help with problem
$\displaystyle y = {e^x}{ln{x}} $
Find
$\displaystyle a) \frac {dy}{dx} $
$\displaystyle b) \int_{e}^{e^2} \frac {1-ln{x}}{xln{x}} dx $
help with problem
$\displaystyle y = {e^x}{ln{x}} $
Find
$\displaystyle a) \frac {dy}{dx} $
$\displaystyle b) \int_{e}^{e^2} \frac {1-ln{x}}{xln{x}} dx $
Here's a kick off for you
$\displaystyle \int_{e}^{e^2} \frac {1-\ln{x}}{x\ln{x}} ~dx$
$\displaystyle u = \ln{x} \implies \frac{du}{dx}= \frac{1}{x}$
Now $\displaystyle \int\frac {1-\ln{x}}{x\ln{x}} ~dx = \int\frac{1}{x}\left(\frac {1-\ln{x}}{\ln{x}}\right) ~dx =\int \frac{1-u}{u}~du$