Evaluate the Integral integral of 5x-7 with respect to x

Problem

(∫_^)(5*x−7*d(x))

Solution

1. Identify the integral as a sum of two separate terms using the linearity property of integration.

(∫_^)(5*x−7*d(x))=(∫_^)(5*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 to the first term.

(∫_^)(5*x*d(x))=5⋅(x2)/2

3. Apply the constant rule for integration, which states that (∫_^)(a*d(x))=a*x to the second term.

(∫_^)(7*d(x))=7*x

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

(5*x2)/2−7*x+C

Final Answer

(∫_^)(5*x−7*d(x))=(5*x2)/2−7*x+C

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