How do you use Integration by Substitution to find dx(16x)4dx?

1 Answer
Aug 6, 2014

(16x)4dx= ?

We will let u=16x. Thus, du=6dx.

=u4dx

This looks difficult since there isn't a 6 in there for us to form a du with. However, there is a rule of integration which states:

cf(x)dx=cf(x)dx

We can exploit this rule to rewrite our integral equivalently as:

=166u4dx

The statements are completely equivalent; note that if we pull the 6 out of the integral, then it cancels with the 16 and leaves us with 1 multiplied by our original integral.

Anyway, we now have a 6dx to form a du with.

=16u4du

=16u3(13)

=118u3

=118u3

Substituting back for u gives us:

=118(16x)3