To find the integral of the function ax^2 + bx + c with respect to x, you can integrate each term separately.

The integral of ax^2 dx is (a/3)x^3. This comes from the power rule of integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1).

The integral of bx dx is (b/2)x^2. This also comes from the power rule, with n=1.

The integral of c dx is cx, since the integral of a constant is just the constant times the variable of integration.

So, the integral of ax^2 + bx + c dx is (a/3)x^3 + (b/2)x^2 + cx + C, where C is the constant of integration.

Question

To find the integral of the function ax^2 + bx + c with respect to x, you can integrate each term separately.

The integral of ax^2 dx is (a/3)x^3. This comes from the power rule of integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1).

The integral of bx dx is (b/2)x^2. This also comes from the power rule, with n=1.

The integral of c dx is cx, since the integral of a constant is just the constant times the variable of integration.

So, the integral of ax^2 + bx + c dx is (a/3)x^3 + (b/2)x^2 + cx + C, where C is the constant of integration.

Knowee AI · Accepted Answer

To find the integral of the function ax^2 + bx + c with respect to x, you can integrate each term separately.

The integral of ax^2 dx is (a/3)x^3. This comes from the power rule of integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1).

The integral of bx dx is (b/2)x^2. This also comes from the power rule, with n=1.

The integral of c dx is cx, since the integral of a constant is just the constant times the variable of integration.

So, the integral of ax^2 + bx + c dx is (a/3)x^3 + (b/2)x^2 + cx + C, where C is the constant of integration.

Find ∫(ax2+bx+c) dx