Question Number 102065 by bramlex last updated on 06/Jul/20

∫ ((x^2  dx)/((1−x)(√x))) ?

Answered by PRITHWISH SEN 2 last updated on 06/Jul/20

∫((1−(1−x^2 ))/((1−x)(√x))) dx=∫(dx/((1−x)(√x))) −∫(((1+x))/(√x))dx  for the 1^(st)  part                  2^(nd)  part  (√x)=t⇒(dx/(√x)) = 2dt              (√x)=u⇒(dx/(√x)) =2du  =∫((2dt)/(t(1−t^2 )))−2∫(1+u^2 )du  =2∫(dt/t)+∫((2tdt)/(1−t^2 )) −2u−(2/3)u^3  +c_1   =ln((x/(1−x)))−2(√x) −(2/3)x(√x) +c  please check