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 89123 by john santu last updated on 15/Apr/20

$$\int \frac{\cos 2x}{\sec x-\cos {}^{2}x}dx?$$

Commented by MJS last updated on 15/Apr/20

$$\mathrm{Weierstrass}\mathrm{leads}\mathrm{to}$$$$-\int \frac{t^6-7t^4+7t^2-1}{t^2(t^2+1)(t^4+3)}dt$$$$\mathrm{and}\mathrm{this}\mathrm{can}\mathrm{be}\mathrm{solved}\mathrm{by}\mathrm{decomposing}$$

Commented by john santu last updated on 15/Apr/20

$$noothermethodsir?$$

Commented by MJS last updated on 15/Apr/20

$$\frac{\cos 2x}{\sec x-{\cos }^{2}x}=\frac{\cos x-{2\cos }^{3}x}{{\cos }^{3}x-1}=$$$$=\frac{5+\cos x}{3({\cos }^{2}x+\cos x+1)}+\frac{1}{3(1-\cos x)}-2$$$$\mathrm{then}\mathrm{only}\mathrm{the}\mathrm{first}\mathrm{is}\mathrm{complicated}$$$$\mathrm{Weierstrass}\mathrm{gives}$$$$\frac{4}{3}\int \frac{2t^2+3}{t^4+3}dt$$$$\mathrm{for}\mathrm{this}\mathrm{one}$$

Commented by john santu last updated on 15/Apr/20

$$ooyes.thankyousir$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com