Another trig sub

1. Feb 4, 2006

silverdiesel

These trig subs are killing me. :yuck:

$$\int\cos^5(x)dx$$

hints?

2. Feb 4, 2006

George Jones

Staff Emeritus
$$\cos^{5} x = \left(1 - \sin^2 x \right)^{2} \cos x$$

Regards,
George

3. Feb 4, 2006

silverdiesel

Thanks George... I am slowly getting the hang of this. I appriciate your help.

4. Feb 4, 2006

HallsofIvy

Staff Emeritus
One of the first things you should have learned: if you have sine or cosine to an odd power, factor out one of them to use with the dx.

cos5 x dx= (cos4 x)(cos x dx)
= (cos2 x)2 (cos x dx)= (1- sin2 x)2(cos x dx)

Now, let u= sin x.