Integrating a Tricky Devil: $\int \frac{\cos^5(\theta)}{\sin^4(\theta)} d\theta$

[gazzo]

$$\int \frac{\cos^5(\theta)}{\sin^4(\theta)} d\theta$$

Anyone mind sparing a little hint for this tricky devil? I can't even get started on it. $\cot^4(\theta)\cos(\theta)$ dosn't seem any better either.

I've tried using identities but I end up with nastier ones?

 

[marlon]

this is an easy one :

$$cos^5(\theta)d \theta = cos^4(\theta)cos(\theta) d \theta = (1-sin^2(\theta))^2d(sin(\theta))$$

Fill this into the fraction and just work out the square in the numerator and integrate each part of the sum seperatly. If you want you can replace each sine by a dummy variable u but that is not necessary

marlon

 

[gazzo]

oooh yes of course!

Thank you very much.