Question:
$\frac{1}{\cos ^{2} x(1-\tan x)^{2}}$
Solution:
$\frac{1}{\cos ^{2} x(1-\tan x)^{2}}=\frac{\sec ^{2} x}{(1-\tan x)^{2}}$
Let $(1-\tan x)=t$
$\therefore-\sec ^{2} x d x=d t$
$\Rightarrow \int \frac{\sec ^{2} x}{(1-\tan x)^{2}} d x=\int \frac{-d t}{t^{2}}$
$=-\int t^{-2} d t$
$=+\frac{1}{t}+\mathrm{C}$
$=\frac{1}{(1-\tan x)}+\mathrm{C}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.