# Intriguing integrals! - one

Calculus Level 3

$\large \int_0^3 \frac{x^3}{1+4x+6x^2+4x^3+x^4} \, dx$

Consider the integral above, if this integral can be represented as $\ln(a) - \frac{b}{c}$ for positive integers $$a,b,c$$ with $$b,c$$ coprime, find the value of $$a+b+c$$.

###### Please post your diverse approaches.
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