Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 15235 by arnabpapu550@gmail.com last updated on 08/Jun/17

$$\int {\left(\log \sqrt{\mathrm{x}}\right)}^2\mathrm{dx}=?$$

Answered by liday last updated on 18/Jun/17

$$\int {\left(log\sqrt{x}\right)}^{2}dx=\frac{1}{4}\int {\left(logx\right)}^{2}dx=\frac{1}{4}[x{\left(logx\right)}^2-\int x\cdot 2logx\cdot \frac{1}{x}dx]$$$$=\frac{1}{4}[x{\left(logx\right)}^2-2\int logxdx]=\frac{1}{4}[x{\left(logx\right)}^2-2(xlogx-x)]$$$$=\frac{x}{4}[{\left(logx\right)}^2-2logx+2]$$

Commented by liday last updated on 18/Jun/17

$$and+c$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com