Question

Find the indefinite integrals ​

Answer 1

Answer:

Below in bold

Step-by-step explanation:

∫ dx / (x^2√(9-x^2))

Substitute x = 3sinu and dx = 3cosu du

then the √(9-x^2) = √( 9 - 9sin^2u) = 3 cos u  and u = arcsin(x/3)

= 3 ∫(csc^2 u du )/ 27

= 1/9 ∫(csc^2 u du

= -1/9 cot u

= -√9-x^2) / 9x.