Answer
$\ln (x+1) \ln (\ln (x+1))-\ln (x+1)+C$
Work Step by Step
We will solve the given integral by using u-substitution method.
Let us consider that $u=\ln (x+1) \implies du=\dfrac{ \ dx}{x+1}$
$\displaystyle \int \dfrac{\ln (x+1)}{(x+1)} \ dx=\int \displaystyle \ln u \ du$
or, $=u \ln u -\int u (1/u) \ du$
or, $=u \ln u-\int du$
Therefore, we have:
$\displaystyle \int \dfrac{\ln (x+1)}{(x+1)} \ dx=\ln (x+1) \ln (\ln (x+1))-\ln (x+1)+C$
