can someone help me with this, it's been a while since i've integrated exponential functions.
$\displaystyle \int{\frac{e^t}{t}dt}$
The only way to integrate this is using a power series.
$\displaystyle \frac{e^t}{t}=\frac{1}{t}\left[1+t+\frac{t^2}{2}+\frac{t^3}{6}+...\right]=\frac{1}{t}+1+\frac{t}{2}+\frac{t^2}{6}+...$
You can integrate that term by term. The final answer will be:
$\displaystyle \ln t+\sum_{n=1}^{\infty}\frac{t^n}{n\cdot n!}$