Evaluate the Integral integral of x^2-5x+4 with respect to x

Problem

(∫_^)(x2−5*x+4*d(x))

Solution

1. Identify the integral as a sum of power functions, allowing 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) for n≠−1

3. Integrate the first term x2 to get (x3)/3

4. Integrate the second term −5*x to get −(5*x2)/2

5. Integrate the constant term 4 to get 4*x

6. Add the constant of integration C to the final expression.

Final Answer

(∫_^)(x2−5*x+4*d(x))=(x3)/3−(5*x2)/2+4*x+C

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