Question

can anyone explain integration of exponential functions presuming that I have no previous knowledge of it. as a novice

Answer 1

the indefinite integral \[\int e^{f(x)}dx\] is given by \[\frac{1}{\frac{df}{dx}}e^{f(x)}\] So for example, if you want \[\int e^{3x^2+6x}\] since \[\frac{d}{dx}(3x^2 + 6x) = 6x+6\] we have \[\int e^{3x^2+6x} = \frac{1}{6x+6}e^{3x^2+6x}\]

Answer 2

I apologize -- I just realized that this is wrong. The formula I gave you will only work if f(x) is only linear in x (for example is f(x) = 6x). If this is not the case, the integral is typically more difficult.