# 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)#