Question

Anti-derivative of 1/(4+x^2)^2 ?

Answer 1

trig sub

Answer 2

Yep, it's trig. Try substituting \(x=2\tan u\).

Answer 3

do you know trig sub?

Answer 4

i have to refresh myself on how to derive the triangles in order to figure out which trig sub it is rather than memorization. I learned a longgg time ago

Answer 5

How do you know by looking that it is trig sub?

Answer 6

the more integrals you see the more you'll notice .. usually i'll start of with trying to split stuff or rewrite it... if that doesn't wrk and it looks someone like a trig derivative like 1+x^2 or sqrt(1-x^2), then i do trig sub. I personally don't like doing trig sub.

Answer 7

Okay thanks

Answer 8

if you look up more info on trig subs they might show you how to derive the triangles that go with trig sub so that you can tell what substitution you need (acos(u), asin(u),atan(u)

Answer 9

@yakeyglee any other way to do this? Can a sin sub be used?

Answer 10

sin is trig function, but it's not the sub you want
Yaykeglee has given the correct substitution
\[x=2\tan\theta\implies dx=2\sec^2\theta d\theta\]make those substitutions and good luck, I'm too tired to go through it right now

here's a reference http://tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx

Answer 11

Sine won't work, since \(1+\sin^2x\) doesn't have a more simple form by trig identity.