Interesting Integral

Calculus Level 5

If the value of the integral

\[\displaystyle\int_{0}^{\infty}\dfrac{(x^{2}+4)\ln x}{x^{4}+16}\text{ }\text{d}x\]

can be expressed as \(\dfrac{\pi\ln a}{b\sqrt{c}}\) where \(a\) is a prime number and \(c\) is square free find \(a+b+c\).

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