Question

Which of these is a rule of integration

1/(a^(2) + x^(2))^(1/2) = arcsin(x/a), a>0
or
1/(a^(2) - x^(2))^(1/2) = arcsin(x/a), a>0

I'm leaning towards the second being a rule but I need clarification

Answer 1

I dont need proof just clerificaiton but if you want to provide proof go nuts :)

Answer 2

\[\int\limits \frac{dx}{\sqrt{a^2-x^2}}= \sin^{-1} \frac{x}{a}+C\]

Answer 3

nvm fine now

Answer 4

thanks

Answer 5

Welcome:)