Search any question & find its solution
Question:
Answered & Verified by Expert
$\int\left(1+e^{-x}\right)^{-1} d x=$
Options:
Solution:
2320 Upvotes
Verified Answer
The correct answer is:
$\log \left(1+e^x\right)+c$
$I=\int\left(1+e^{-x}\right)^{-1} d x=\int \frac{e^x}{e^x+1} d x$
Put $e^x+1=t \Rightarrow e^x d x=d t$
So, $I=\int \frac{d t}{t}=\log _e|t|+C=\log _e\left(1+e^x\right)+C$
Put $e^x+1=t \Rightarrow e^x d x=d t$
So, $I=\int \frac{d t}{t}=\log _e|t|+C=\log _e\left(1+e^x\right)+C$
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.