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 Homework Statement:
 Evaluate ##\int{\ln{(e^x+1)}}##
 Relevant Equations:

##\ln{x} = \sum_{n=1}^{\infty} \frac{(1)^{n1}x^n}{n}##
##(x+y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{nk}y^k##
Given the integral $$\int \ln{(e^x+1)} dx$$ we can rewrite this as the integral of the Taylor expansion of ##\ln{(e^x+1)}##. $$\int \sum_{n=1}^{\infty} \frac{(1)^{n1}(e^x+1)^n}{n} dx$$ Which can then be rewritten using the binomial theorem: $$\int \sum_{n=1}^{\infty} \left [ \frac{(1)^{n1}}{n} \sum_{k=0}^{n} \binom{n}{k} e^{x(nk)} \right] dx $$ What I want: a way to rewrite this such that I can directly integrate the binomial term, as this is simply a linear combination of ##e^{x(nk)}## which is trivial to integrate.
Any help?
Any help?