Do not go for E axe

Calculus Level 3

If \(\displaystyle f(x)=\int f(x) \, dx \) with \( \displaystyle \int \left[f''(x) + (f'(x))^2+(f(x))^3\right]\, dx =0 \), find the value of \( \displaystyle \sum_{r=1}^3 \frac{(f(x))^r}r \).

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