Proofs involving logs

**Mathman87** · April 26th 2010, 04:22 AM

Can anyone show the following?:

$\int$ log(x)dx = xlog(x) - x

**Soroban** · April 26th 2010, 04:39 AM

Hello, Mathman87!

Can anyone show the following?:

. . $\int \ln x \,dx \;=\; x\ln x - x + C$

Integrate by parts . . .

. . $\begin{array}{ccccccc}u &=& \ln x && dv &=& dx \\ du &=& \frac{dx}{x} && v &=& x \end{array}$

We have: . $x\ln x - \int x\left(\tfrac{dx}{x}\right) \;\;=\;\;x\ln x - \int dx \;\;=\;\; x\ln x - x + C$

**Mathman87** · April 26th 2010, 05:36 AM

thank you! much easier than i thought :-)

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