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 167596 by cortano1 last updated on 20/Mar/22

$$\int \frac{\cos 7\mathrm{x}-\cos 8\mathrm{x}}{1+2\cos 5\mathrm{x}}\mathrm{dx}=?$$

Answered by MJS_new last updated on 20/Mar/22

$$\frac{\cos 7x-\cos 8x}{1+2\cos 5x}=$$$$[c=\cos x]$$$$=-\frac{(c-1)(2c+1)(4c^2+2c-1)(16c^4-8c^3-16c^2+8c+1)}{(2c+1)(16c^4-8c^3-16c^2+8c+1)}=$$$$=-4c^3+2c^2+3c-1=\cos 2x-\cos 3x$$$$\Rightarrow$$$$\int \frac{\cos 7x-\cos 8x}{1+2\cos 5x}dx=\int (\cos 2x-\cos 3x)dx=$$$$=\frac{\sin 2x}{2}-\frac{\sin 3x}{3}+C$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com