Evaluate the Integral integral of 6e^(-7x) with respect to x

Problem

(∫_^)(6*e(−7*x)*d(x))

Solution

1. Identify the constant and move it outside the integral.

(∫_^)(6*e(−7*x)*d(x))=6*(∫_^)(e(−7*x)*d(x))

2. Apply the rule for the integral of an exponential function of the form e(a*x) which is (∫_^)(e(a*x)*d(x))=1/a*e(a*x)+C

a=−7

3. Substitute the value of a into the formula.

6*(∫_^)(e(−7*x)*d(x))=6*((e(−7*x))/(−7))+C

4. Simplify the expression by multiplying the constant and the fraction.

6*((e(−7*x))/(−7))+C=−6/7*e(−7*x)+C

Final Answer

(∫_^)(6*e(−7*x)*d(x))=−6/7*e(−7*x)+C

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