IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

magiclko

Here's a question which was thr in full test 5 , fiitjee's aits

_{[ -1]}

^{[0 ]} [ (x² +2x) / { ln(x+1) } ]

m getting noway to solve this, help me out!!! the answer given is ln 3

shakirshafi12

i think that we should use
ln(1+x)=x-x^2+x^3/3--------infinity
and
(1-x)^(-1)=1+x+x^2+x^3.............infinty x<1
and then try

think so!
i even used properties and
i got
i=integral 0 to 1 (x^2-1)/ln x
i also wanna know how to get the answer
experts plzzz help!!!

gorakavipraveen

hey I got it Look at the answere(Indefinite and then apply the limits yourself)
answere is 1/3*(x+1)^2*ln(x+1)-ln(x+1)

gorakavipraveen

hey it looks not defined for lower limit. are you sure of question as i am with the answere????????

shakirshafi12

hey praveen it(ln(1+x)) is divided by and not multiplied as u have done

aditya_arora04

First of all, hi mansi, how are you ?

Now, lets come to the business part

The question can be done as follows :

_{[ -1]}^{[0 ]} [ x(x +1 +1) / { ln(x+1) } ]

_{[ -1]}^{[0 ]} [ x(x +1) / { ln(x+1) } ] + _{[ -1]}^{[0 ]}x / { ln(x+1) }

Now in both these parts, put t=x+1

So, x becomes t-1 and ln(x+1) can be substituted by e^t

Then use By parts and you'll have your answer.

Well, if you like the solution, i won't mind a salute !!!!!

gorakavipraveen

shakirshafi I have applied the same function boss. Look x^2+x and x+1 have a releavance. That has made my soolution easy

magiclko

Hey guys,first of all, dnt suggest a way for doing this, instead give the full solution, what hav u done, cuz i hav done evrything u hav all mentioned, but havnt got any answer, leav aside ln3, i hav given almost 1 hr to this, but havnt been successful!!!!

@ aditya,

hi aditya, m fyn, wat bout u???

well the question,..... ofcourse, u'll get a salute, but pls give me the full solution, cuz i hav done this, n later i got stuck!!! pls give the full solution, !!!

madhuri_goteti

hai multiply numerator and denominatior with 2 then 2ln(x+1)we get
now let (x+1)²=e^t ans solve i got solu. like that but if iam wrong plz say correct ans

AAKRITI

madhuri excellent, i was about to say the same thing

magiclko

hey madhuri, i wish if u cud post the solution here, cuz if we taking (x+1)^2= e^t, what we'll do for numerator????? pls post the solution!!!

AAKRITI

oh greatness, i was highly mistaken

this can never be integrated

mansi , you are right yaar

magiclko

yeah aakriti, thats what m trying to say, its not getting integrated !!!

madhuri_goteti

e^t-1 is tyhe numerator and dx value will be dt /e^t/2

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