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Math Help - integration

  1. #1
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    integration

    can someone help me with this, it's been a while since i've integrated exponential functions.

    \int{\frac{e^t}{t}dt}
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by yaykittyeee View Post
    can someone help me with this, it's been a while since i've integrated exponential functions.

    \int{\frac{e^t}{t}dt}
    The only way to integrate this is using a power series.

    \frac{e^t}{t}=\frac{1}{t}\left[1+t+\frac{t^2}{2}+\frac{t^3}{6}+...\right]=\frac{1}{t}+1+\frac{t}{2}+\frac{t^2}{6}+...

    You can integrate that term by term. The final answer will be:

    \ln t+\sum_{n=1}^{\infty}\frac{t^n}{n\cdot n!}
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