[MOVED] partial integration: int ye^xy dx= e^xy

tegra97

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Sep 2, 2006
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Hi was was doing some differential equations and need to refresh my skills on partial integration. int ye^xy dx= e^xy. Can someone explain this. Thanks a bunch!!!!
 
treat y as though it were a konstant ...
(in other words, let \(\displaystyle y = k\))

\(\displaystyle \L \int k e^{kx} dx\)

let \(\displaystyle \L u = kx\)
\(\displaystyle \L du = k dx\)

substitute ...

\(\displaystyle \L \int e^u du = e^u + C\)

back-substitute ...

\(\displaystyle \L e^{kx} + C\)
 
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