Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Integration (p-1)1 Mark
Question
Evalute : $\int x \log x$
✓
Answer
$ \begin{aligned} & \int x \log x d x=\int(\log x) \cdot x d x \\ = & (\log x) \int x d x-\int\left[\frac{d}{d x}(\log x) \int x d x\right] d x \\ = & (\log x) \cdot \frac{x^2}{2}-\int \frac{1}{x} \cdot \frac{x^2}{2} d x \\ = & \frac{1}{2} x^2 \log x-\frac{1}{2} \int x d x \\ = & \frac{x^2}{2} \log x-\frac{1}{2} \cdot \frac{x^2}{2}+c=\frac{x^2}{2} \log x-\frac{x^2}{4}+c . \end{aligned} $
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.