Question

Integrate the function: $\frac {1}{\sqrt {9-25x^2}}$

Answer 1

$Let \ 5x = t$

$∴ 5 dx = dt$

⇒ $∫\frac {1}{\sqrt {9-25x^2}} \ dx$ $=$ $\frac {1}{5} ∫\frac {1}{9-t^2} dt$

$=\frac 15 ∫\frac {1}{\sqrt {3^2-t^2}} \ dt$

$=\frac 15 sin^{-1}(\frac t3)+C$

$=\frac 15 sin^{-1}(\frac {5x}{3})+C$