How to find the integral of sqrt(x)/(sqrt(x+1)) using u=sqrt(x)?

Question

Must solve using u substitution where u=sqrt(x).

Answer 1

Let u=sqrt(x) ... u²=x and 2udu=dx. Thus the problem becomes 2u²du/sqrt(u²+1). This can be integrated by parts to find y=2sqrt(x)sqrt(x+1)-xsqrt((x+1)/x)-ln((x+1)+sqrt(x))+C