How do you use Integration by Substitution to find intdx/(1-6x)^4dx?
1 Answer
Aug 6, 2014
int (1 - 6x)^(-4) dx = ?
We will let
= int u^(-4) dx
This looks difficult since there isn't a
int c*f(x) dx = c * int f(x) dx
We can exploit this rule to rewrite our integral equivalently as:
= -1/6 int -6 u^(-4) dx
The statements are completely equivalent; note that if we pull the
Anyway, we now have a
= -1/6 int u^(-4) du
= -1/6 u^(-3) * (-1/3)
= 1/18 u^(-3)
= 1/(18u^3)
Substituting back for
= 1/(18(1 - 6x)^3)