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anonymous

  • one year ago

How can I integrate this

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  1. anonymous
    • one year ago
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    X^2+2xy-y^2/(x+y)^2

  2. anonymous
    • one year ago
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    (X^2+2xy-y^2/(x+y)^2)dx

  3. ganeshie8
    • one year ago
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    please take a screenshot of complete problem and post

  4. anonymous
    • one year ago
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    \[\frac{ (x ^{2}+2xy-y ^{2}) }{ (x+y)^2 } dx\]

  5. anonymous
    • one year ago
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    integrate pls

  6. anonymous
    • one year ago
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    sir @ganeshie8

  7. ganeshie8
    • one year ago
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    is this part of an iterated integral (double integral) ?

  8. anonymous
    • one year ago
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    Im just answering an exact differential equation and the last part to find my equation is to integrate that.

  9. anonymous
    • one year ago
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    y are consider as constant

  10. anonymous
    • one year ago
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    y are consider as a constant

  11. anonymous
    • one year ago
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    @ganeshie8

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

  13. freckles
    • one year ago
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    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
    • one year ago
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    I already got that I use long division

  15. freckles
    • one year ago
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    u=x+y then du=dx

  16. freckles
    • one year ago
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    \[\int\limits_{}^{}1 dx-2y^2 \int\limits \frac{1}{(x+y)^2} dx\]

  17. ganeshie8
    • one year ago
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    Hey @EinsteinMorse if you're solving an exact differential equation, you cannot integrate it like this x and y are dependent

  18. anonymous
    • one year ago
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    yeeaah thanks . I wanted to confirm my answwer

  19. ganeshie8
    • one year ago
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    `y are consider as constant` how do you know ?

  20. anonymous
    • one year ago
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    I already got the same idea like what've frekles told . I just want confirmation on that.

  21. anonymous
    • one year ago
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    y is constant because it is dx

  22. ganeshie8
    • one year ago
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    may i know the starting differential equaiton ?

  23. ganeshie8
    • one year ago
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    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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