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April 13th, 2010, 12:10 PM   #1
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improper integral

[1,inf] (x^2+2x+5)/(x^3+x+1) dx

[0,1] (e^x)/sqrt(x) dx


I know both of them have to do with the p-integral

but I am not sure how to can break them down algebraically so they can be solve just the form like (1/x)^p
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April 13th, 2010, 03:37 PM   #2
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Re: improper integral

Quote:
Originally Posted by izseekzu
[1,inf] (x^2+2x+5)/(x^3+x+1) dx

[0,1] (e^x)/sqrt(x) dx


I know both of them have to do with the p-integral

but I am not sure how to can break them down algebraically so they can be solve just the form like (1/x)^p
The first integral diverges. The integrand ~ 1/x for large x, which is not integrable.

For the second integral, let u=sqrt(x) and see what you get.
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