Evaluate the Integral integral of e^(3x) with respect to x

Problem

(∫_^)(e(3*x)*d(x))

Solution

1. Identify the form of the integral, which is (∫_^)(e(a*x)*d(x)) where a=3

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

3. Substitute the value a=3 into the formula.

4. Add the constant of integration C to complete the indefinite integral.

Final Answer

(∫_^)(e(3*x)*d(x))=(e(3*x))/3+C

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