Search any question & find its solution
Question:
Answered & Verified by Expert
Integrate the function
$x \log 2 x$
$x \log 2 x$
Solution:
1173 Upvotes
Verified Answer
$\int x \log 2 x d x=(\log 2 x) \frac{x^2}{2}-\int \frac{1}{2 x} \cdot 2\left(\frac{x^2}{2}\right) d x$
$=\frac{x^2}{2} \log |2 x|-\frac{1}{2} \int x d x=\frac{x^2}{2} \log |2 x|-\frac{x^2}{4}+\mathrm{C}$
$=\frac{x^2}{2} \log |2 x|-\frac{1}{2} \int x d x=\frac{x^2}{2} \log |2 x|-\frac{x^2}{4}+\mathrm{C}$
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.