Question

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

Answer 1

Use integration by parts with a dummy function:

`int uv'dx = uv - int u'vdx`

`u(x) = ln(2x) implies u'(x) = 1/x`

`v'(x) = 1 implies v(x) = x`

`int ln(2x) dx = xln(2x) - int dx`

`= x(ln(2x) - 1) + C`