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u= 2ln(x)
du = 2/x

then

integral of 1/2*u*du

and

u srs?

or should I say u^2/2 srs?

don't get it, because the answer is \[\frac{ 1 }{3 }lnx ^{3}+c\]

i just don't know how to solve it

don't think you can write it like that...

yep

Were you replying to me or Algebraic?

you

Do you know your logarithm properties? for example\[\ln x ^{n}=n \ln x\]Do you know this property?

yeah it's supposed to be (ln(x))^2

@Callisto, it's the former.

For the first one, I don't think you can get (1/3)(lnx)^3 +C

nope:)

turn it to \[\int\limits_{?}^{?}\frac{ 1 }{ x } \times \ln x ^{2} dx\]

that clear it up @lambchamps ?

You see... That's why...

sorry it is the second guys

so it's
u = ln(x)
u^2 = (ln(x))^2
du = 1/x
go to town.

@calculusfunctions it's the second. based on what @Callisto have mentioned

@Algebraic! please continue

OK! so then we don't need the logarithm property I proposed earlier.

that's it man, plug em in and integrate.

@lambchamps, do you now what the derivative of\[y =\ln x\]is?

@calculusfunctions he or she is in calc. 2 so yeah probably. good question though.

dy = 1/x dx?

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

i mean (ln x)^2

OH, OK! Sorry, I see you did fix it.

sorry it's \[(\ln x)^{2}\]

Do you notice that the derivative of ln x is in the integrand? So then what should u equal?

don't know please do tell

is it the \[\frac{ (\ln x)^{n+1} }{ n+1 } ?\]

Here are your options. Do you think u should equal a). ln x or b). 1/x c). (ln x)²

the derivative of ln x is 1/x so i choose b

So what should u equal?

a?

Excellent!

and then

So now\[u =\ln x\]so then\[du =?\]

1/x

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

ok sorry

So now if you substitute u and du into your integral, what do you have?

@calculusfunctions effort appreciated.. thanks to both of you

sorry for interrupting .you may go on

@integralsabiti, thank you, no worries now that I know your intentions were genuine.

so I would need to find the dx then substitute the value to it?

ok calculausfunction after your done here would you help me on my problem pleases

Of course but let's hurry and finish this one first because I have to log out soon.

So what does the integral look like after substitution?

dx would be xdu?

so the 1/x in (ln x)^2/x would be cancelled?

@mikala, I'll help you right after I finish here.

because of the x.du

please tell me i'm right

Cancelled is a poor choice of words.

ok, but where did the 1/x go? the one below (ln x)^2

oh i'm sorry didn't see at first

yes

i see the 1/x dx

after finding that, then is the time to integrate, right?

Sorry, I don't know what happened there let me try again.

ok

Yes, now find the\[\int\limits_{}^{}u ^{2}du\]Can you do that please?

\[\frac{ 1 }{ 3 }u ^{3} + c\]

Right!

Now what's the final step?

then substitute

ln x right?

Yes so can you please write the final answer now?

\[\frac{ (\ln x)^{3} }{ 3 } + C\] ayt?

Perfect!!!

on more question is the c suppose to capitalized?

one*

The most commonly used ones are c and k.

thank you very much Sheldon Cooper you're the best

HAHAHA! @lambchamps, thank you very much! "The Big Bang Theory" is my favourite show!

i bet.. later dude

Later!