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Algebraic! Group TitleBest ResponseYou've already chosen the best response.3
u= 2ln(x) du = 2/x
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.3
integral of 1/2*u*du
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.3
or should I say u^2/2 srs?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
don't get it, because the answer is \[\frac{ 1 }{3 }lnx ^{3}+c\]
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
i just don't know how to solve it
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.3
don't think you can write it like that...
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Alright, do you know the substitution rule for integrals? Also do you know the derivatives of logarithm functions? If you do, then we're off to a great start!
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Were you replying to me or Algebraic?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
OK, so then when you see\[\int\limits_{}^{}\frac{ \ln x ^{2} }{ x }dx\]What do you see as the first potential step?
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Sorry to interrupt, is the question (i) \(\int \frac{lnx^2}{x}dx\) or (ii) \(\int \frac{(lnx)^2}{x}dx\)? They are different...
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Do you know your logarithm properties? for example\[\ln x ^{n}=n \ln x\]Do you know this property?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.3
yeah it's supposed to be (ln(x))^2
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
@Callisto, it's the former.
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
For the first one, I don't think you can get (1/3)(lnx)^3 +C
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
turn it to \[\int\limits_{?}^{?}\frac{ 1 }{ x } \times \ln x ^{2} dx\]
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.3
that clear it up @lambchamps ?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
the second @Callisto
 2 years ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
You see... That's why...
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
sorry it is the second guys
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.3
so it's u = ln(x) u^2 = (ln(x))^2 du = 1/x go to town.
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
@Callisto, you are right but @lambchamps, Is the question written correctly before we proceed further?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
@calculusfunctions it's the second. based on what @Callisto have mentioned
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
@Algebraic! please continue
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
OK! so then we don't need the logarithm property I proposed earlier.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.3
that's it man, plug em in and integrate.
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
@lambchamps, do you now what the derivative of\[y =\ln x\]is?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.3
@calculusfunctions he or she is in calc. 2 so yeah probably. good question though.
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
dy = 1/x dx?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Great, so then if\[\int\limits_{}^{}\frac{ (\ln x)^{2} }{ x }dx\]then in order to apply the substitution rule what should u equal?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
\[=\int\limits_{}^{}\frac{ 1 }{ x } \times \ln x ^{2} dx\]
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
i mean (ln x)^2
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
First of all you keep confusing the issue by writing\[\ln x ^{2}\]instead of\[(\ln x)^{2}\]They are not the same!\[(\ln x)^{2}\neq \ln x ^{2}\]Do you understand? So we're not going to get anywhere until this gaffe is resolved.
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
OH, OK! Sorry, I see you did fix it.
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
sorry it's \[(\ln x)^{2}\]
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Do you notice that the derivative of ln x is in the integrand? So then what should u equal?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
don't know please do tell
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
is it the \[\frac{ (\ln x)^{n+1} }{ n+1 } ?\]
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Here are your options. Do you think u should equal a). ln x or b). 1/x c). (ln x)²
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Which option do you think? a, b, or c? Just keep in mind that whichever option you choose, it's derivative must be in the integrand.
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
the derivative of ln x is 1/x so i choose b
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
NO! I said that the derivative of the chose option must be in the integrand. NOT the antiderivative of the option must be in the integrand.
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
So what should u equal?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Excellent!
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
and then
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
So now\[u =\ln x\]so then\[du =?\]
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
\[du =\frac{ 1 }{ x }dx\]OK?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
ok sorry
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
So now if you substitute u and du into your integral, what do you have?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
@integralsabiti, how is giving the solution helping the student who is trying to learn? I spent all this time trying to teach @lambchamps so that she can then do other similar problems with confidence, and you just came in wasted her time and my effort. NOT COOL!
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
@calculusfunctions effort appreciated.. thanks to both of you
 2 years ago

integralsabiti Group TitleBest ResponseYou've already chosen the best response.0
sorry for interrupting .you may go on
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
@integralsabiti, thank you, no worries now that I know your intentions were genuine.
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
@lambchamps, are you still there? I'm still waiting for your response to my last question regarding your problem.
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
so I would need to find the dx then substitute the value to it?
 2 years ago

mikala1 Group TitleBest ResponseYou've already chosen the best response.0
ok calculausfunction after your done here would you help me on my problem pleases
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
So what do you you now have after substituting\[u =\ln x\]and\[du =\frac{ 1 }{ x }dx\]into\[\int\limits_{}^{}\frac{ (\ln x)^{2} }{ x }dx\]
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Of course but let's hurry and finish this one first because I have to log out soon.
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
So what does the integral look like after substitution?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
dx would be xdu?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
NO! If \[u =\ln x\]and\[du =\frac{ 1 }{ x }dx\]then\[\int\limits\limits_{}^{}\frac{ (\ln x)^{2} }{ x }dx =\int\limits_{}^{}u ^{2}du\]Do you see how?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
so the 1/x in (ln x)^2/x would be cancelled?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
@mikala, I'll help you right after I finish here.
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
because of the x.du
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
please tell me i'm right
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
No, the\[\frac{ 1 }{ x }dx\]is being replaced with du because\[du =\frac{ 1 }{ x }dx\]Please tell me you see that.
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Cancelled is a poor choice of words.
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
ok, but where did the 1/x go? the one below (ln x)^2
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
oh i'm sorry didn't see at first
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
\[\int\limits\limits_{}^{}\frac{ (\ln x)^{2} }{ x }dx\]is exactly the same as\[\int\limits_{}^{}(\frac{ 1 }{ x }∙(\ln x)^{2})dx\]correct?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
i see the 1/x dx
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
after finding that, then is the time to integrate, right?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
So I replaced the factor of\[\frac{ 1 }{ x }dx\]with du because\[du =\frac{ 1 }{ x }dx Yes, now you may integrate\[\int\limits_{}^{}u ^{2}du\]
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Sorry, I don't know what happened there let me try again.
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Yes, now find the\[\int\limits_{}^{}u ^{2}du\]Can you do that please?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
\[\frac{ 1 }{ 3 }u ^{3} + c\]
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Right!
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Now what's the final step?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
then substitute
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
ln x right?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Yes so can you please write the final answer now?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
\[\frac{ (\ln x)^{3} }{ 3 } + C\] ayt?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Perfect!!!
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
on more question is the c suppose to capitalized?
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
That doesn't matter. C represents a constant. Whether you write c or C or k or K etc. is irrelevant. Just don't use x, y, or z.
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
The most commonly used ones are c and k.
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
thank you very much Sheldon Cooper you're the best
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
HAHAHA! @lambchamps, thank you very much! "The Big Bang Theory" is my favourite show!
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
i bet.. later dude
 2 years ago

calculusfunctions Group TitleBest ResponseYou've already chosen the best response.3
Later!
 2 years ago
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