Is the Integral of (sinx)/(1+cos^2(x)) convergent or divergent?

[tbone413]

Homework Statement

State whether the problem is convergent or divergent and if its convergent solve the integral. Integral from 0 to inf of (sinx)/(1+cos^2(x))dx

Homework Equations

there isn't really an equation for this, I don't think.

The Attempt at a Solution

Im not really sure how to even start this problem. I know it converges, and I know the answer is pi/4 (the book has the answer) but I am stuck on how to figure out that it A) converges and B) how to solve it.

*I know there are several tests you can use to test for convergence (ratio test, p test, etc.) but I am not sure which one applies here.

 

[Dick]

It doesn't converge. Find the antiderivative, use u=cos(x). Evaluate it between 0 and L and then let L->infinity. Does it approach a limit?