Step 01:- let x - 3 = t and D.w.r to x

step 02:- in function x+2 add 3 and substract 3 and make it in form of x-3

step 03:- then simply split it and integrate it .

Solution is in this given attachment .

Hope it's helpful .

(x+2) dx

Let

x-3 = t

dx = dt

I = (x-3+5) .dt

(t+5)t½dx

+ 5t½dx

2 ( + ) + c

2( ) + c

(3x+16) + c