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

1 Answer

Jul 11, 2016

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#

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