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lambchamps
 2 years ago
\[\int\frac{ (lnx) ^{2} }{ x }dx\]
lambchamps
 2 years ago
\[\int\frac{ (lnx) ^{2} }{ x }dx\]

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

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

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

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

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

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.3Alright, 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!

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.3First 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.

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

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

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

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

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

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

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.3Which 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.

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

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.3NO! 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.

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

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

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

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

calculusfunctions
 2 years ago
Best 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!

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

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

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

calculusfunctions
 2 years ago
Best 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.

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

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

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

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

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

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.3NO! 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?

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

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

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

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

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

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

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

calculusfunctions
 2 years ago
Best 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?

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

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

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

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

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

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

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

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

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

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.3That 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.

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

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

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