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Math Help - please help with this integral?

  1. #1
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    please help with this integral?

    integral ln/sqroot of x dx?
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  2. #2
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    Sub u = \sqrt{x} and integrate by parts.
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  3. #3
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    Quote Originally Posted by andrewsx View Post
    integral ln/sqroot of x dx?
    The obvious substitution is u = \sqrt{x}. Do it. Now use integration by parts.
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  4. #4
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    \int \ln \left(\sqrt{x}\right) dx

    You can use integration by parts: \begin{array}{ll} u = \ln \left(\sqrt{x}\right) & dv = dx \\ du = \frac{1}{\sqrt{x}} \cdot \frac{1}{2\sqrt{x}} \ dx  = \frac{1}{2x} \ dx& v = x \end{array}
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  5. #5
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    Alternatively, you can just rewrite the integral as:
    \frac{1}{2} \int \ln{x} dx

    I think it's obvious what u and dv should be in this case.
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