U Substitution question

Question

Integral: x^2(x-6)^9 dx

Answer 1

∫x²(x - 6)⁹dx

Let u = x - 6. Then x = u + 6 and dx = du.

So, the given integral can be rewritten as ∫(u + 6)²u⁹du = ∫[(u² + 12u + 36)u⁹]du

= ∫[u¹¹ + 12u¹⁰ + 36u⁹]du = (1/12)u¹² + (12/11)u¹¹ + (18/5)u¹⁰ + C

= (1/12)(x - 6)¹² + (12/11)(x - 6)¹¹ + (18/5)(x - 6)¹⁰ + C