∫x−111+x212dx is equal to

∫x−111+x412dx=∫1+x4x11dx=∫x21+1x4x11dx=∫1+1x4x9dx=∫1+1x4x4x5dx Put 1+1x4=t2−4x5dx=2tdtdxx5=−24tdt=∫tt2−1−12tdt=−12∫t2t2−1dt=−12∫t4−t2dt=−12t55−t33+C=161x4+132−1101x4+152+C