Exponential Integration

Calculus Level 4

ex2 ex (2x2+x+1)dx=ex2f(x)+C \large \int e^{x^2} \ e^x \ (2x^2+x+1) \, dx=e^{x^2} f(x)+C

Above shows an indefinite integral for some non-constant function f(x)f(x) and arbitrary constant CC.

If the minimum value of f(x)f (x) is equal to mm, then find the value of 1m\left \lfloor -\dfrac{1}{m} \right \rfloor.

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