Answer:
[tex]e^{2n}x + C[/tex] (since n is assumed to be a constant when integrating with respect to x)
Step-by-step explanation:
You are integrating with respect to x, but [tex]e^{2n}[/tex] has no x-terms. Thus, it is considered a constant. The integral of any constant is equal to the constant multiplied by x.
Example: the integral of 2 is 2x, since the derivative of 2x is 2.
[tex]\int {e^{2n}} \, dx = e^{2n}x + C[/tex]
If you were integrating [tex]e^{2x}[/tex] with respect to x, it would look like this:
Since...
[tex]\frac{d}{dx} (e^{ax}) = ae^{ax}[/tex]
The integral of [tex]e^{ax}[/tex] is:
[tex]\int{e^{ax}} \, dx = \frac{e^{ax}}{a} + C[/tex]
[tex]\int {e^{2x}} \, dx = \frac{e^{2x}}{2} + C[/tex]
Note: C is a constant. It can be any number.
Answer: [tex]e^{2n}x + C[/tex] (since n is assumed to be a constant)
