Question

integrate

Answer 1

what have you considered?

Answer 2

what is the derivative of: e^(kx) with respect to x? for some constant k

Answer 3

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)

Answer 4

\[\int\frac{-1}{-1}\frac14e^{-x/4}dx\]
\[\int\frac{1}{-1}\frac{-1}4e^{-x/4}dx\]
\[\frac{1} {-1}\int\frac{-1}4e^{-x/4}dx\]
or simply
\[-\int-\frac{1}4e^{-x/4}dx\]

Answer 5

we know an antiderivative of the integral so, we should certainly be able to use it for a solution

Answer 6

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 :)