Evaluate the Integral integral of e^(-8x) with respect to x

Problem

(∫_^)(e(−8*x)*d(x))

Solution

1. Identify the form of the integral, which is (∫_^)(e(a*x)*d(x)) where a=−8

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

3. Substitute a=−8 into the formula.

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

Final Answer

(∫_^)(e(−8*x)*d(x))=−1/8*e(−8*x)+C

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