Question

Найти одну из первообразных функции f(x)=5x^4+2x^3, заранее спасибо.

Answer 1

F(x)=5x⁴+2x³
F(x)=5x⁴⁺¹/(4+1)+2x³⁺¹/(3+1)+C
F(x)=x⁵+x⁴/2+C

Answer 2

Finding the Antiderivative of f(x) = 5x^4 + 2x^3

To find the antiderivative of the function f(x) = 5x^4 + 2x^3, we can use the power rule for integration. The power rule states that the antiderivative of x^n with respect to x is (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.

Applying the Power Rule: The antiderivative of 5x^4 with respect to x is (1/(4+1)) * x^(4+1) = (1/5) * x^5 + C1, where C1 is the constant of integration. The antiderivative of 2x^3 with respect to x is (1/(3+1)) * x^(3+1) = (1/4) * x^4 + C2, where C2 is the constant of integration.

Therefore, the antiderivative of f(x) = 5x^4 + 2x^3 is (1/5) * x^5 + (1/4) * x^4 + C, where C is the constant of integration.

Snippet: `: x / - ; . . . : , 2016. 342 . ISBN 978-5-9614-5588-5.`