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.