∫x−111+x4−1/2dx is equal to

Let I=∫dxx111+x41/2=∫dxx11⋅x21+1/x41/2Let 1+1x4=t2 .  Then −4x5dx=2tdt⇒ I=∫dxx131+1/x41/2             =−14∫2tdtx8t             =−12∫t2−12dt            =−12∫t4−2t2+1dt           =−12t55−2t33+t+c, where t=1+1x4