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Math Help - integral

  1. #1
    Member akhayoon's Avatar
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    integral

     \int \sqrt {\frac{1}{t^{2}}+4+4t^{2}}dt

    apparently reduces to  \int( \frac{1}{t}+2t)dt

    how is this possible? I tried simplifying and stuff but no result on my end...
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  2. #2
    Junior Member roy_zhang's Avatar
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    Realize that 4t^4+4t^2+1=(2t^2+1)^2.


    Roy
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by akhayoon View Post
     \int \sqrt {\frac{1}{t^{2}}+4+4t^{2}}dt

    apparently reduces to  \int( \frac{1}{t}+2t)dt

    how is this possible? I tried simplifying and stuff but no result on my end...
    \frac 1{t^2} + 4 + 4t^2 = \frac 1{t^2} (1 + 4t^2 + 4t^4) ...........now factorzie

    = \frac 1{t^2}(2t^2 + 1)^2

    i think you can take it from here
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