Evaluate the Integral integral of 1/(e^x) with respect to x

Problem

(∫_^)(1/(ex)*d(x))

Solution

1. Rewrite the integrand using negative exponents to make it easier to integrate.

1/(ex)=e(−x)

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

a=−1

3. Apply the rule of integration for e(−x) by dividing by the coefficient of x

(∫_^)(e(−x)*d(x))=(e(−x))/(−1)+C

4. Simplify the expression by moving the negative sign to the front and optionally rewriting the negative exponent as a fraction.

−e(−x)+C=−1/(ex)+C

Final Answer

(∫_^)(1/(ex)*d(x))=−1/(ex)+C

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