Question
Integrate (2+×-×^2)d×
Answers
GPT 3.5
To integrate (2+×-×^2) with respect to x, we can find the antiderivative of each term separately and then sum them up.
1. Integrate 2 with respect to x:
∫2 dx = 2x + C1
2. Integrate × with respect to x:
∫× dx = 1/2 x^2 + C2
3. Integrate -×^2 with respect to x:
∫-×^2 dx = -1/3 x^3 + C3
Putting it all together, the antiderivative of (2+×-×^2) with respect to x is:
2x + 1/2 x^2 - 1/3 x^3 + C
where C = C1 + C2 + C3 is the constant of integration.
1. Integrate 2 with respect to x:
∫2 dx = 2x + C1
2. Integrate × with respect to x:
∫× dx = 1/2 x^2 + C2
3. Integrate -×^2 with respect to x:
∫-×^2 dx = -1/3 x^3 + C3
Putting it all together, the antiderivative of (2+×-×^2) with respect to x is:
2x + 1/2 x^2 - 1/3 x^3 + C
where C = C1 + C2 + C3 is the constant of integration.