Evaluate the Integral integral of -e^x with respect to x

Problem

(∫_^)(−e^x*d(x))

Solution

1. Identify the constant factor in the integrand. The expression −e^x can be written as −1⋅e^x

2. Apply the constant multiple rule for integration, which allows the constant −1 to be moved outside the integral sign.

(∫_^)(−e^x*d(x))=−(∫_^)(e^x*d(x))

3. Apply the exponential rule for integration, which states that the integral of e^x is e^x

−(∫_^)(e^x*d(x))=−e^x+C

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

Final Answer

(∫_^)(−e^x*d(x))=−e^x+C

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