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1. Homework Statement

1. Homework Statement

Given the following vector field,

$$

\dfrac{2(x-1)\,dy - 2(y+1)\,dx}{(x-1)^2+(y+1)^2}

$$

how do I integrate :

The integral over the curve x^4 + y^4 = 1

x^4 + y^4 = 11

x^4 + y^4 = 21

x^4 + y^4 = 31

## Homework Equations

Green's theorem and related equations for line integrals.

## The Attempt at a Solution

None of the techniques I know seem to work for this problem and if there's a shortcut or trick I'm not seeing it.

There are multiple incorrect solutions available online, but no correct ones. I know that the integral over the first curve is 0 because one solution said they should all be 0 (because F is conservative, which it is not).

How do I parameterize this curve in a way that I can integrate the result?

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