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Calculus Made Easy
until ascertained in some other way. So, if differentiating yields , going backwards from will give us ; where stands for the yet undetermined possible constant.
Clearly, in dealing with powers of , the rule for working backwards will be: Increase the power by , then divide by that increased power, and add the undetermined constant.
So, in the case where
,
working backwards, we get
.
If differentiating the equation gives us
,
it is a matter of common sense that beginning with
,
and reversing the process, will give us
.
So, when we are dealing with a multiplying constant, we must simply put the constant as a multiplier of the result of the integration.