anonymous
  • anonymous
How can I integrate this
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
X^2+2xy-y^2/(x+y)^2
anonymous
  • anonymous
(X^2+2xy-y^2/(x+y)^2)dx
ganeshie8
  • ganeshie8
please take a screenshot of complete problem and post

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anonymous
  • anonymous
\[\frac{ (x ^{2}+2xy-y ^{2}) }{ (x+y)^2 } dx\]
anonymous
  • anonymous
integrate pls
anonymous
  • anonymous
sir @ganeshie8
ganeshie8
  • ganeshie8
is this part of an iterated integral (double integral) ?
anonymous
  • anonymous
Im just answering an exact differential equation and the last part to find my equation is to integrate that.
anonymous
  • anonymous
y are consider as constant
anonymous
  • anonymous
y are consider as a constant
anonymous
  • anonymous
@ganeshie8
freckles
  • freckles
I would probably write it like this: \[\int\limits_{}^{}(1-\frac{2y^2}{(x+y)^2}) dx\] then evaluate
freckles
  • freckles
notice: \[\frac{x^2+2xy-y^2}{(x+y)^2}=\frac{x^2+2xy+y^2 -2y^2}{(x+y)^2}=\frac{(x+y)^2-2y^2}{(x+y)^2}\]
anonymous
  • anonymous
I already got that I use long division
freckles
  • freckles
u=x+y then du=dx
freckles
  • freckles
\[\int\limits_{}^{}1 dx-2y^2 \int\limits \frac{1}{(x+y)^2} dx\]
ganeshie8
  • ganeshie8
Hey @EinsteinMorse if you're solving an exact differential equation, you cannot integrate it like this x and y are dependent
anonymous
  • anonymous
yeeaah thanks . I wanted to confirm my answwer
ganeshie8
  • ganeshie8
`y are consider as constant` how do you know ?
anonymous
  • anonymous
I already got the same idea like what've frekles told . I just want confirmation on that.
anonymous
  • anonymous
y is constant because it is dx
ganeshie8
  • ganeshie8
may i know the starting differential equaiton ?
ganeshie8
  • 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.

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