Solution: The first step that needs to be taken is choosing the correct substitution for the problem:
Step 1: Choose u = x2 + 3x + 5 since its derivative, du = (2x + 3)dx will substitute for the rest of the integral.
Step 2: Plug in u and du into the integral and use the Constant Multiply Rule:
ò3(x2 + 3x + 5)2(2x + 3)dx = 3 ò u2 du
Step 3: Integrate using the Power Rule:
3 ò u2 du = u(2 + 1) + C = u3 + C
Step 4: Plug in the value u represents:
u3 + C = (x2 + 3x + 5)3 + C.