differential equation
- Thread starter david
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- Apr 12, 2005
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Well, do it...
\(\displaystyle \int e^{-st}\cdot \cos(t) \;dt\)
\(\displaystyle = \int\cos(t) \; d(\frac{e^{-st}}{-s})\)
\(\displaystyle = \cos(t)\cdot \frac{e^{-st}}{-s} - \int\frac{e^{-st}}{-s} \;d(\cos(t))\)
\(\displaystyle = \cos(t)\cdot \frac{e^{-st}}{-s} + \int\frac{e^{-st}}{-s}\cdot\sin(t) \;dt\)
Okay, there is the first pass. Now, do it again. What coudl be more fun!
\(\displaystyle \int e^{-st}\cdot \cos(t) \;dt\)
\(\displaystyle = \int\cos(t) \; d(\frac{e^{-st}}{-s})\)
\(\displaystyle = \cos(t)\cdot \frac{e^{-st}}{-s} - \int\frac{e^{-st}}{-s} \;d(\cos(t))\)
\(\displaystyle = \cos(t)\cdot \frac{e^{-st}}{-s} + \int\frac{e^{-st}}{-s}\cdot\sin(t) \;dt\)
Okay, there is the first pass. Now, do it again. What coudl be more fun!