Question

solve the indefinite integral

∫ (dx)/(√1-(x/3)^2)

Answer 1

\[\int\frac{dx}{\sqrt{1-\frac{x^2}{9}}}~~?\]

Answer 2

If that is your integral, substitute \(x=3\sin u\), then \(dx=3\cos u~du\):
\[\int\frac{3\cos u}{\sqrt{1-\frac{1}{9}\left(3\sin u\right)^2}}~du\\
\int\frac{3\cos u}{\sqrt{1-\sin^2u}}~du\\
\int\frac{3\cos u}{\cos u}~du\\
3\int du\]