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Math Help - Evaluate Indefinite integral as an infinite series

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    Evaluate Indefinite integral as an infinite series

    Evaluate Indefinite integral as an infinite series

    Last edited by mr fantastic; April 16th 2010 at 05:49 AM. Reason: Restored deleted question
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    Quote Originally Posted by racewithferrari View Post
    Evaluate Indefinite integral as an infinite series

    \int\frac{e^x-1}{x}\,dx = \int\frac{\sum_{k=0}^\infty\frac{x^k}{k!}-1}{x}\,dx=\int\sum_{k=1}^\infty\frac{x^{k-1}}{k!}\,dx= \sum_{k=1}^\infty\int \frac{x^{k-1}}{k!}=\sum_{k=1}^\infty \frac{x^k}{k\cdot k!}+C
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