I am wondering if I did this correctly.

Integrate

x square root(2x+1)

u=2x+1 x=(1/2)(u-1)

(1/2)(u-1) square root(u)

(1/2) (u)^(3/2)-(u)^(1/2)

(1/2) (2/5)(u)^(5/2)-(2/3)(u)^(3/2)

(2/10)u^(5/2)-(2/6)(u)^(3/2)+c

Any help would be appreciated on this difficult topic.