Integral: How would you do it?

Calculus Level 5

\[ \large \int_0^\pi \ln( 25\sin^2 x + 16\cos^2 x) \, dx = C \pi \ln\left(\frac AB\right) \]

where \(A\) and \(B\) are co-prime integers and \(C\) is also an integer. \(C\) is greater than \(1\).

Then, find \(A^2+B^2+C^2 \).

Looking for a challenge in algebra/trigonometry? Try this.
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