Power Rule
Historically the power rule was derived as the inverse of Cavalieri's quadrature formula which gave the area under for any integer . Nowadays the power rule is derived first and integration considered as its inverse.
For integers, the derivative of is that is,
The power rule for integration
for is then an easy consequence. One just needs to take the derivative of this equality and use the power rule and linearity of differentiation on the right-hand side.
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