Question

How to solve this: integrate 1/(x^2+9)dx?

Answer 1

look in the back cover of your calc book for integrals of the form
\[\int\frac{dx}{a^2+x^2}\] and you will see that it is
\[\frac{1}{a}\tan^{-1}(\frac{x}{a})\]

Answer 2

you know
\[\Large \frac{d}{dx}(\tan^{-1}(x)=\frac{1}{x^2+1}\]

Answer 3

guys mind if I watch this?

Answer 4

or recall that
\[\frac{d}{dx}[\tan^{-1}(x)]=\frac{1}{1+x^2}\] and adjust for the constant

Answer 5

what @sami-21 said

Answer 6

Thanks!