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Math Help - evaluate the infinte integral as an infinite series

  1. #1
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    evaluate the infinte integral as an infinite series

    the integral is

    3[int.] e^x - 1 / 8x

    Im not sure what exactly its asking me... infinite integral using infinite series??

    i know that e^x = [Sum.]n=0 to infinite x^n / n!

    but i dont know what comes next or even if i have to use that??

    An explanation about how to go about solving this would be great
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  2. #2
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    e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ...

    e^x - 1 = x + \frac{x^2}{2!} + \frac{x^3}{3!} + ...

    \frac{e^x - 1}{8x} = \frac{1}{8}\left(1 + \frac{x}{2!} + \frac{x^2}{3!} + ... \right)

    now integrate the series on the RHS term for term ...
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  3. #3
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    Thank you!
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