Find the Domain (x)dx

Problem

(∫_^)(x*d(x))

Solution

1. Identify the function to be integrated, which is ƒ(x)=x

2. Apply the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C for n≠−1

3. Substitute n=1 into the power rule formula.

4. Simplify the expression to find the antiderivative.

5. Add the constant of integration C to represent the family of all possible antiderivatives.

Final Answer

(∫_^)(x*d(x))=(x2)/2+C

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