Question

Determine whether the statement is true or false, and explain why.

Integration by parts should be used to evaluate ∫ln(4x) dx.

Answer 1

True

Explanation:

The problem ∫ln(4x) dx can be solved with integration by parts.

∫ udvdx = uv − ∫ vdu dx ..............equ1

where u=ln4x, dv=1dx

du/dx = 1/4x v=x

subtituting those values into the equ 1,we have

∫ln(4x) dx = ln4x *x - ∫x*(1/4x)dx

= xln4x - ∫(1/4)dx

=xln4x- x/4 +C