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 and move it outside the integral.

(∫_^)(−e(−x)*d(x))=−(∫_^)(e(−x)*d(x))

2. Apply the integration rule for exponential functions of the form e(a*x) where (∫_^)(e(a*x)*d(x))=1/a*e(a*x)+C

−(∫_^)(e(−x)*d(x))=−((e(−x))/(−1))+C

3. Simplify the expression by canceling the negative signs.

−((e(−x))/(−1))+C=e(−x)+C

Final Answer

(∫_^)(−e(−x)*d(x))=e(−x)+C

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