What is the Integral of -e^(-x)?

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SUMMARY

The integral of -e^(-x) is derived using u-substitution, where u = -x. The integral of e^u du equals e^u + C, and when applying this to e^(-x), the negative sign arises from the derivative of -x, which is -1. Thus, the integral becomes -e^(-x) + C. This method can be generalized; for any function f(x), the integral of e^(f(x)) requires dividing by the derivative f'(x) when f'(x) is not constant.

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Reading through this thread I can't help thinking to myself, "How many Mathematicians does it take to change a light bulb?"
 
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