integral from 0 to 1 (3+xsqrtx)dx

Soo i just need to see if im on the right track

I rewrote it to (3+x.x^-1/2) soo then would the antiderivative be (3x+ (2/5)x^(5/2) )??

obviously then subbing in the x values after but i just want to make sure i got the antiderivative correct.