A Calculus Problem

f(x) = x⁹ + 7x⁵ - 4x² + 1/x.

Find f'(x) and F(x).

f'(x) = 9x⁸ + 35x⁴ - 8x - 1/x².

F(x) = ∫ f(x) dx,
F(x) = ∫ (x⁹ + 7x⁵ - 4x² + 1/x) dx,
F(x) = x¹⁰/10 + 7x⁶/6 - 4x³/3 + ln |x| + c.

Ah, the Poetics.