# A calculus problem by Sourabh Jangid

Calculus Level 3

Consider a continuous function $$f(x)$$ in $$(0,1 )$$ satisfying $$\displaystyle \int_0^1 x \sqrt x f(x) \left(1 - \sqrt x \; f(x) \right) \, dx = \dfrac18$$.

Find the number of solutions of $$n$$ such that $$f(n) = e^n$$.

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