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 37028 by nishant last updated on 08/Jun/18

$$\int \frac{2x-1}{5x^2-x+2}dx=?$$

Answered by ajfour last updated on 08/Jun/18

$$I=\frac{1}{5}\int \frac{10x-1}{5x^2-x+2}dx-\frac{4}{25}\int \frac{dx}{{(x-\frac{1}{10})}^2+\frac{2}{5}-\frac{1}{100}}$$$$=\frac{1}{5}\ln \mid 5x^2-x+2\mid -\frac{4}{25}\int \frac{dx}{{(x-\frac{1}{10})}^2+{\left(\frac{\sqrt{39}}{10}\right)}^2}$$$$=\frac{1}{5}\ln \mid 5x^2-x+2\mid -\frac{4}{25}\times \frac{10}{\sqrt{39}}{\tan }^{-1}\left(\frac{10x-1}{\sqrt{39}}\right)+c.$$$$$$

Commented by nishant last updated on 08/Jun/18

$$thankssir.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com