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CALC

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Evaluate the integral: the integral of [5e^(2t)]/[1+4e^(2t)]dt. I used u sub and let u=e^2t and got 5/2arctan(e^2t)+C. But this answer is incorrect. Please help. Thanks

  • CALC - ,

    There are certain pattern that you should recognize in derivatives

    e.g. if y = ln(anything)
    then dy/dx = derivative(anything)/anything

    I noticed that the derivative of the denominator appears at the top, differing only in a constant

    so let's start with
    y = ln(1 + 4e^(2t))
    dy/dt = 8e^(2t)/(1 + 4e^(2t) )

    instead of the 5 I need on top I see an 8

    so how about

    y = (5/8)ln(1 + 4e^(2t) ) + C

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