Start by noticing that, from the definition of integration as the inverse process of differentiation:
Now multiply both sides by a constant k. Since k is a constant it is not dependent on[?] x:
Take the constant factor rule in differentiation:
Integrate with respect to x:
Now from (1) and (2) we have:
Therefore:
Now make a new differentiable function:
Subsitute[?] in (3):
Now we can re-substitute[?] y for something different from what it was originally:
So:
This is the constant factor rule in integration.
A special case[?] of this, with k=-1, yields:
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