Integrals of (-3csc(theta))/(1+cos(theta))

[Jessicamgray]

Homework Statement

integrate (-3csc(theta))/(1+cos(theta))

Homework Equations

i'm not sure

The Attempt at a Solution

i tried using u sub. but i got nowhere.

U=1+costheta
Du=-sintheta

 

[gopher_p]

Homework Statement

integrate (-3csc(theta))/(1+cos(theta))

Homework Equations

i'm not sure

The Attempt at a Solution

i tried using u sub. but i got nowhere.

U=1+costheta
Du=-sintheta

The reason why your $u$-sub doesn't get you anywhere (yet) is because (1) there isn't a $\sin\theta$ in the numerator and (2) we'd still need to deal with the $\csc\theta$. I recommend that you

(1) Put a $\sin\theta$ in the numerator so that your $u$-sub at least has a chance of working. Of course you can't just put one there, but you can multiply the integrand by $\frac{\sin\theta}{\sin\theta}$ so that there is one there.

(2) Write the $\csc\theta$ in terms of $\sin\theta$ and see if you can make something happen with what you end up with.

 

[Dick]

I'd try just u=cos(theta). Then since du=sin(theta)dtheta multiply numerator and denominator by sin(theta). That gives you your du. Now see if you can use trig identities to express the other functions of theta as u.