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 70686 by mathmax by abdo last updated on 06/Oct/19

$$find\int \frac{dx}{1+x^6}$$

Answered by kaivan.ahmadi last updated on 06/Oct/19

Answered by MJS last updated on 07/Oct/19

$$\int \frac{dx}{x^6+1}=$$$$=\frac{1}{3}\int \frac{dx}{x^2+1}+\frac{1}{6}\int \frac{\sqrt{3}x+2}{x^2+\sqrt{3}x+1}dx-\frac{1}{6}\int \frac{\sqrt{3}x-2}{x^2-\sqrt{3}x+1}dx=$$$$=\frac{1}{3}\arctan x+$$$$+\frac{\sqrt{3}}{12}\ln (x^2+\sqrt{3}x+1)+\frac{1}{6}\arctan (2x+\sqrt{3})-$$$$-\frac{\sqrt{3}}{12}\ln (x^2-\sqrt{3}x+1)+\frac{1}{6}\arctan (2x-\sqrt{3})+C$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com