# Thread: One differentiation question and one integration question.

1. ## One differentiation question and one integration question.

help with problem

$y = {e^x}{ln{x}}$

Find

$a) \frac {dy}{dx}$

$b) \int_{e}^{e^2} \frac {1-ln{x}}{xln{x}} dx$

2. Originally Posted by Beachball
help with problem

$y = {e^x}{ln{x}}$

Find

$a) \frac {dy}{dx}$

$b) \int_{e}^{e^2} \frac {1-ln{x}}{xln{x}} dx$
a) Use the product rule.

b) Substitute $u = \ln x$.

If you need more help, please show all your work and say where you're stuck.

3. im still having trouble with it.. ive tried the substitution but i couldnt quite get it.. would someone be able to post the step by step result?

4. Here's a kick off for you

$\int_{e}^{e^2} \frac {1-\ln{x}}{x\ln{x}} ~dx$

$u = \ln{x} \implies \frac{du}{dx}= \frac{1}{x}$

Now $\int\frac {1-\ln{x}}{x\ln{x}} ~dx = \int\frac{1}{x}\left(\frac {1-\ln{x}}{\ln{x}}\right) ~dx =\int \frac{1-u}{u}~du$

5. yea ive got that far.. but just stuck and dont know where togo after that. :/

6. $\frac{1-u}{u} = \frac{1}{u} - 1$

7. thankyou all so much