1) i) u = 2x + 7, therefore x = (u-7)/2
du/dx = 2, therefore du/2 = dx
Int. [x*rt(2x+7)] dx
= Int. [(u-7)/2 * rt(u)] * du/2
= 1/4 Int. [(u-7)rt(u)] du
= 1/4 Int. [u3/2 - 7u1/2] du
From there, you integrate as normal, then substitute in u = 2x+7 when you have finished integrating.
ii)...