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$\int_0^\infty{x\tan x\over x^2+1}\cos(\tan^2x)\; dx$

I labored it, but I can't it. How can I solve this integral?

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    where is the labor ? – 2017-01-06

1 Answers 1

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The integrand has singularities at all odd multiples of $\pi/2$. There's no way this thing converges. I'm pretty sure that even just $\int_0^{\pi/2}$ diverges.

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    Good point, and since you are taking cos of infinity, its not just a pole, it seems to be an essential singularity. – 2017-01-06