Find each indefinite integral and check the result by differentiating.

Question

1) ∫(6x-1)³(6)dx

2) ∫(x⁶+1)⁴(6x⁵)dx

Answer 1

1)

Try substitution u = 6x -1. Then du=6*dx so dx=(du)/6

∫(6x-1)³*6 dx = (6/6)*∫ u³ du = ∫ u³ du = u⁴/4 + Constant = (6x-1)⁴/4 + Constant

Use the same reasoning for 2)