Evaluate ∫sinx/(1+x^2)dx?

Question

Evaluate ∫sinx/(1+x^2)dx?
∫sinx/(1+x^2)dx
u = arctanx
du = 1/(1+x^2)dx
x = tanu
sinx=sin(tanu)
evaluate ∫sin(tanu)du
u = cosx
du = -sinx dx
cant get further

Answer 1

This is an improper integral involving trig functions. I'm also guessing that this is not an indefinite integral, but that it has limits going from 0 to ∞ or -∞ to ∞. It requires the use of complex variables and the residue theorem to integrate.

See if the link below helps you out.
http://math.fullerton.edu/mathews/c2003/IntegralsTrigImproperMod.html

Answer 2

this is not an elementary integration.