Calculus

Calculus Level 4

7x13+5x15(x7+x2+1)3dx=1axb(x7+x2+1)c\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, what's the value of a+b+c, a+b+c, where a,b, and ca,b,\text{ and }c are positive integers?

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