integral dx/(1+x ^4 )^5/4 =C+f(x) if f(x)=.......................................................................................................................

integral dx/(1+x^4)^5/4
= integral dx/x^5(1/x^4 + 1)
now 1/x^4 +1 = t
-4/x^5dx = dt
dx/x^5= -dt/4
so now integral -dt/4t^5/4
I= t^-1/4+c
= (1+ 1/x^4)^-1/4+c
therefore f(x)= (1+1/x^4)^-1/4.............. [ans]