Question

Evaluate the following integral: (Question will be posted ASAP)

Answer 1

\[\int\limits_{1}^{2}\frac{ 2\ln x }{ x } dx\]

Answer 2

pull out the 2

\[2\int \frac{ln(x)}{x}dx\]

Answer 3

let u=ln(x), what is du/dx?

Answer 4

du/dx= 1/x am I right? ._.

Answer 5

yep so if you multiply by dx you get

\[du=\frac{1}{x}dx\]

Answer 6

putting that into the equatino you get
\[2\int udu\]

Answer 7

okay...

Answer 8

now integrate that and replace u with ln(x) after

Answer 9

if integrated becomes u^2?

Answer 10

ohhhh I think I get it now :) thank you so much!