Evaluate the Integral integral of 5e^z+4 with respect to z

Problem

(∫_^)(5*ez+4*d(z))

Solution

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

(∫_^)(5*ez+4*d(z))=(∫_^)(5*ez*d(z))+(∫_^)(4*d(z))

2. Factor out constants from the integrals to simplify the terms.

5*(∫_^)(ez*d(z))+4*(∫_^)(1*d(z))

3. Integrate each term using the basic integration rules (∫_^)(ez*d(z))=ez and (∫_^)(1*d(z))=z

5*ez+4*z+C

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

5*ez+4*z+C

Final Answer

(∫_^)(5*ez+4*d(z))=5*ez+4*z+C

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