Question

integrate: 1/ (sqrt(9+x^2))
Award and Fan!! Help please! :)

Answer 1

Trig substitution: \(x=3\tan u\)

Answer 2

i never learned that method :/ because the teacher was like that's not on the AP test apparently

Answer 3

Then \(dx=3\sec^2u ~du\), so the integral becomes
\[\int\frac{dx}{\sqrt{9+x^2}}=\int\frac{3\sec^2u}{\sqrt{9+\left(3\tan u\right)^2}}~du=\int\frac{3\sec^2u}{\sqrt9\sqrt{1+\tan^2 u}}~du\]

Answer 4

Does the method make sense here?

Answer 5

Depending on the form of the quadratic in these types of integrals, you have to choose the right trig sub in order to apply the corresponding Pythagorean identity.

Answer 6

sorta i'll figure it out thanks man..but is there another way to do this or no?

Answer 7

Not that I'm aware of, unfortunately... Substituting algebraically won't work, and integration by parts also won't work (I think). I've never handled partial fractions that contain a radical function, so that's a possibility. Otherwise, you can try rewriting the integrand as a series, but that method would be nothing if not tedious.