Integrate ae^bx
![Integrate ae^bx](integrate-ae_bx/step-1.gif)
To integrate ae^bx, also written as ∫aebx dx, we notice that "a" is a constant multiplier.
![Take the constant multiplier outside of the integral.](integrate-ae_bx/step-2.gif)
We bring the constant multiplier outside of the integral; hence, we get a simpler version that is the same thing.
![Using the general rule for integrating e^bx dx](integrate-ae_bx/step-3.gif)
We use this general rule for integrating an exponential.
![Answer](integrate-ae_bx/step-4.gif)
Hence, the answer is this. The constant multiplier remains outside of the square brackets.
![Simplifying the answer.](integrate-ae_bx/step-5.gif)
We then simplify by removing the square brackets.
Examples
ae^bx2e^2x
3e^2x
4e^2x
5e^2x
6e^2x
7e^2x
8e^2x
8e^-2x
9e^2x
10e^2x