Question

F(x)=5x^4-3x^2 Первообразование

Answer 1

F(x)=5x⁴-4x²

F(x)=5/5 *x^5-4*x³/3+C=

x^5-4x³/3+C

Answer 2

To find the primitive function (antiderivative) of the function F(x) = 5x^4 - 3x^2, we need to use the power rule of integration.

The power rule states that if we have a function of the form x^n, then its antiderivative is (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.

Applying the power rule to each term of F(x), we get:

∫(5x^4 - 3x^2) dx = (5/5)x^5 - (3/3)x^3 + C = x^5 - x^3 + C

Therefore, the primitive function of F(x) is:

F(x) = x^5 - x^3 + C, where C is an arbitrary constant.