I'm having a tough time trying to do integration by parts with one of my limits being infinity. My Integral looks like:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_0^\infty x^z e^{-x} dx[/tex] with [tex] z = \frac{-1}{\pi}[/tex]

Now if I let [tex]u = e^{-x} [/tex] and [tex]dv = x^z dx[/tex],

I will have: [tex]du = -e^{-x} dx [/tex] and [tex] v = \frac{1}{z + 1} x^{z + 1}

[/tex] and so

[tex] uv - \int_0^\infty v du

= e^{-x} \frac{1}{z + 1} x^{z + 1} - \int_0^\infty \frac{1}{z + 1} x^{z + 1} -e^{-x} dx[/tex]

However, since one of the limit is infinity, the term

[tex] uv = e^{-x} \frac{1}{z + 1} x^{z + 1}[/tex] has a freakin infinity subbed in it. The answer is actually,

[tex] \frac{1}{z + 1} \int_0^\infty x^{z + 1} e^{-x} dx[/tex], which is what my integral part looks like. What am I doing wrong? Why do I get a term with infinity at the front?

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# Integration by parts when a limit is infinity.

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