Find the Antiderivative e^(3x)

Problem

(∫_^)(e(3*x)*d(x))

Solution

1. Identify the form of the integral, which is the exponential function 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=3 into the formula.

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

Final Answer

(∫_^)(e(3*x)*d(x))=(e(3*x))/3+C

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