Question

solve the integral:
\[\int\limits_{0}^{\infty}((arctanx)/(1+x))dx\]

Answer 1

Is it 1+x or 1+x^2?

Answer 2

1 + x^2 sorry for that mistake.

Answer 3

I don't think it converges

Answer 4

This is very easy. Just substitute \(\tan^{-1}(x)\). The integral will be \(\frac{1}{2}(\tan^{-1}x)^+c\).

Answer 5

\[\frac{1}{2}\arctan^{2}x+c\]

Answer 6

ok gimme a sec, I'm doing it on paper

Answer 7

OK got it, thanks

Answer 8

But your integral is definite. So it would be \[\frac{1}{2}\arctan^{2}(x)|_0^{\infty}.\]

Answer 9

You're welcome.

Answer 10

Oh Cool, I thought 1 + x