Make the substitution u = (x+1). This will leave you with:
(u-1)ln(u). Deal separately with u*ln(u) and -ln(u). Each of them can be integrated using integration by parts. In the first case, integrate u and differentiate ln(u); the product of this will be a linear function easy to integrate. The second one is similar, write it as -1 * ln(u). I'll leave the details to you, tell me if this was too vague.