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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
ok sorry
 one year 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?
 one year 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!
 one year ago

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

integralsabiti Group TitleBest ResponseYou've already chosen the best response.0
sorry for interrupting .you may go on
 one year 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.
 one year 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.
 one year 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?
 one year 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
 one year 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\[\int\limits_{}^{}\frac{ (\ln x)^{2} }{ x }dx\]
 one year 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.
 one year ago

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

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

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

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

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

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

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

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

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

lambchamps Group TitleBest ResponseYou've already chosen the best response.2
after finding that, then is the time to integrate, right?
 one year 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\[\int\limits_{}^{}u ^{2}du\]
 one year ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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