# Recursive Integration

Calculus Level 3

I integrated an integer $$n$$ with respect to a variable $$x$$ from $$1$$ to $$n$$, and had a result of $$c$$. I then integrated $$c$$ with respect again to $$x$$ from $$1$$ to $$c$$ and had a result of $$c_2$$. Then I integrated $$c_2$$ with respect again to $$x$$ from $$1$$ to $$c_2$$ and had a result of $$c_3$$. If $$c_3 = n$$, and $$n$$ is a nonzero integer greater than 1, then the value of

$$\huge \int^{n}_{1} nx^{n} dx$$

can be expressed in the form $$\frac {a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. Determine $$a+b$$.

×