Question

integral of dx over (a-x) to power 3

Answer 1

assume a-x =z then -dx= dz or dx=-dz

Answer 2

\[ \large \int {dx \over {(a-x)^3}} = \int (a-x)^{-3}dx\]

This looks like a good place for advanced guessing.

Since the exponent is -3 we know the antiderivate must involve the power -2,

So what does the derivative of \( (a-x)^{-2} \) look like?