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

Problem

(∫_^)(e^(−x)*d(x))

Solution

1. Identify the integral as a basic exponential form (∫_^)(e^(a*u)*d(u)) where a=−1

2. Apply the rule for integrating e^(a*x) which states that (∫_^)(e^(a*x)*d(x))=1/a*e^(a*x)+C

3. Substitute a=−1 into the formula.

4. Simplify the expression by dividing by −1

Final Answer

(∫_^)(e^(−x)*d(x))=−e^(−x)+C

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