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 122875 by pipin last updated on 20/Nov/20

 ∫(((x^2 +1)dx)/(x^4 +x^2 +1)) = ...

$$\:\int\frac{\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}\right)\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}\:=\:... \\ $$$$\: \\ $$

Answered by som(math1967) last updated on 20/Nov/20

∫(((x^2 +1)/x^2 )/((x^4 +x^2 +1)/x^2 ))dx  ∫((1+(1/x^2 ))/(x^2 +(1/x^2 )+1))dx  ∫((1+(1/x^2 ))/((x−(1/x))^2 +2.x.(1/x)+1))dx  ∫((d(x−(1/x)))/((x−(1/x))^2 +((√3))^2 ))  (1/( (√3)))tan^(−1) (((x−(1/x))/( (√3))))+Cans

$$\int\frac{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }}{\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }}\mathrm{dx} \\ $$$$\int\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }}{\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }+\mathrm{1}}\mathrm{dx} \\ $$$$\int\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }}{\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{2}} +\mathrm{2}.\mathrm{x}.\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{1}}\mathrm{dx} \\ $$$$\int\frac{\mathrm{d}\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)}{\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{2}} +\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} } \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}}{\:\sqrt{\mathrm{3}}}\right)+\mathrm{Cans} \\ $$

Commented by pipin last updated on 20/Nov/20

thank you very much sir

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{sir} \\ $$

Commented by som(math1967) last updated on 20/Nov/20

welcome

$$\mathrm{welcome} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com