Find the Integral 1/(e^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. Apply the rule for integrating exponential functions of the form e(a*x) which is (∫_^)(e(a*x)*d(x))=1/a*e(a*x)+C

(∫_^)(e(−x)*d(x))=1/(−1)*e(−x)+C

3. Simplify the expression by moving the negative sign to the front and optionally rewriting the exponent.

−1*e(−x)=−e(−x)

Final Answer

(∫_^)(1/(ex)*d(x))=−e(−x)+C

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