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
$\int_1^x \frac{\log x^2}{x} d x=$
MathematicsDefinite IntegrationJEE Main
Options:
  • A $(\log x)^2$
  • B $\frac{1}{2}(\log x)^2$
  • C $\frac{\log x^2}{2}$
  • D None of these
Solution:
1804 Upvotes Verified Answer
The correct answer is: $(\log x)^2$
$\begin{aligned} & I=\int_1^x \frac{2 \log x}{x} d x \\ & \text { Let } \log x=t \Rightarrow \frac{d x}{x}=d t \\ & \therefore I=2 \int_0^{\log x} t d t=2\left[\frac{t^2}{2}\right]_0^{\log x}=(\log x)^2\end{aligned}$

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.