integrate dx/x(root x^4-1)

Given $\int$dx /(x root(x⁴ - 1))

Now multiply and divide by x in numerator and denominator we get,

 $\int$ x dx / (x² root(x⁴ -1))

Substitute t = x²

dt/dx=2x

dt/2=x dx
Now put this value ,

=1/2 $\int$ dt/(t root(t² -1)

= 1/2 sec^-1(t) + C

= 1/2 sec^-1 (x²) +C