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how would i calculate the principle part of:

[tex]\int_{-\infty}^{\infty} \frac{cos(x)}{x^2} dx [/tex]

it seems like this would diverge at 0, which might be ok except that it also osciallates and goes to 0 at infinity, so it doesn't look like you could balance the infinity at 0 by extending the bounds to infinity. does this converge, and if so, how would i find the value?

Also, I put this into the Integrator thing(search for integrator if you dont know what im talking about), and it gave me the answer -cos(x)/x - SinIntegral(x). SinIntegral is finite at infinity, and 0 at 0, so doesnt this mean it diverges? does the fact that im looking for the principal part change this?

[tex]\int_{-\infty}^{\infty} \frac{cos(x)}{x^2} dx [/tex]

it seems like this would diverge at 0, which might be ok except that it also osciallates and goes to 0 at infinity, so it doesn't look like you could balance the infinity at 0 by extending the bounds to infinity. does this converge, and if so, how would i find the value?

Also, I put this into the Integrator thing(search for integrator if you dont know what im talking about), and it gave me the answer -cos(x)/x - SinIntegral(x). SinIntegral is finite at infinity, and 0 at 0, so doesnt this mean it diverges? does the fact that im looking for the principal part change this?

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