Evaluate the Integral integral of e^t with respect to t

Problem

(∫_^)(e^t*d(t))

Solution

1. Identify the integrand as the natural exponential function e^t

2. Apply the rule for the integral of the exponential function, which states that the derivative and integral of e^t are both e^t

3. Add the constant of integration C to represent the family of all possible antiderivatives.

Final Answer

(∫_^)(e^t*d(t))=e^t+C

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