# Thread: Proofs involving logs

1. ## Proofs involving logs

Can anyone show the following?:

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

2. Hello, Mathman87!

Can anyone show the following?:

. . $\displaystyle \int \ln x \,dx \;=\; x\ln x - x + C$
Integrate by parts . . .

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

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

3. thank you! much easier than i thought :-)