Search any question & find its solution
Question:
Answered & Verified by Expert
$\int \frac{\sec x}{\sec x+\tan x} d x=$
Options:
Solution:
1772 Upvotes
Verified Answer
The correct answer is:
$\tan x-\sec x+C$
Let $I=\int \frac{\sec x}{\sec x+\tan x} d x$ $$ =\int \frac{1}{1+\sin x} d x=\int \frac{1-\sin x}{1-\sin ^{2} x} d x $$ $=\int \frac{1-\sin x}{\cos ^{2} x} d x$ $=\int\left(\sec ^{2} x-\sec x \tan x\right) d x$ $=\tan x-\sec x+\bar{C}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.