# Math Help - integral 2

1. ## integral 2

use substitution to evaluate the definite integral \int_e^e^2{dx\ x(lnx)^2}

2. Originally Posted by fastman390
use substitution to evaluate the definite integral \int_e^e^2{dx\ x(lnx)^2}

do you mean $\int_e^{e^2} \frac {dx}{x (\ln x)^2}$ ??

if so, the substitution you want is $u = \ln x$

3. Assuming it is $\int_e^{e^2} \frac {dx}{x (\ln x)^2}$, use $u = \ln x$. Thus $du = \frac{dx}{x}$. The bounds become $\ln(e)\to\ln(e^2) = 1\to 2$

Now you have $\int_1^2\frac{du}{u^2}$

If you need it:
Spoiler:

$\int_1^2\frac{du}{u^2} = \left(-\frac{1}{u}\right)\bigg|_1^2 = -\frac{1}{2}+1 = \frac{1}{2}$