Solution: The first step that needs to be taken is choosing the correct substitution for the problem:

Step 1: Choose *u *= *x*^{2} + 3*x* + 5 since its derivative, *du *= (2*x* + 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:

ò 3(*x*^{2} + 3*x* + 5)^{2}(2*x* + 3)*dx *= 3 ò *u*^{2} *du *

Step 3: Integrate using the Power Rule:

3 ò *u*^{2} *du *=
*u ^{}*(2 + 1)

Step 4: Plug in the value *u *represents:

*u ^{}*3 +

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