Find a power series for f(x)=xln(1+x). \[f(x)=xln(1+x)\]. \[\frac{d}{dx}xln(1+x)\]. \[=\frac{x}{x+1}+ln(x+1)\]. \[=\sum_{n=0}^{\infty}(-1)^nx^n+\fr ac{d}{dx}ln(x+1)\]. \[\sum_{n=0}^{\infty}(-1)^nx^n+\sum _{n=0}^{\infty}(-1)^n\frac{x^{n+1}} {n+1}\]