# Integral ( I was too lazy to make a good name... )

Calculus Level 3

$\int _{ 1 }^{ 2 }{ \frac { x }{ { x }^{ 2 }+4x+8 } }\, dx = \arctan { \frac { a }{ b } } -\arctan { c } +\frac { 1 }{ d } \ln { \frac { e }{ f } }$

The equation above holds true for some positive integers $a$, $b$, $c$, $d$, $e,$ and $f$, with $\gcd(a,b) = \gcd(e,f) = 1$. What is $a+b+c+d+e+f ?$

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