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Mathematics 68 Online
OpenStudy (anonymous):

does anyoe know how to find the integral of (ln x )^2

OpenStudy (anonymous):

You should set ln(x) = u

OpenStudy (anonymous):

Then du=dx/x

OpenStudy (anonymous):

But x=e^u from the definition of u.

OpenStudy (anonymous):

So dx=e^(-u)du

OpenStudy (anonymous):

You then use integration by parts a couple of times.

OpenStudy (anonymous):

Since the integrand is u^2e^(-u), pick on the u^2 as the part in IBP that you differentiate. When you repeat the process, eventually the derivative will be zero, and you'll be done.

OpenStudy (anonymous):

Learn 'tabular integration by parts' http://en.wikipedia.org/wiki/Integration_by_parts You will be able to punch these out in a flash.

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