I need some help integrating :

$\displaystyle \int e^{-|y|}e^{ty} dy $

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- Apr 7th 2008, 10:05 PMlllllintegral with absolute value
I need some help integrating :

$\displaystyle \int e^{-|y|}e^{ty} dy $ - Apr 7th 2008, 11:33 PMOpalg
You just have to split it up as a sum of two integrals, by considering saparately the intervals on which y is positive and negative:

$\displaystyle \int e^{-|y|}e^{ty}\, dy = \int_{y\leqslant0} e^{y}e^{ty}\, dy + \int_{y\geqslant0} e^{-y}e^{ty}\, dy = \int_{y\leqslant0} e^{(t+1)y}\, dy + \int_{y\geqslant0} e^{(t-1)y}\, dy$