Interesting Integral

Calculus Level pending

The value of

\(e^{\int^1_{-1} \frac{15x-25}{4x^2+15x-25}dx}\)

Can be expressed as \(\frac{a\sqrt{b}}{c}\) where \(a, b, c\) are integers, \(a, c\) are relatively prime, and \(b\) is not divisible by any square number greater than 1. Find a+b+c.

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