Computing Arc Length and Cannot Solve the Integral

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Voodoo583
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Homework Statement



Find the length of the polar curve.

Complete the cardioid r=1+cosθ

Homework Equations



L=∫αβ√[f(θ)2+f'(θ)2] dθ

The Attempt at a Solution



Given f(θ)2 is equal to cos2θ+2cosθ+1

and f'(θ)2=sin2θ

I arrive at the integral ∫αβ√[2cosθ+2] dθ which I cannot for the life of me solve for. It's been a while since my calc II class so I flipped through my textbook to see if I could find a solution. I cannot do u substitution as far as I can tell nor integration by parts and I couldn't find anything similar to the form above in the table of integrals.
 
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