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**1. solve the problem first finding an integrating factor of susceptible form.**

y(x+y)dx+(xy+1)dy=0

y(x+y)dx+(xy+1)dy=0

## Homework Equations

form: M(x,y)dx+N(x,y)dy=0

intigrating factor: e

^{int(1/n(dm/dy-dndx)dx}

## The Attempt at a Solution

u(x)=e

^{int(1/(xy+1)(y(x+y)d/dy-(xy+1)d/dx)dx}

this reduces to

e

^{int((x+y)/(xy+1))dx}

This is where I need help. my integration is not good. I know that if I can solve for the integrating factor then I can solve for the equation because it will be in exact form.

Thanks for any help.