Math

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step 1:
x = integral(from 0 to v) dv/(z^2-v^2)

step 2:
x = 1/2z ln((q+v)/(q-v))

How do you get from step 1 to step 2 ?

  • Math -

    The indefinite integral of
    dv/(z^2-v^2),
    with z being a constant, is
    [1/(2z)]log[(z+v)/(z-v)]
    Evaluate that at v=v' and subtract the value for v=0, to get the definite integral.

    The method of partial fractions can used to get the integral. It involves rewriting 1/[(z^2-v^2} as
    [1/(2z)][1/(z+v) - 1/(z-v)]

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