Question

I REALLY DISLIKE INTEGRATION. Another one that has me stumped:

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ {1+4\sin^2x} }dx\]

Answer 2

I've tried every simple substitution possible--it's gotta be some trig substitution, right?

Answer 3

looks like arctangent or sommat

Answer 4

how would you know D= how would I know

Answer 5

because it is almost \[\frac{1}{1+x^2}\] only with x replaced by \(2\sin(x)\)

Answer 6

i am trying to think of an easy way to get it
wolfram tells me the answer, and gives me a method i do not like
it does involve arctangent as i suspected

Answer 7

oo, I tried making \[4\sin^2(x) = \tan^2(\theta)\] but it didn't work out for me. but that could just be because I'm working w/ the numbers wrong

Answer 8

but the wolfram method is very complicated
too complicated i think

Answer 9

i can tell you what it does if you like

Answer 10

I can see the worked solution using symbolab where they let x = arccot(u)

Answer 11

=D the file name

Answer 12

i considered just \(u=2\sin(x)\)

Answer 13

Ahh, their solution looks like something I'd be expected to do
Thank you for that

Answer 14

integration like this is boring and stupid
let the machine do it, it teaches you nothing

Answer 15

really wish my prof thought so too