Answer:
f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)
Explanation:
We can find the function f(x) by integrating f'(x) with respect to x:
â«f'(x) dx = â«(2/(x^3) + 4e^x + 5) dx
f(x) = -1/x^2 + 4e^x + 5x + C
To find the constant C, we can use the given initial conditions:
f(-1) = 1 = -1/(-1)^2 + 4e^(-1) - 5 + C
C = 1 + 1/1 - 4e^(-1)
f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)
Therefore, the function f(x) is:
f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)