Evaluate the Integral integral of 2x+9 with respect to x

Problem

(∫_^)(2*x+9*d(x))

Solution

1. Apply the sum rule for integration, which allows the integral of a sum to be split into the sum of the integrals.

(∫_^)(2*x*d(x))+(∫_^)(9*d(x))

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

(∫_^)(2*x*d(x))=2⋅(x2)/2=x2

3. Apply the constant rule for the second term, where (∫_^)(a*d(x))=a*x

(∫_^)(9*d(x))=9*x

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

x2+9*x+C

Final Answer

(∫_^)(2*x+9*d(x))=x2+9*x+C

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