# A nested integral

Calculus Level 4

Let $$F(f(x))$$ denote $$\int_0 ^ x f(s) \, ds$$.

If the algebraic expression of $$x^0 \cdot F(x^1 \cdots F(x^8 \cdot (F(x^9 \cdot F(x^{10} )))) \cdots )$$ is equal to $$\dfrac {x^A}{B}$$, what is the value of $$(A+B) \pmod {10^{10}}$$.

×