Question Number 101808 by Ar Brandon last updated on 04/Jul/20

∫_(1/3) ^1 (((x−x^3 )^(1/3) )/x^4 )dx

Answered by Dwaipayan Shikari last updated on 04/Jul/20

∫_(1/3) ^1 ((x((1/x^2 )−1)^(1/3) dx)/x^4 )=−(1/2)∫_(1/3) ^1 ((−2)/x^3 )((1/x^2 )−1)^(1/3) dx=(1/2)∫_0 ^8 t^(1/3) dt=(3/8)[t^(4/3) ]_0 ^8 =6     {Assuming ((1/x^2 )−1)=t

Commented byAr Brandon last updated on 04/Jul/20

Cool 💞

Commented byDwaipayan Shikari last updated on 04/Jul/20

😛😃

Answered by bobhans last updated on 05/Jul/20

∫ (((x−x^3 )/x^(12) ))^(1/(3  ))  dx = ∫ (((1/x^(11) )−(1/x^9 )))^(1/(3  ))  dx  = ∫(1/x^3 ) (((1/x^2 )−1))^(1/(3  ))  dx = −(1/3)∫ (((1/x^2 )−1))^(1/3)  d((1/x^2 )−1)  = −(1/3)×(3/4) ((((1/x^2 )−1)^4 ))^(1/3)  + C    (Bob  )