Hi everyone!
I am having trouble doing this integration by parts. Mine got really ugly and it doesn't seem like is should. Can y'all work this for me?
$\displaystyle \int\limits_{1}^{8} 5\cdot\frac{(\ln{x})^2}{x^3} dx$
Thanks!
Molly
Hi everyone!
I am having trouble doing this integration by parts. Mine got really ugly and it doesn't seem like is should. Can y'all work this for me?
$\displaystyle \int\limits_{1}^{8} 5\cdot\frac{(\ln{x})^2}{x^3} dx$
Thanks!
Molly
Yo, Molly.
Read my signature about how to increase your speed when integrating by parts.
Now, if you want to make it to the classic way, put $\displaystyle u=\ln^2x$ and $\displaystyle dv=\frac{dx}{x^3}.$ (You're gonna have to make another integration by parts after this one.)
let $\displaystyle t = \ln{x}$
$\displaystyle x = e^t$
$\displaystyle
dt = \frac{1}{x} \, dx
$
$\displaystyle
\int \frac{(\ln{x})^2}{x^2} \cdot \frac{1}{x} \, dx
$
substitute ...
$\displaystyle
\int \frac{t^2}{e^{2t}} \, dt
$
$\displaystyle
\int t^2 \cdot e^{-2t} \, dt
$
now use parts ... in fact, tabular integration works well.