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Math Help - Exponential Integral - Integration by Parts with Inverse Functions

  1. #1
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    Lightbulb Exponential Integral - Integration by Parts with Inverse Functions

    Can someone walk through this and let me know if everything is all right? I have a bad habit of making mistakes with my math and getting excited over nothing .

    You can find my work here: http://img9.imageshack.us/img9/4702/...279204d696.png


    Please post back whatever you find. I'd like to know if you feel it's valid, if it's invalid, why it's invalid, and I'd be glad to explain how I got any particular part.
    ...yeah I know, reusing variables is a nasty habit but you get the idea =-P.
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  2. #2
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    Krizalid's Avatar
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    When integrating by parts e^x\ln x, the RHS is wrong, it should be e^{x}\ln x-\int{\frac{e^{x}}{x}\,dx}.

    And well... no elementary primitive for this thing.

    (Please reduce the size of your image.)
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  3. #3
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    You even caught it with the e^x*dx that weren't supposed to be there ><. How did I not catch that?

    Thank you!
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