What is the antiderivative of ln(2x)x12?

1 Answer
Feb 9, 2017

=2x12(ln(2x)2)+C

Explanation:

ln(2x)x12dx

We set it up for IBP:
=ln(2x)ddx(2x12)dx

Applying the IBP:
=2x12ln(2x)ddx(ln(2x))(2x12)dx

=2x12ln(2x)1x2x12dx

=2x12ln(2x)2x12dx

=2x12ln(2x)22x12+C

=2x12(ln(2x)2)+C