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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    You should set ln(x) = u

  2. anonymous
    • 5 years ago
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    Then du=dx/x

  3. anonymous
    • 5 years ago
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    But x=e^u from the definition of u.

  4. anonymous
    • 5 years ago
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    So dx=e^(-u)du

  5. anonymous
    • 5 years ago
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    You then use integration by parts a couple of times.

  6. anonymous
    • 5 years ago
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    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.

  7. anonymous
    • 5 years ago
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    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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