EDIT: wait... no, forgot the chain rule.

EDIT EDIT:

Take u = 5x + 1, so that x = (u - 1)/5 and du = 5 dx

=> the integral of (1/5) * (1/5) [(u-1)(sqrt(u)] du (substituting **x**, u and du)

=> the integral of (1/25) (u^3/2 - u^1/2) du

(1/25) * (2/5)u^5/2 - (2/3)u^3/2