Final Answer:
The integral ∫(4⁴)ex dx is evaluated to be as (4^4)ex + C.
Step-by-step explanation:
The integral ∫(4⁴)ex dx can be solved by using the following steps:
Recognize the constant multiple rule:
The integrand consists of a constant multiple of another function. The constant multiple rule states that:
∫ (k * f(x)) dx = k * ∫ f(x) dx
where k is a constant.
In this case, k = 4^4 and f(x) = ex.
Apply the constant multiple rule:
∫(4⁴)ex dx = 4^4 ∫ ex dx
Integrate the function:
The integral of ex is known to be ex + C, where C is the constant of integration. ∫ ex dx = ex + C
Apply the result:
Substituting the result back into the previous step:
∫(4⁴)ex dx = 4^4 ∫ ex dx = 4^4 (ex + C)
Simplify the result:
Finally, simplify the expression to obtain the final answer:
∫(4⁴)ex dx = (4^4)ex + C