Find the Antiderivative 4x^2

Problem

(∫_^)(4*x2*d(x))

Solution

1. Identify the integral as a power rule problem, where the constant multiple 4 can be moved outside the integral.

(∫_^)(4*x2*d(x))=4*(∫_^)(x2*d(x))

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

4*(∫_^)(x2*d(x))=4⋅(x(2+1))/(2+1)+C

3. Simplify the expression by performing the addition in the exponent and the denominator.

4⋅(x3)/3+C

4. Combine the constant and the fraction to reach the final form.

(4*x3)/3+C

Final Answer

(∫_^)(4*x2*d(x))=(4*x3)/3+C

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