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

Problem

(∫_^)(e(2*x)*d(x))

Solution

1. Identify the form of the integral, which is an exponential function with a linear exponent of the form e(a*x)

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

3. Substitute the constant a=2 into the formula.

4. Add the constant of integration C to represent the family of all possible antiderivatives.

Final Answer

(∫_^)(e(2*x)*d(x))=(e(2*x))/2+C

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