Find the indefinite integral. (Use C for the constant of integration.)

Question

∫x⁴(5x⁵ + 8)⁵ dx

Answer 1

Let u = 5x⁵ + 8. Then du = 25x⁴ and we have:

∫x⁴(5x⁵ + 8)⁵ dx = (1/25) ∫ u⁵du = u⁶/150 + C

Substituting back in terms of x, we have as our final answer:

∫x⁴(5x⁵ + 8)⁵ dx = (5x⁵ + 8)⁶/150 + C