Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
$\int_{5}^{10} \frac{1}{(x-1)(x-2)} d x$ is equal to
MathematicsIndefinite IntegrationMHT CETMHT CET 2009
Options:
  • A $\log \frac{27}{32}$
  • B $\log \frac{32}{27}$
  • C $\log \frac{8}{9}$
  • D $\log \frac{3}{4}$
Solution:
2580 Upvotes Verified Answer
The correct answer is: $\log \frac{32}{27}$
Let $I=\int_{5}^{10} \frac{1}{(x-1)(x-2)} d x$
$\quad=\int_{5}^{10}\left[\frac{-1}{x-1}+\frac{1}{x-2}\right] d x$
$=[-\log (x-1)+\log (x-2)]_{5}^{10}$
$=-\log 9+\log 8+\log 4-\log 3$
$=-2 \log 3+3 \log 2+2 \log 2-\log 3$
$=-3 \log 3+5 \log 2$
$=-\log 27+\log 32$
$=\log \frac{32}{27}$

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.