Search any question & find its solution
Question:
Answered & Verified by Expert
$\int_0^3 \frac{3 x+1}{x^2+9} d x$ is equal to :
Options:
Solution:
2011 Upvotes
Verified Answer
The correct answer is:
$\log (2 \sqrt{2})+\frac{\pi}{12}$
$=\frac{3}{2}\left[\log \left(x^2+9\right)\right]_0^3+\frac{1}{3}\left[\tan ^{-1} \frac{x}{3}\right]_0^3$
$=\frac{3}{2}[\log 18-\log 9]+\frac{1}{3}\left[\tan ^{-1}(1)-\tan ^{-1}(0)\right]$
$=\frac{3}{2}[\log 2]+\frac{\pi}{12}$
$=\log (2 \sqrt{2})+\frac{\pi}{12}$
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.