How do you use Integration by Substitution to find ∫dx(1−6x)4dx?
1 Answer
Aug 6, 2014
∫(1−6x)−4dx= ?
We will let
=∫u−4dx
This looks difficult since there isn't a
∫c⋅f(x)dx=c⋅∫f(x)dx
We can exploit this rule to rewrite our integral equivalently as:
=−16∫−6u−4dx
The statements are completely equivalent; note that if we pull the
Anyway, we now have a
=−16∫u−4du
=−16u−3⋅(−13)
=118u−3
=118u3
Substituting back for
=118(1−6x)3