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Use differentiation to verify the integration formulas

  1. Dec 1, 2005 #1
    ok, so my problem goes like this:

    I have that the integral of dx/((cx+a)(dx+b))=1/(ad-bc)lnabs((dx+b)/cx+a)) + C
    I have to use differentiation to verify the integration formulas.

    So far I've gotten to:

    D(1/(ad-bc)lnabs((dx+b)/cx+a)))=(1/ad-bc)((cx=a)/(dx+b)) => (cx+a)/((ad-bc)(dx+b))

    where do I go from here to get back to the original integration formula? :confused:
     
  2. jcsd
  3. Dec 1, 2005 #2

    Fermat

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    Homework Helper

    You differentiation is at fault.

    if you have F = ln{f(x)/g(x)}, then

    F = lnf(x) - lng(x)

    dF/dx = f'/f - g'/g

    where f' = df/dx, g' = dg/dx
     
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