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Math Help - Help integration problem

  1. #1
    Junior Member
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    Help integration problem

    the question is (y^2)/(25+y^2) dy.

    here are my steps:
    a=5
    y=5tanx
    dy=5secx^2 dx

    [(5tanx)^2 * 5secx^2]/[25*(1+tanx^2)] dx
    = [(5tanx)^2 * 5secx^2]/[25*secx^2] dx
    =5tanx^2 dx
    im stuck here.

    I tried to use integration by parts to solve 5tanx^2 dx. but it didn't work out

    The final answer should be y-5arctan(y/5)+C which c is any constant
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  2. #2
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    Quote Originally Posted by questionboy View Post
    the question is (y^2)/(25+y^2) dy.

    here are my steps:
    a=5
    y=5tanx
    dy=5secx^2 dx

    [(5tanx)^2 * 5secx^2]/[25*(1+tanx^2)] dx
    = [(5tanx)^2 * 5secx^2]/[25*secx^2] dx
    =5tanx^2 dx
    im stuck here.

    I tried to use integration by parts to solve 5tanx^2 dx. but it didn't work out

    The final answer should be y-5arctan(y/5)+C which c is any constant

    y^2/(y^2+25) = [1 - 25/(y^2+25)] = [ 1 - 1/(1 +(y/5)^2)], and you have the sum of two almost immediate integrals

    Tonio
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  3. #3
    Super Member Matt Westwood's Avatar
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    Reading, UK
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    Quote Originally Posted by questionboy View Post
    the question is (y^2)/(25+y^2) dy.

    here are my steps:
    a=5
    y=5tanx
    dy=5secx^2 dx

    [(5tanx)^2 * 5secx^2]/[25*(1+tanx^2)] dx
    = [(5tanx)^2 * 5secx^2]/[25*secx^2] dx
    =5tanx^2 dx
    im stuck here.

    I tried to use integration by parts to solve 5tanx^2 dx. but it didn't work out

    The final answer should be y-5arctan(y/5)+C which c is any constant
    Try setting 5 \tan^2 x = 5 (\sec^2 x - 1) Integrating \sec^2 is easy because of what the differential of \tan is ...
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  4. #4
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    Quote Originally Posted by Matt Westwood View Post
    Try setting 5 \tan^2 x = 5 (\sec^2 x - 1) Integrating \sec^2 is easy because of what the differential of \tan is ...
    thank you very much

    5(secx^2-1) dx =5tanx-5x
    which x= arctan(y/5)
    5tanx-5arctan(y/5) since y=5tanx
    y-5arctan(y/5)

    I got it...Thank you very much
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