How to integrate 1/(x^2*(x^4+1)^(3/4)) Ans: – (1+1/x^4)^(1/4)

Hi,

This one is very simple.
Whate ever is inside the root, you need to bring x in negetive power.
So take x^4 common from the root.
When it comes out of root it will become x^3 and the x^2 already present will make it x^5.

Now look inside the root, we have 1 + x^-4, Substitute this expression, differential is available outside the root.