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[tex]

\int_{-\infty}^\infty \sin{x}\frac{1}{x}dx=\pi

[/tex]

Now I try integration by parts

[tex]

\int_{-\infty}^\infty \sin{x}\frac{1}{x}dx=[-\cos{x}\frac{1}{x}]_{-\infty}^\infty-\int_{-\infty}^\infty \cos{x}\frac{1}{x^2}dx = -\int_{-\infty}^\infty \cos{x}\frac{1}{x^2}dx = \infty

[/tex]

Why don't I get the same result?

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# Integration by parts

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