Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use 𝐶 for the arbitrary constant. Absorb into 𝐶 as muсh as possible.) ∫𝑥(5𝑥+9)^10𝑑𝑥=

Answer 1

Let u = 5x+9. So x = (u-9)/5 and dx = (1/5)du.

The given integral is equivalent to (1/25)∫(u-9)u¹⁰du = (1/25)∫(u¹¹ - 9u¹⁰)du

Apply the power rule.