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

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Sum

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"`

Notes

[Note: Answer in the textbook is incorrect.]

Concept: Methods of Integration: Integration by Parts
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