Question

integral of (dx/sqrt(9-x^2))

Answer 1

To solve this integral, it's easiest to utilize the identity that the integral of dx/(sqrt(a^2-x^2)) is equivalent to (1/a)arcsin(x/a)+c. You should get the answer (1/3)arcsin(x/3)+c

Answer 2

you can integrate by using the identity as given by sakiz008.
If you have forgotten the identity ,then use the substitution given below.
\[I=\int\limits \frac{ dx }{ \sqrt{9-x ^{2}} },put x=3\sin \theta ,dx=3 \cos \theta d \theta \]
substitute and integrate.