Given the function f(x) = 1/(25x^4), we want to find the integral of this function with respect to x.
First, let's rewrite the function f(x) in terms of simpler exponents. Noting that x^4 in the denominator is equivalent to x^-4 in the numerator, we can write:
f(x) = 1/(25x^4) = (1/25)*x^-4
Now we integrate this function with respect to x. Recall that the integral of x^n dx with respect to x is given by (1/(n+1))*x^(n+1), for all real number values of n that are not equal to -1. Here, our n = -4.
So,
∫ f(x) dx = ∫ (1/25)*x^-4 dx
By applying the formula, we get:
∫ f(x) dx = (1/(25*(-4 + 1)))*x^(-4 + 1)
= -(1/75)*x^-3
= -1/(75x^3)
This is our result. Hence, the integral of the function f(x) = 1/(25x^4) with respect to x is -1/(75x^3).