Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I am still having trouble with taking the integral of the following:

integral of ln(x+1) dx

I am trying to do it by parts but I end up getting stuck. I had no problem doing:

integral of ln x dx

But I can't seem to get

integral of ln (x+1) dx

Let u = ln (x+1) then du = 1/ (x+1)

Let dv = dx then v = x.

So then

integral of ln (x+1) dx =

ln(x+1)*x - integral of x/(x+1) dx

I then though that I would integrate the last part by parts again.

Let u = x then du = dx

Let dv = 1/(x+1) then v = ln(x+1)

So then

integral of x/(x+1) dx =

x*ln(x+1) - integral of ln(x+1) dx.

So far I now have

integral of ln (x+1) dx =

ln(x+1)*x - [x*ln(x+1) - integral of ln(x+1) dx]

But then all I end up getting is

integral of ln (x+1) dx = integral of ln (x+1) dx

So I am back to where I started. What am I doing incorrectly?

Any help is appreciated. Thankyou.

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# Homework Help: Integral of Natural Log Part II

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