Interesting integral: $\int_0^1{\frac{nx^{n-1}}{x+1}}dx$ Find the value of $$\int_0^1{\frac{nx^{n-1}}{x+1}}dx.$$
I had no luck while integrating it. I also tried differentiating w.r.t n but still couldn't reach anywhere. Need help.

HINT:
If $\displaystyle I_n=\int_0^1\dfrac{nx^{n-1}}{x+1}dx,$
$$I_{m+1}+I_m=\int_0^1\dfrac{(m+1)x^m+mx^{m-1}}{x+1}dx$$ 
$$=m\int_0^1x^{m-1}\ dx+\int_0^1\dfrac{x^m}{1+x}dx=1+\int_0^1\dfrac{x^m}{1+x}dx$$
Again if $\displaystyle J_m=\int_0^1\dfrac{x^m}{1+x}dx,$
$$J_{m+1}+J_m=?$$
