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 81279 by jagoll last updated on 11/Feb/20

$$\int \frac{\sqrt{2x+1}}{3x}dx=?$$

Commented by john santu last updated on 11/Feb/20

$$let{u}^2=2x+1\Rightarrow x=\frac{u^2-1}{2}$$$$\Rightarrow \frac{2}{3}\int \frac{u.udu}{u^2-1}=\frac{2}{3}\int \frac{u^2-1+1}{u^2-1}du$$$$=\frac{2}{3}\int du+\int \frac{1du}{(u+1)(u-1)}$$$$=\frac{2}{3}u+\frac{1}{2}(ln\mid \frac{u-1}{u+1}\mid )+c$$$$=\frac{2}{3}\sqrt{2x+1}+\frac{1}{2}ln(\mid \frac{\sqrt{2x+1}-1}{\sqrt{2x+1}+1}\mid )+c$$

Commented by jagoll last updated on 11/Feb/20

$$thankyoumister$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com