Ln: Integral

**dhiab** · July 28th 2009, 08:44 AM

Calculate :

**Chop Suey** · July 28th 2009, 09:10 AM

Split the integrals into:
$\int \frac{2}{x}\ln{(x)}~dx + \int \frac{1}{2}(\ln{(x)})^2~dx$

First integral is dealt with by the substitution $u = \ln{x}$

$\int \frac{1}{2}(\ln{(x)})^2~dx = \int \frac{1}{2}(x)'(\ln{(x)})^2~dx$

Second integral requires the use of integration by parts with $u = (\ln{(x)})^2$ and $v = x$

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