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

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SUMMARY

The integral of (sinx)/(1+cos^2(x)) from 0 to infinity is convergent, with the solution yielding a value of π/4. The convergence can be established using the comparison test, as the integrand behaves similarly to sin(x) for large x. The antiderivative can be found using the substitution u=cos(x), which simplifies the evaluation of the limit as L approaches infinity.

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tbone413
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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.
 
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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?
 

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