## anonymous one year ago How can I integrate this

1. anonymous

X^2+2xy-y^2/(x+y)^2

2. anonymous

(X^2+2xy-y^2/(x+y)^2)dx

3. ganeshie8

please take a screenshot of complete problem and post

4. anonymous

$\frac{ (x ^{2}+2xy-y ^{2}) }{ (x+y)^2 } dx$

5. anonymous

integrate pls

6. anonymous

sir @ganeshie8

7. ganeshie8

is this part of an iterated integral (double integral) ?

8. anonymous

Im just answering an exact differential equation and the last part to find my equation is to integrate that.

9. anonymous

y are consider as constant

10. anonymous

y are consider as a constant

11. anonymous

@ganeshie8

12. freckles

I would probably write it like this: $\int\limits_{}^{}(1-\frac{2y^2}{(x+y)^2}) dx$ then evaluate

13. freckles

notice: $\frac{x^2+2xy-y^2}{(x+y)^2}=\frac{x^2+2xy+y^2 -2y^2}{(x+y)^2}=\frac{(x+y)^2-2y^2}{(x+y)^2}$

14. anonymous

I already got that I use long division

15. freckles

u=x+y then du=dx

16. freckles

$\int\limits_{}^{}1 dx-2y^2 \int\limits \frac{1}{(x+y)^2} dx$

17. ganeshie8

Hey @EinsteinMorse if you're solving an exact differential equation, you cannot integrate it like this x and y are dependent

18. anonymous

yeeaah thanks . I wanted to confirm my answwer

19. ganeshie8

y are consider as constant how do you know ?

20. anonymous

I already got the same idea like what've frekles told . I just want confirmation on that.

21. anonymous

y is constant because it is dx

22. ganeshie8

may i know the starting differential equaiton ?

23. ganeshie8

I'm asking because I feel that you're doing it wrong.. your goal in solving a differential equation is to find the curve $$y$$, it is not constant, it is a function of x.