How do you use Integration by Substitution to find intdx/(1-6x)^4dx∫dx(1−6x)4dx?
1 Answer
int (1 - 6x)^(-4) dx =∫(1−6x)−4dx= ?
We will let
= int u^(-4) dx=∫u−4dx
This looks difficult since there isn't a
int c*f(x) dx = c * int f(x) dx∫c⋅f(x)dx=c⋅∫f(x)dx
We can exploit this rule to rewrite our integral equivalently as:
= -1/6 int -6 u^(-4) dx=−16∫−6u−4dx
The statements are completely equivalent; note that if we pull the
Anyway, we now have a
= -1/6 int u^(-4) du=−16∫u−4du
= -1/6 u^(-3) * (-1/3)=−16u−3⋅(−13)
= 1/18 u^(-3)=118u−3
= 1/(18u^3)=118u3
Substituting back for
= 1/(18(1 - 6x)^3)=118(1−6x)3
