Evaluate the Integral integral of e^(-x/2) with respect to x

Problem

(∫_^)(e(−x/2)*d(x))

Solution

1. Identify the form of the integral, which is an exponential function of the form (∫_^)(e(a*x)*d(x))

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

3. Substitute the constant a=−1/2 into the formula.

4. Simplify the coefficient by calculating the reciprocal of −1/2 which is −2

5. Add the constant of integration C

Final Answer

(∫_^)(e(−x/2)*d(x))=−2*e(−x/2)+C

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