What is the integral of ln(2x+1)?

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Answer 1 · 2014-12-14T23:11:30

$int u dv=uv - int v du$

$int ln(2x+1) dx$

by Substitution $t=2x+1$ . $=> {dt}/{dx}=2 => dx={dt}/2$

$=1/2int ln t dt$

by Integration by Parts,

Let $u=ln t$ and $dv=dt$
$=> du = 1/{t}dt" "$ $v=t$

$=1/2(t ln t - int dt)$

$=1/2(t ln t - t) + C$

by putting $t=2x+1$ back in,

$=1/2[(2x+1)ln(2x+1)-(2x+1)]+C$

I hope that this was helpful.