Integration help for someone who is a little rusty

Hi everyone, first post and already whining for help, but ok.. (Crying)

Could someone help me out a little with the following problem:

F(x)= [(1+x)^0.5 -1]/(2^0.5 - 1) ; This represents a cumulative distribution function. I have to calculate the average by integrating "x*F'(x)" from 1 to 0.

I'm supposed to use Integration by parts etc.

My little help needed is: what is the integral of F(x) ==> I came up with something but I think it is wrong...[([(1+x)^1.5]/1.5)-1]/(2^0.5 - 1). Any help would be greatly appreciated!