Evaluate the indefinite integral. (Use symbolic notation and fractions where needed.) ∫𝑥^29(𝑥^(15)−7)^3/2𝑑𝑥=

Answer 1

Let u = x¹⁵-7 Then du = 15x¹⁴dx So x¹⁴dx = (1/15)du

∫x²⁹(x¹⁵-7)^3/2dx = ∫x¹⁵(x¹⁵-7)^3/2x¹⁴dx = ∫ (u+7)u^3/2(1/15)du = (1/15)∫ [u^5/2 +7u^3/2]du

Apply the power rule