Integrate (x+3)^(1/2) .dx

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Here we need to make a U sibstitution. So we take (x+3) and make this equal U so we now have the integral of u^1/2   . dx

In order to switch to .du and do this integral we need to find du in terms of dx. 

Hence by writting u=(x+3)  we find that du/dx =  =2   so du=2.dx This leaves us with the integral of 2u^(1/2) .du which we can evaluate to be (4/3)(u^1.5). 

Now to get this in terms of x for a final answer we know u=(x+3) so we just rewrite the answer in terms of x giving a final answer: 

(4/3)((x+3)^1.5)