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

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Answer 1 · 2016-07-11T09:05:09

Use integration by parts with a dummy function:

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

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

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

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

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

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