Evaluate the Integral integral of 4x-5 with respect to x

Problem

(∫_^)(4*x−5*d(x))

Solution

1. Identify the integral as a sum of two terms, which allows for the use of the sum rule for integration.

2. Apply the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1) to the first term 4*x

3. Apply the constant rule for integration, which states that (∫_^)(k*d(x))=k*x to the second term −5

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

5. Simplify the expression by performing the division in the first term.

Final Answer

(∫_^)(4*x−5*d(x))=2*x2−5*x+C

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