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. Simplify the expression by placing the negative sign in front of the fraction.

Final Answer

(∫_^)(e^(−3*x)*d(x))=−1/3*e^(−3*x)+C

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