Integrate x²-1/√x^4 +x²+1dx Help me pls to solve this

Let (x + 1/x)= y then (1-1/x²)dx= dy & x² +1/x² +1 = y²-1....

Integration can be written as( 1-1/x²)/(x² + 1/x² + 1)dx which can be written as dy/y²-1 which is standard integral and equal to (1/2)ln|(y-1)/(y+1)| + C