}{-n+1}$
$y=-\frac{t^{-2}}{-2}+c$
Again, put $t=\cos x$
$y=\frac{1}{2(\cos x)^{2}}+c$