f(x)=x3+5x F(x)=5x3 F(x)=13x2+26

It looks like you’ve provided three different expressions, presumably for the same variable \( x \). Let's clarify and analyze them one by one:

1. \( f(x) = x^3 + 5x \): This is a polynomial function. You can analyze its characteristics such as roots, derivative, etc.

2. \( F(x) = 5x^3 \): This is also a polynomial function. If this is related to \( f(x) \), you could be looking for the relationship in terms of derivatives or integrals.

3. \( F(x) = 13x^2 + 26 \): This appears to be another expression for \( F(x) \). However, it seems inconsistent to have two different expressions for \( F(x) \) unless you meant different functions altogether.

Possible Interpretations:

• If you want to find the derivative of \( f(x) \), you can do so: \[ f'(x) = \frac{d}{dx}(x^3 + 5x) = 3x^2 + 5 \]

• If you want to set \( F(x) = 5x^3 \) equal to \( F(x) = 13x^2 + 26 \), you can equate them: \[ 5x^3 = 13x^2 + 26 \] This polynomial equation can be solved for \( x \).

• If you are looking for the integral of \( f(x) \), it would be: \[ \int f(x) \, dx = \int (x^3 + 5x) \, dx = \frac{x^4}{4} + \frac{5x^2}{2} + C \] where \( C \) is the constant of integration.

Please clarify what you would like to do with these functions, and I would be happy to assist!