Problem 1. Calculate $\int \frac{12 x+17}{(x+2)(2 x+3)(3 x+4)(6 x+5)+2016} \mathrm{~d} x, x \in(0 ; \infty)$.
Problem 1. Calculate $\int \frac{12 x+17}{(x+2)(2 x+3)(3 x+4)(6 x+5)+2016} \mathrm{~d} x, \quad x \in(0 ; \infty)$.

Grading criteria. If we denote by $I$ the integral from the statement, we have:

(2p) $I=\int \frac{12 x+17}{\left(6 x^{2}+17 x+10\right)\left(6 x^{2}+17 x+12\right)+2016} \mathrm{~d} x$

$(3 p) \quad=\int \frac{12 x+17}{\left(6 x^{2}+17 x+11\right)^{2}+2015} \mathrm{~d} x$

$(2 p)=\frac{1}{\sqrt{2015}} \cdot \operatorname{arctg} \frac{6 x^{2}+17 x+11}{\sqrt{2015}}+\mathcal{C}$.