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Integrate e^2x/e^x 1....plzz note e^x 1 as a whole is the denominator

  • calculus - eh? -

    ok, what is "e^x 1" ?

  • calculus -

    .Sorry its e^x+1.....:P

  • calculus -

    If it is e^(2x)/(e^x + 1) the way you typed it, then the integral is

    e^c - ln(e^x + 1) + C

    if you meant:
    e^(2x)/e^(x+1) then it would simplify to

    e^(x-1) and the integral of that is simply

    e^(x-1) + c

  • calculus -

    Could u plzz tell it in detail...the 1st 1

  • calculus -

    let u = e^x+1.
    du = e^x dx

    and you have

    ∫(u-1)/u du = ∫ 1 - 1/u du = u - lnu = (e^x+1) - ln(e^x+1) + C
    by absorbing the +1 into the C, you end up with

    = e^x - ln(e^x+1) + C

  • calculus -

    ...u see the numrtr is e^2x and how can u write it as u-1?

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