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Question
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
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Solution
Let I =`int "e"^x ((x - 1)/2x^2) "d"x`
= `1/2 int "e"^x (x/x^2 - 1/x^2) "d"x`
= `1/2 int "e"^x (1/x - 1/x^2) "d"x`
Take f(x) = `1/x`
f'(x) = `- 1/x^2`
`[int "e"^x ["f"(x) + "f"(x)] "d"x = "e"^x "f"(x) + "c"]`
∴ I = `1/2 "e"^x 1/x + "c"`
I = `"e"^x/(2x) + "c"`
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