Calculus

Calculus Level 4

$\displaystyle \int\frac{7x^{13}+5x^{15}}{\left(x^7+x^2+1\right)^3}dx = \frac{1}{a}\cdot \frac{x^{b}}{\left(x^7+x^2+1\right)^c}$

Given that the indefinite integral above is true, then what is the value of $a+b+c,$ where $a,b,\text{ and }c$ are positive integers?