Question

S(X+1)(x-2)dx интеграл

Answer 1

Ответ:

$\int\limits {(x+1)(x-2)} \, dx =\int\limits {(x^{2}-x-2) } \, dx =\frac{x^3}{3}-\frac{x^2}{2} -2x+C$

Пошаговое объяснение:

Answer 2

To find the integral of the expression S(X+1)(X-2) with respect to x, we can use the rules of integration. First, let's expand the expression:

S(X+1)(X-2) = S(X^2 - 2X + X - 2) = S(X^2 - X - 2).

Now, we can integrate term by term. The integral of each term is as follows:

∫(X^2 - X - 2) dx = ∫X^2 dx - ∫X dx - ∫2 dx

To integrate each term, we use the power rule of integration:

∫X^2 dx = (1/3)X^3 + C1, where C1 is the constant of integration for this term. ∫X dx = (1/2)X^2 + C2, where C2 is the constant of integration for this term. ∫2 dx = 2X + C3, where C3 is the constant of integration for this term.

Now, combining the results:

∫(X^2 - X - 2) dx = (1/3)X^3 - (1/2)X^2 - 2X + C,

where C = C1 + C2 + C3 is the overall constant of integration.

So, the integral of S(X+1)(X-2) with respect to x is (1/3)X^3 - (1/2)X^2 - 2X + C.