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Math Help - evaluate the integral Q2

  1. #1
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    evaluate the integral Q2

    integrate 1/(e^xsquareroot1-e^-2x)dx
    how i started it:
    u= 1-1/e^2x du= -2e^-2xdx

    integrate dx/[(-u +1)u^1/2]

    dont know how to integrate the above
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by twilightstr View Post
    integrate 1/(e^xsquareroot1-e^-2x)dx
    how i started it:
    u= 1-1/e^2x du= -2e^-2xdx

    integrate dx/[(-u +1)u^1/2]

    dont know how to integrate the above
    i assume you mean \int \frac 1{e^x \sqrt{1 - e^{-2x}}}~dx

    note that this is the same as

    \int \frac 1{\sqrt{e^{2x} - 1}}~dx = \int \frac {e^{2x}}{e^{2x} \sqrt{e^{2x} - 1}}~dx

    now, a substitution of u^2 = e^{2x} - 1 yields the integral

    \int \frac 1{u^2 + 1}~du

    i suppose you can take it from here. i leave it to you to fill in the steps i omitted
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