Question

Evaluate the integral from -inf to inf of
( 1 / (x^2 +1)^2 ) dx ?

Answer 1

First, do you know how to take the primitive?

Answer 2

Or rather, do you know improper integrals and simmetry?

Answer 3

Yes, improper integrals and symmetry.

Answer 4

Looks so arctany to me

Answer 5

I can show you how to solve this by an integral in the complex plane, but only if this is a complex analysis course. I think there's probably some way to do it with trig substitution though.

Answer 6

Yeah x = tanu should do the trick

Answer 7

You should get \(sec^{4}(u)\)

Answer 8

Actually as the function is even you should rewrite the integral first as \(\large2\int_{0}^{\infty}f(x)dx\)

Answer 9

Having trouble with the trig substitution?

Answer 10

is that (secxtanx )^2

Answer 11

Nom, no uh yea taking a bit

Answer 12

As you sunstitute \(x=tan(u)\) you get \(dx=sec^{2}(u)du\). Plugging in the substitution in the function we will have \((tan(u)^2+1\)). We recognize that the inside function as a fundamental trig relation, \(tan^{2}(u)+1=sec^2(u)\).

Answer 13

@Kainui, feel free to give your input, you're way better than me XD

Answer 14

Oh I am afk I have barely read the question it looks fine to me though!

Answer 15

Any advances so far?

Answer 16

so cos^2 x revaluate as a limit..

Answer 17

You're getting there!

Answer 18

I'll be afk for a bit.

Answer 19

Need I in Indeterminate form?

Answer 20

It blew up

Answer 21

Trading off into complex tinkering...

Answer 22

What does your integral look like as of right now?

Answer 23

Is the ans π/2?

Answer 24

gtg for now... later

Answer 25

hmmm... As @ChillOut aptly mentioned.. we will be using the substitution x = tan(u)...

Answer 26

That will give you dx = \(\sec^2 t \ dt\)...