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anonymous

  • 5 years ago

can someone please show me how to find the integral of y^2/25+y^2

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  1. anonymous
    • 5 years ago
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    do you mean y^2/(25+y^2)? or (y^2/25) + y^2?

  2. anonymous
    • 5 years ago
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    the first one

  3. anonymous
    • 5 years ago
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    ok, did you get past the long division at the beginning which gives you 1- (25/y^2+25)?

  4. anonymous
    • 5 years ago
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    why do i have to use long division

  5. anonymous
    • 5 years ago
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    i would, you have same degree of y in numerator & denominator.

  6. anonymous
    • 5 years ago
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    oh yes you are correct

  7. anonymous
    • 5 years ago
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    long division gives 1 - (25/(y^2+25))...integral of 1 = y, integral of -25/(y^2+25) = -5arctan(y/5).....so the solution is y-5arctan(y/5)...

  8. anonymous
    • 5 years ago
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    can you please explain how you got the integral of -25/(y^2+25)

  9. anonymous
    • 5 years ago
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    25 * (1/(Y^2 + 5^2))--once you see the trig integrals enough, they just become easy to recognize.

  10. anonymous
    • 5 years ago
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    integral of 1/(x^2 + a^2) = (1/a)arctan(x/a)

  11. anonymous
    • 5 years ago
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    okay thank you

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spraguer (Moderator)
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