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Integration of Exponential Functions
About this document ... The following problems involve the integration of exponential functions. We will assume knowledge of the following well-known differentiation formulas : where , and where is any positive constant not equal to 1 and is the natural (base ) logarithm of . As you do the following problems, remember these three general rules for integration : where is any constant not equal to -1, where is any constant, and Because the integral where is any nonzero constant, appears so often in the following set of problems, we will find a formula for it now using u-substitution so that we don't have to do this simple process each time. so that or Now substitute into the original problem, replacing all forms of , and getting We now have the following variation of formula 1 The following often-forgotten, misused, and unpopular rules for exponents will also be helpful : and Most of the following problems are average. Integrate . Click HERE to see a detailed solution to problem 1. Integrate .

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