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Integration by Parts


Date: 5/24/96 at 9:19:11
From: Anonymous
Subject: integration

How do you integrate x^x? 

First, I tried changing x^x to e^xln x.

Then, I changed e^xln x to a Maclaurin series, which I then tried to
integrate. I ended up with such an intricate series of terms that 
I couldn't express it in series sum notation. Is there an easier way 
to do it, if it can even be done? I would really appreciate it if you 
could help.  Thank you.
                         - Anthony


Date: 6/14/96 at 1:8:32
From: Doctor Dave
Subject: Re: integration

Anthony,

I would use integration by parts. Choose u = lnx and dv = xdx. 
Find du by taking the derivative of lnx and find v by taking the 
anti-derivative of xdx. Then the integral of udv = uv - the integral 
of vdu.

-Doctor Dave,  The Math Forum
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Associated Topics:
High School Calculus

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