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    Hi I have a difficult double integral that I am trying to compute. In the link below you can see what it is that I have to show and what my calculations look like so far.

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    Is there any smart way to calculate

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    l e*(-x)/x * dx
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    (Original post by Christian87)
    Is there any smart way to calculate

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    No, not in terms of elementary functions.

    I really know nothing about how measures work, so although I do know how to do basic double integrals I can't really be of any help.
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    (Original post by Christian87)
    Hi I have a difficult double integral that I am trying to compute. In the link below you can see what it is that I have to show and what my calculations look like so far.

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    In consideration of your final term:

    If I understand this correctly.

    \displaystyle\int_1^{\infty}\int  _1^{\infty}ce^{-x_1x_2}\;dx_2dx_1=1

    by defintion(??? Missed all my measure theory classes long time ago due to v.longterm illness)

    So,

    \displaystyle\int_1^{\infty}\lef  t[-\frac{ce^{-x_1x_2}}{x_1}\right]_1^{\infty}}\;dx_1=1

    and \displaystyle\int_1^{\infty}\fra  c{ce^{-x_1}}{x_1}}\;dx_1=1

    Hence your final term evaluates to 1.
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    Hi, yeah, found out that since the final term is an integral of a density function it is equal to 1. A bit unfair of me not to mention that in my question :-)
 
 
 
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