Find the Antiderivative 2x^2

Problem

(∫_^)(2*x^2*d(x))

Solution

1. Identify the integral form for the power rule, which states that the antiderivative of x^n is (x^(n+1))/(n+1) for any n≠−1

2. Apply the constant multiple rule by moving the constant 2 outside of the integral.

(∫_^)(2*x^2*d(x))=2*(∫_^)(x^2*d(x))

3. Apply the power rule to the term x^2 by increasing the exponent by 1 and dividing by the new exponent.

2*(∫_^)(x^2*d(x))=2⋅(x^(2+1))/(2+1)

4. Simplify the expression and add the constant of integration C

2⋅(x^3)/3+C=(2*x^3)/3+C

Final Answer

(∫_^)(2*x^2*d(x))=(2*x^3)/3+C

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