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

Problem

(∫_^)(−ex*d(x))

Solution

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

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

(∫_^)(−ex*d(x))=−(∫_^)(ex*d(x))

3. Apply the exponential rule for integration, which states that the integral of ex is ex

−(∫_^)(ex*d(x))=−ex+C

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

Final Answer

(∫_^)(−ex*d(x))=−ex+C

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