Integral: How would you do it?

Calculus Level 5

0πln(25sin2x+16cos2x)dx=Cπln(AB) \large \int_0^\pi \ln( 25\sin^2 x + 16\cos^2 x) \, dx = C \pi \ln\left(\frac AB\right)

where AA and BB are co-prime integers and CC is also an integer. CC is greater than 11.

Then, find A2+B2+C2A^2+B^2+C^2 .

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