Find the Antiderivative f(x)=e^(-2x)

Problem

(∫_^)(e(−2*x)*d(x))

Solution

1. Identify the form of the integral, which is (∫_^)(e(a*x)*d(x)) where a=−2

2. Apply the rule for the antiderivative of an exponential function with a linear exponent, which states (∫_^)(e(a*x)*d(x))=1/a*e(a*x)+C

3. Substitute a=−2 into the formula to find the specific antiderivative.

4. Simplify the expression by writing the fraction clearly.

Final Answer

(∫_^)(e(−2*x)*d(x))=−1/2*e(−2*x)+C

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