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Question
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
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Solution
Let I = `int e^x (1/x - 1/x^2)`dx
Put f(x) = `1/x`
∴ f '(x) = `1/x`
∴ I = `int e^x [f(x) + f '(x)]` dx
`= e^x * f(x) + c`
∴ I = `e^x * 1/x + c`
∴ I = `(e^x)/x + c`
Notes
The answer in the textbook is incorrect.
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