Interesting Integral

Calculus Level 5

If the value of the integral

0(x2+4)lnxx4+16 dx\displaystyle\int_{0}^{\infty}\dfrac{(x^{2}+4)\ln x}{x^{4}+16}\text{ }\text{d}x

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

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