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

Problem

(∫_^)(e(−2*x)*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=−2 into the integration formula.

4. Simplify the expression by writing the fraction clearly and adding the constant of integration C

Final Answer

(∫_^)(e(−2*x)*d(x))=−1/2*e(−2*x)+C

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