# Yeah I know!

Calculus Level 4

$\large \lim_{x\to\infty} \dfrac{x^2 f''(x)}{f(x) } \lim_{t \to0} (1+\sin t)^{1 - \cos t} = n^3 - 5n^2 + 2n + 10$

Let $$f$$ be a polynomial of degree $$n$$ satisfying the equation above. Given that $$f'(x)$$ has only one real root and $$f(1) = f(-1)$$.

If there exists a real $$k$$ satisfying $$f'(k) = 0$$, find $$\displaystyle \int_{2k+1}^{k^2-k+1} f(x) \, dx$$.

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