Find the Integral 3x-2

Problem

(∫_^)(3*x−2*d(x))

Solution

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

(∫_^)(3*x−2*d(x))=(∫_^)(3*x*d(x))−(∫_^)(2*d(x))

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

(∫_^)(3*x*d(x))=3⋅(x2)/2

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

(∫_^)(2*d(x))=2*x

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

(3*x2)/2−2*x+C

Final Answer

(∫_^)(3*x−2*d(x))=(3*x2)/2−2*x+C

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