Please help with this indefinite intergral questionquestion

Question

x(4x+5)^14

Answer 1

Let u = 4x + 5. Then du = 4dx and x = (u-5)/4.

So, the integral can be rewritten as (1/4)∫u¹⁴(u - 5)(1/4)du = (1/16)∫[u¹⁵ - 5u¹⁴]du =

(1/256)u¹⁶ - (5/240)u¹⁵ + C = (1/256)(4x+5)¹⁶ - (1/48)(4x+5)¹⁵ + C