how do you integrate
3-e^1?
that's just a number, so
∫3-e^1 dx = (3-e)x + c
I suspect a typo.
maybe you mean
( 3 - e)^1 dx ???
or maybe
3 dx - e^1 dx ???
anyway the power 1 changes nothing
so it is maybe
(3-e) dx
which is
(3-e) x + C ???
To integrate the function "3 - e^1," you can follow these steps:
Step 1: Identify the function parts:
- The constant term, which is "3".
- The exponential term, which is "e^1".
Step 2: Recognize the integral formula for an exponential function:
∫ e^x dx = e^x + C
Step 3: Apply the integral formula and integrate each term individually:
∫ (3 - e^1) dx = ∫ 3 dx - ∫ e^1 dx
- For the first term, integrating a constant yields:
∫ 3 dx = 3x + C1
- For the second term, using the integral formula mentioned earlier:
∫ e^1 dx = e^1 + C2
Step 4: Combine the results:
∫ (3 - e^1) dx = 3x + C1 - (e^1 + C2)
Step 5: Simplify the equation:
∫ (3 - e^1) dx = 3x - e^1 + (C1 - C2)
Step 6: Represent the combined constants as a single constant:
∫ (3 - e^1) dx = 3x - e^1 + C
where C = C1 - C2, which is a constant.
Therefore, the integral of "3 - e^1" is equal to 3x - e^1 + C.