Proof by integrating Bionomial Theorem

[whitendark]

1. The problem statement,

Prove that for any n\inN and any real umber x,
\sum\stackrel{n}{i=0}\left(\stackrel{n}{i}\right)\frac{x^{i+1}}{i+1}=\frac{1}{n+1}((1+x)^{n+1}-1)


2.
I tried to integrate both sides of Bionomial Theorem
However, I'm not sure what to do at the first place. :(

 

[Office_Shredder]

There are some 0s and ns floating around that I think are misplaced