Integral

[silk hamlet]

Can i have some help with this one?

[chilly tide]

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[silk hamlet]

taking the derivative of x^-1 i get log|x|

[azure depot]

The first term is a power function, so it can be integrated directly.
Use integration by parts for the second term.

[silk hamlet]

and for the second term im having problems

im not sure how to approach it

[azure depot]

Well, integration by parts, as I said.

[silk hamlet]

idk how to do it

[azure depot]

You mean in this case? Or that you don't know the approach at all?

[silk hamlet]

uhh

i dont have much xp with integration by parts

i know it has something to do with the product rule

[azure depot]

Ah, ok. We have:
∫(ln(2x)d, 1, e)
Take u = ln(2x), dv = dx.

[silk hamlet]

ooh wait thats the integration by parts thing

[azure depot]

Well, yeah. That's what me and you said.

[silk hamlet]

ok now?

[azure depot]

Then apply the formula.

[silk hamlet]

ohh

so then

i have to calculate du

but i have to substitute 2x by another letter?

why is the derivative of log(2x) = 1/x

i thought its 2/x cuz chain rule

[silk hamlet]

i still get it wrong bruh

i get xlog(2x) but there it should be xlog(2x)-x

[azure depot]

Can you show what you did?

[silk hamlet]

I hope u understand?

So ye rn im trying to understand why log(2x) isnt 2/x

And why when i put it correctly in i still get xlog(2x) and not xlog(2x)-1