Evaluate the Integral integral of 3x-7 with respect to x

Problem

(∫_^)(3*x−7*d(x))

Solution

1. Apply the sum rule for integration, which allows the integral of a sum or difference to be split into separate integrals.

(∫_^)(3*x−7*d(x))=(∫_^)(3*x*d(x))−(∫_^)(7*d(x))

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

(∫_^)(3*x*d(x))=3⋅(x(1+1))/(1+1)

(∫_^)(3*x*d(x))=(3*x2)/2

3. Integrate the constant term using the rule (∫_^)(k*d(x))=k*x

(∫_^)(7*d(x))=7*x

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

(3*x2)/2−7*x+C

Final Answer

(∫_^)(3*x−7*d(x))=(3*x2)/2−7*x+C

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