Question

Find the integral of arctan((x^2)-1).
*Do I use the chain rule after I plug it in?
This is what I have so far:
(1)/((1)+((x^2)-1)^2)

Answer 1

You'll want to start with integration by parts, but be aware this is an incredibly ugly integral.

Answer 2

substitute x = sec theta

Answer 3

u sure you not missing anything in the integrand ?

Answer 4

perhaps it is "xarctan((x^2)-1)"

Answer 5

Yup.. let me draw it to make it easier:

Answer 6

http://www.wolframalpha.com/input/?i=%5Cint+arctan%28x%5E2-1%29+dx

Answer 7

doesnt look pleasant

Answer 8

What class is this for?

Answer 9

Calculus AB; I'm a junior in highschool

Answer 10

Unless you already know how to do partial fractions and integration by parts, and your teacher hates you, you probably read the integral wrong (or it was printed wrong).

Answer 11

AB doesn't do partial fractions or integration by parts if I recall correctly so there is no way you would be expected to do this.

Answer 12

Hm... That's odd.. How would I do the derivative of it then?

Answer 13

As @rsadhvika said, I think it is very likely that if this was an integral problem that it was meant to have a factor of \(x\) out front.

Answer 14

Taking the derivative of it isn't too bad, do you know the derivative of arctan?

Answer 15

Yes; isn't it (1)/(1+x^2) ?

Answer 16

Yeah, so just use the chain rule.

Answer 17

It makes more sense that you asked about the chain rule initially now.

Answer 18

okay, gotcha :) It was probably printed incorrectly as the integral instead of the derivative, so I'm just going to do the work for the derivative lol

Answer 19

yup, that's why I was trying to use the rule for the derivative :P

Answer 20

You should get
\[\frac{2x}{1+(1-x^2)^2}\]

Answer 21

Got it :P Thank you!