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

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

True

Step-by-step 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