Evaluate ∫ex(1x-1x2) dx - Mathematics and Statistics

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Sum

Evaluate  `int"e"^x (1/x - 1/x^2)  "d"x`

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Solution

Let I = `int"e"^x (1/x - 1/x^2)  "d"x`

Put f(x) = `1/x`

∴ f'(x) = `-1/x^2`

∴ I = `int"e"^x ["f"(x) + "f'"(x)]  "d"x`

= `"e"^x*"f"(x) + "c"`

∴ I = `"e"^x* 1/x + "c"`

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Chapter 1.5: Integration - Q.4

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