Final answer:
The indefinite integral of 3/eˣ is computed by recognizing it as 3 * e^(-x) and using reverse chain rule, resulting in -3/eˣ + C, where C is the constant of integration.
Step-by-step explanation:
The question asks us to consider the indefinite integral of 3/eˣ. To solve an indefinite integral involving an exponential function, we typically apply rules of integration such as the reverse chain rule or integration by parts, if applicable. However, in this case, recognizing that the integral of this form, when the variable x is in the exponent base e, directly leads to -3/eˣ + C, where C represents the constant of integration. The division by eˣ is the same as multiplying by e^(-x), thus simplifying the integration process.
To provide a step-by-step explanation, we start by rewriting the integrand as 3 * e^(-x). Then, we integrate e^(-x) which equals to -e^(-x). Multiplying by the constant 3, the resulting integral is thus -3 * e^(-x) + C, which simplifies to -3/eˣ + C. This is because the antiderivative of e^u, where u is a linear function of x, is e^u / u' (according to the reverse chain rule), and since u' (the derivative of -x) is -1, the result of the integration is -1 times the antiderivative.