Step 1 :Given the integral \(\int_{3}^{5}(2 x+6) d x\)
Step 2 :Find the antiderivative of the function \(2x + 6\), which is \(x^2 + 6x\)
Step 3 :Evaluate the antiderivative at 5, which gives \(5^2 + 6*5 = 55\)
Step 4 :Evaluate the antiderivative at 3, which gives \(3^2 + 6*3 = 27\)
Step 5 :Subtract the two results to get the final answer, \(55 - 27 = 28\)
Step 6 :So, the integral of the function from 3 to 5 is \(\boxed{28}\)