Find the Antiderivative 8x

Problem

(∫_^)(8*x*d(x))

Solution

1. Identify the integral form for the given expression, which is the power rule for integration.

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

3. Substitute n=1 into the formula, resulting in (8*x(1+1))/(1+1)

4. Simplify the expression by performing the arithmetic in the exponent and the denominator.

5. Divide the coefficient 8 by 2 to get the final coefficient.

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

Final Answer

(∫_^)(8*x*d(x))=4*x2+C

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