Note that the derivative for (x+1) is 1.
So you have something like u'(x)/u(x), with u(x)=1+x.
The antiderivative of u'(x)/u(x) is ln(|u(x)|)
Chain Rule, you must carry out the derivative of what's inside the natural log. In this case, it is 2, so . To make this adjustment for the integral of , you must divide the integral by 2, so you have an answer of .