Question

Integrate (please show steps!):
e^-5x

Answer 1

we know that

\[\frac{d}{dx} e^{kx} = ke^{kx}\]

so doing this in reverse we get

\[\int\limits{e^{kx} }dx = \frac{e^{kx}}{k}\]

Answer 2

+ c of course

Answer 3

e^-5x dx

e^-5x / -5 +c

so it is -1/5*e^-5x + C

Answer 4

First assume that e^5x is the result of integration. Then differentiate e^-5x and obtain -5 * e^5x. So if the trial result is divided by -5 we have the solution which is:
(e^-5x)/-5

Answer 5

Plus C the constant of integration of course.