Evaluate the Integral integral of 6x-5 with respect to x

Problem

(∫_^)(6*x−5*d(x))

Solution

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

(∫_^)(6*x−5*d(x))=(∫_^)(6*x*d(x))−(∫_^)(5*d(x))

2. Apply the power rule for the first term, where (∫_^)(xn*d(x))=(x(n+1))/(n+1) and the constant rule for the second term.

(∫_^)(6*x*d(x))=6⋅(x2)/2

(∫_^)(5*d(x))=5*x

3. Simplify the coefficients and combine the terms.

6⋅(x2)/2=3*x2

4. Add the constant of integration C to represent the family of antiderivatives.

3*x2−5*x+C

Final Answer

(∫_^)(6*x−5*d(x))=3*x2−5*x+C

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