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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
start by factoring
 one month ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
then break apart in to two pieces then integrate term by term
 one month ago

Elsa213 Group TitleBest ResponseYou've already chosen the best response.0
erm.... 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
 one month ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
@Elsa213 i am pretty sure that is some other answer to some other question
 one month ago

Elsa213 Group TitleBest ResponseYou've already chosen the best response.0
it was just an example
 one month ago

cutelilgirl Group TitleBest ResponseYou've already chosen the best response.0
log  (2x+1)(2x1)  ??
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
log a.b=loga +logb then integrate each at a time
 one month ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
right
 one month ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
now \[\int \log(2x+1)dx+\int (2x1)dx\]
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
you forgot log lol
 one month ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
then you should be done because you should have the integral of the log memorized
 one month ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
so i did \[\int \log(2x+1)dx+\int \log(2x1)dx\]
 one month ago

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

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
yes continue this way
 one month ago

cutelilgirl Group TitleBest ResponseYou've already chosen the best response.0
ok thanks @xapproachesinfinity and @satellite73
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
you should know what is int logxdx
 one month ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i 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
 one month ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i would say this integral looks nothing like that at all
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
satellite you assumed that the expression will take positive values only you need the absolute value theere
 one month ago

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

cutelilgirl Group TitleBest ResponseYou've already chosen the best response.0
yes the  4x^2 1  was there
 one month ago

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

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
yes i doesn't :)
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
it*
 one month ago

cutelilgirl Group TitleBest ResponseYou've already chosen the best response.0
or dx/x^2a^2
 one month ago

satellite73 Group TitleBest 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
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
@satellite73 , any reason why you took off absolute values?
 one month ago

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

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
laziness is all that and the stupid \(+ c\) got omitted as well
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
but you excluded the negative values?
 one month ago

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

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
wolfram is crazy hehe
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
i say the absolute value cannot be taken off. as we are excluding negative interval here
 one month ago

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Integration by parts should even work for the first way this expression appears
 one month ago

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

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
i agree. i looks that the answer would look much simpler
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
x/(2x1)(2x+1) partial fraction here
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
the other part is good xlog4x^21
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Whenever 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) \[=x \ln(f(x))\int\limits_{}^{}x \frac{f'(x)}{f(x)} dx\]
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
so far it looks nice to me
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
where did you get that @xapproachesinfinity ?
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
dw:1408559618618:dw
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
from by part integration
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
this now going to that expression she wrote as the answer!
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I don't see where that integral comes from
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
i wonder if you forget f' on top dw:1408559852906:dw
 one month ago

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
derivative of ln(f) is equal to f'/f
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
yup you are right forgot that xD
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
it should be what you wrote above
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
@cutelilgirl are you still there?
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
8x^2/4x^21
 one month ago

cutelilgirl Group TitleBest ResponseYou've already chosen the best response.0
yes but this seems a little beyond me :(
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
have you talked about integration by parts?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
that is the only way i know how to do this problem
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
so i assume you have had it mentioned in class
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
is that a correct assumption
 one month ago

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
can't do partial fraction here
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
do you know how to evaluate \[\int \ln(x) dx ]
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\int\limits_{}^{} \ln(x) dx\]
 one month ago

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

xapproachesinfinity Group TitleBest ResponseYou've already chosen the best response.0
we need another integration by part? i guess
 one month ago
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