Can anyone show the following?:
$\displaystyle \int$log(x)dx = xlog(x) - x
Hello, Mathman87!
Integrate by parts . . .Can anyone show the following?:
. . $\displaystyle \int \ln x \,dx \;=\; x\ln x - x + C$
. . $\displaystyle \begin{array}{ccccccc}u &=& \ln x && dv &=& dx \\ du &=& \frac{dx}{x} && v &=& x \end{array}$
We have: .$\displaystyle x\ln x - \int x\left(\tfrac{dx}{x}\right) \;\;=\;\;x\ln x - \int dx \;\;=\;\; x\ln x - x + C$