Question

How can I integrate this

Answer 1

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

Answer 2

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

Answer 3

please take a screenshot of complete problem and post

Answer 4

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

Answer 5

integrate pls

Answer 6

sir @ganeshie8

Answer 7

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

Answer 8

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

Answer 9

y are consider as constant

Answer 10

y are consider as a constant

Answer 11

@ganeshie8

Answer 12

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

Answer 13

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

Answer 14

I already got that I use long division

Answer 15

u=x+y
then
du=dx

Answer 16

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

Answer 17

Hey @EinsteinMorse if you're solving an exact differential equation, you cannot integrate it like this

x and y are dependent

Answer 18

yeeaah thanks . I wanted to confirm my answwer

Answer 19

`y are consider as constant`

how do you know ?

Answer 20

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

Answer 21

y is constant because it is dx

Answer 22

may i know the starting differential equaiton ?

Answer 23

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.