Sorry I must not have been clear. The denominator is simply L(mgcos(r/L) to the power of a half) i.e. in your last step there is no theta outside of the cos(theta).

To answer your question I...uh

... well I figured the lecturers were lying to us about the motion of a pendulum being simple harmonic even at small theta so I endevoured to come up with a proof to show the real equation for period lol.

Anyways I guess 10 weeks into advanced physics isn't long enough to be arrogant enough to think you can come up with an equation of periodic motion for a pendulum huh?

Anyways I ended up with that integral and I'm really hoping to get a final equation, even if its incorrect (I'm a tad stubborn). However if this integral is unsolvable chances are I went wrong somewhere huh.

Oh and I'm really hoping that you can integrate it in terms of dr and not dtheta as I spent a while converting it into that form (as it involved integrating a function of theta by dt so I had to find an alternate form of dt).

If you are interested in my method I'll be happy to tell you (not sure if its sound though; as I said only 10 weeks in

) still I would really appreciate it if you were able to integrate the function anyway (in terms or dr

)

Edit: I know it would be a simple matter to switch it back after the dtheta integral but I'd like to see the working out for dr thats all. However since your the one helping me, then whatever works for you