integrate

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what have you considered?
|dw:1442184148009:dw|
what is the derivative of: e^(kx) with respect to x? for some constant k

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ok, so this derivative looks similar to what we have, it differs by a sign right? lets alter its appearance some; multiply it by (-1/-1)
\[\int\frac{-1}{-1}\frac14e^{-x/4}dx\] \[\int\frac{1}{-1}\frac{-1}4e^{-x/4}dx\] \[\frac{1} {-1}\int\frac{-1}4e^{-x/4}dx\] or simply \[-\int-\frac{1}4e^{-x/4}dx\]
we know an antiderivative of the integral so, we should certainly be able to use it for a solution
u-subbing is a valid process, but i find that training yourself to see the possibilities of where it comes from is more conducive with timed tests :)
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Thank you so much @amistre64
good luck
put -x/4=t x=-4t dx=-4 dt \[I=\frac{ 1 }{ 4 }\int\limits e^t(-4~dt)=-e^t+c=-e ^{\frac{ -x }{ 4 }}+c\]

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