Find the most general antiderivative of the function( check your answer by derivation) f(x) = 5/x^4

Question

Find the most general antiderivative of the function( check your answer by derivation) f(x) = 5/x^4

Answer 1

f(x) = 5/x⁴

"Find the most general antiderivative"---To me, this just means the indefinite integral.

I find it easier to write this kind of fractional expression like this:

f(x) = 5*x^-4

The antiderivative is the inverse of the power rule:

F(x) = ∫ f(x)dx = -5/3 * x^-3 + C (C is the constant of integration, which is what makes this the "general" solution.)

Take the derivative of this to verify that you get the original expression