Solution: This problem needs to be broken up into steps.
Step 1: Rewrite by breaking up the problem into two integrals:
ò(4x2 + 1)dx = ò 4x2 dx + ò 1 dx (Sum Rule)
Step 2: Use the Constant Multiple Rule and place a x0 into the second integral:
ò4x2 dx + ò 1 dx = 4 ò x2 dx + 1 ò x0 dx
Step 3: Finally, use the Power Rule on both of the integrals and combine the constants into one:
4 ò x2 dx + 1 ò x0 dx = x(2 + 1) + C + x(0 + 1) + C (Power Rule)
= x3 + x + C,
where C is an arbitrary constant.