Find the Antiderivative x^2-14x-6

Problem

(∫_^)(x2−14*x−6*d(x))

Solution

1. Identify the integral as a sum of power functions.

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

3. Integrate each term individually:

(∫_^)(x2*d(x))=(x3)/3

(∫_^)(−14*x*d(x))=−14⋅(x2)/2=−7*x2

(∫_^)(−6*d(x))=−6*x

4. Combine the results and add the constant of integration C

Final Answer

(∫_^)(x2−14*x−6*d(x))=(x3)/3−7*x2−6*x+C

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