Integrate: ∫dx/[x^2(1+x^4)^3]
THIS IS A WRONG QUESTION GIVEN BY FIITJEE.... QUIT IT....
62i dont think this worked very well for me... it bcomes very complex..
i could think of one good solution.. but to many of u it may seem overwhelming.. Actually it is not..
break down the given fraction as a partial fraction! That, right now seems to be the only way out of the complexities involved here..
Some one who can give a better proof?
1I had done the integ in this way…
I) divided the num n deno with x^12
II) so we have ∫(x^-14)dx /(1 + x^(-4))^3
= ∫x^(-9) dx/ x^5(1+x^(-4))^3
III) let (1+x^(-4)) =t
=> -4 x^-5 dx =dt
So, I = (t-1)^(9/4) dt/(-4)( t^3)
….now I got stuck up here….
ny one integrate this one….
Or giv sum other method…
62i dont see a way out from here :(
I think u will have to goto partial fractions :(
That is what i feel...