Thread: [SOLVED] Calculus: Integration by substitution

1. [SOLVED] Calculus: Integration by substitution

Find by substitution: the integral e to e^2 of dx/x(lnx)^2

2. $\int_e^{e^2 } {\frac{{dx}}
{{x\left( {\ln (x)} \right)^2 }}} = \left. {\frac{{ - 1}}
{{\ln (x)}}} \right|_e^{e^2 }$

3. Hello,
Originally Posted by juicysharpie

Find by substitution: the integral e to e^2 of dx/x(lnx)^2
Just substitute $t=\ln(x)$

4. I'm sorry. I still don't understand...

5. It's basic stuff according to substitution method. What is exactly you don't get?

6. I found u=ln x. du/dx = 1/x and du= 1/x dx. I found the new limits, 1 (lower) 2 (upper). So the new equation is the integral from 1 to 2 of 1/u^2 du. How do I derivate that so that I can plug in 1 and 2 to solve? I tried ln u x ln u but I don't think that's correct because I did not get 1/2 like the answer is supposed to be...

7. Originally Posted by juicysharpie
I found u=ln x. du/dx = 1/x and du= 1/x dx. I found the new limits, 1 (lower) 2 (upper). So the new equation is the integral from 1 to 2 of 1/u^2 du.
$\int_1^2 {\frac{{du}}
{{u^2 }}} = \int_1^2 {u^{ - 2} du}
$

8. oh, i see...thanks for the help!!