Evaluate the Integral integral of e^(-6x) with respect to x

Problem

(∫_^)(e(−6*x)*d(x))

Solution

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

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

3. Substitute the value a=−6 into the formula.

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

Final Answer

(∫_^)(e(−6*x)*d(x))=−1/6*e(−6*x)+C

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