Search any question & find its solution
Question:
Answered & Verified by Expert
Integrate the function
$x^2 \log x$
$x^2 \log x$
Solution:
1189 Upvotes
Verified Answer
$\int x^2 \log x d x=\log |x|\left(\frac{x^3}{3}\right)-\int \frac{1}{x}\left(\frac{x^3}{3}\right) d x$
$=\frac{x^3}{3} \log |x|-\frac{1}{3} \int x^2 d x=\frac{x^3}{3} \log |x|-\frac{x^3}{9}+\mathrm{C}$
$=\frac{x^3}{3} \log |x|-\frac{1}{3} \int x^2 d x=\frac{x^3}{3} \log |x|-\frac{x^3}{9}+\mathrm{C}$
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.