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cutelilgirl
 9 months ago
how to integrate log  4x^21 dx ?
cutelilgirl
 9 months ago
how to integrate log  4x^21 dx ?

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satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1start by factoring

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1then break apart in to two pieces then integrate term by term

Elsa213
 9 months ago
Best ResponseYou've already chosen the best response.0erm.... integral 4x/(1+x^2) = I Let 1+x^2 = t ...........(1) > 2x = dt/dx > 2x dx = dt ...........(2) Now I = integral 2 [2x dx / (1+x^2) ] = integral 2 [dt / t ] since from (2) = 2 [integral dt / t ] = 2 (ln t) +c = 2 ln(1+x^2) + c We have integral 1/t dt = ln t +c Therefore I = 2 ln(1+x^2) +c where ln is log to the base e https://answers.yahoo.com/question/index?qid=20110416060345AAVswO7

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1@Elsa213 i am pretty sure that is some other answer to some other question

Elsa213
 9 months ago
Best ResponseYou've already chosen the best response.0it was just an example

cutelilgirl
 9 months ago
Best ResponseYou've already chosen the best response.0log  (2x+1)(2x1)  ??

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0log a.b=loga +logb then integrate each at a time

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1now \[\int \log(2x+1)dx+\int (2x1)dx\]

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0you forgot log lol

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1then you should be done because you should have the integral of the log memorized

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1so i did \[\int \log(2x+1)dx+\int \log(2x1)dx\]

cutelilgirl
 9 months ago
Best ResponseYou've already chosen the best response.0the answer given is : x log  4x^21  1/2 log  (2x1)/(2x+1)  .. will i get this answer this way ?

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0yes continue this way

cutelilgirl
 9 months ago
Best ResponseYou've already chosen the best response.0ok thanks @xapproachesinfinity and @satellite73

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0you should know what is int logxdx

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1i have no idea when you integrate you will get something then using the properties of the log you can change it in to many different forms don't get married to the answer in the book

cutelilgirl
 9 months ago
Best ResponseYou've already chosen the best response.0because this exercise was about the problems of integral dx / (a^2_x^2) type

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1i would say this integral looks nothing like that at all

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0satellite you assumed that the expression will take positive values only you need the absolute value theere

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0i would say this integral looks nothing like that at all === is this to my reply^_^

cutelilgirl
 9 months ago
Best ResponseYou've already chosen the best response.0yes the  4x^2 1  was there

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1i would say \[\int \log(4x^21)dx\] looks nothing like \[\int \frac{dx}{a^2x^2}\]

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0yes i doesn't :)

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1\[\int \log(x)dx=x\log(x)x\] so \[\int \log(2x+1)dx=\frac{1}{2}\left((2x+1)\log(2x1)(2x+1)\right)\] by a mental u sub second part is similar

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0@satellite73 , any reason why you took off absolute values?

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1damn typo \[\int \log(2x+1)dx=\frac{1}{2}\left((2x+1)\log(2x+1)(2x+1)\right)\]

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1or if you prefer \[\frac{1}{2}(2x+1)(\log(2x+1)1)\]

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1laziness is all that and the stupid \(+ c\) got omitted as well

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0but you excluded the negative values?

ganeshie8
 9 months ago
Best ResponseYou've already chosen the best response.0why wolfram is giving this mess http://www.wolframalpha.com/input/?i=%5Cint+log%28abs%284x%5E21%29%29

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0wolfram is crazy hehe

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0i say the absolute value cannot be taken off. as we are excluding negative interval here

satellite73
 9 months ago
Best ResponseYou've already chosen the best response.1wolfram gave that mess because of the sign problem here it is neater http://www.wolframalpha.com/input/?i= \int+log%284x^21%29

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0\(\Large \rm\color{midnightblue}{\int log(2x+1)(2x1)dx=\int log2x+1dx+\\ \int log2x1dx}\)

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1Integration by parts should even work for the first way this expression appears

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1integration by parts will be needed polynomial division partial fractions look like they are needed as well

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0i agree. i looks that the answer would look much simpler

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0x/(2x1)(2x+1) partial fraction here

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0the other part is good xlog4x^21

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1Whenever I see something that looks like \[\int\limits_{}^{}1 \cdot \ln(f(x)) dx \] one of my first instincts it to go with the integration by parts (assuming f>0) \[=x \ln(f(x))\int\limits_{}^{}x \frac{f'(x)}{f(x)} dx\]

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0so far it looks nice to me

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1where did you get that @xapproachesinfinity ?

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0dw:1408559618618:dw

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0from by part integration

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0this now going to that expression she wrote as the answer!

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1I don't see where that integral comes from

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1i wonder if you forget f' on top dw:1408559852906:dw

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0u=log(4x^21) ===> du=1/4x^21 dv=1 ====> v=x may be there is an error lol

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1derivative of ln(f) is equal to f'/f

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0yup you are right forgot that xD

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0it should be what you wrote above

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1@cutelilgirl are you still there?

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.08x^2/4x^21

cutelilgirl
 9 months ago
Best ResponseYou've already chosen the best response.0yes but this seems a little beyond me :(

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1have you talked about integration by parts?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1that is the only way i know how to do this problem

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1so i assume you have had it mentioned in class

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1is that a correct assumption

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0can't do partial fraction here

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1do you know how to evaluate \[\int \ln(x) dx ]

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{} \ln(x) dx\]

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1If you don't I can show you that may help you seeing this more simple integral evaluated first

xapproachesinfinity
 9 months ago
Best ResponseYou've already chosen the best response.0we need another integration by part? i guess
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