Evaluate the Integral integral of x^2 with respect to x

Problem

(∫_^)(x2*d(x))

Solution

1. Identify the form of the integral as a power of x which follows the general power rule for integration (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C

2. Apply the power rule by increasing the exponent by 1 changing 2 to 3

3. Divide the expression by the new exponent, which is 3

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

Final Answer

(∫_^)(x2*d(x))=(x3)/3+C

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