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There's a skill needed for integrals (we'll explain integrals later) that we'll consider now: thinking backwards. Instead of taking a function and figuring out its derivative, think about looking at a derivative and figuring out what sort of function it came from. Try this out when looking over solutions to derivatives.
If f ' (x) = 5x4, what could the original function f(x) be?
f'(x) = 5x4 = 5x5–1
looks like it came from the rule for derivatives of power functions. The original exponent must have been 5, therefore the original function could have been