integral of cos^3xcos(2x)dx

Question

kira_yamato · Answer

$$\cos3x = =4 \cos^3 x - 3\cos x $$
Use integration by parts

anonymous · Answer

how did you arrive to 4cos^3x

kira_yamato · Answer

Triple angle formula for cosines is given in my last reply. Add 3cosx on each side and then divide both sides of the equation (or identity) to get the following:
$$\cos^3x = \frac{\cos3x + 3\cos x}{4}$$

kira_yamato · Answer

If you want to derive the triple angle formula, use cos 3x = cos (x + 2x), then the addition formula, and finally the double angle formula...

anonymous · Answer

Triple angle formula? I don't think we cover that in my calculus 2 class... but I knew it's suppose to be solve with integral by parts

kira_yamato · Answer

Triple angle formula is under trigonometry...

anonymous · Answer

Thanks for the help. I have another question. $$\int\limits_{0}^{\infty} (16\tan^-1)/1+x^2$$. I know it's solve by using trig substitution but how do you set it up. The Tan inverse is throwing me off

kira_yamato · Answer

Sorry... I don't know either...