Day 14: Christmas is the Solution

Calculus Level 3

C=03π[1cos2x121sin2x12+1]dxC = \int_0^{3\pi} \bigg [ \frac{1 - \cos^2{\frac{x}{12}}} {1 - \sin^2{\frac{x}{12}}} + 1 \bigg ] \, \mathrm{d}x If the value of 2+C1442 + \frac{C}{144} is in the form a/ba/b where aa and bb are positive coprime integers and enter a+ba+b as your answer.

This problem is part of the set Advent Calendar 2014.
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