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Evaluate the following. ∫[1logx-1(logx)2] dx - Mathematics and Statistics

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Question

Evaluate the following.

`int [1/(log "x") - 1/(log "x")^2]` dx

Sum
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Solution

Let I = `int [1/(log "x") - 1/(log "x")^2]` dx

Put log x = t

∴ x = et

∴ dx = edt

∴ I = `int "e"^"t" [1/"t" - 1/"t"^2]` dt

Put f(t) = `1/"t"`

∴ f '(t) = `(-1)/"t"^2`

∴ I = `int "e"^"t" ["f"("t") + "f" '("x")]` dt

`= "e"^"t"  "f"("t")` + c

∴ I = `"e"^"t" (1/"t") + "c" = "x"/(log "x")` + c

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Notes

The answer in the textbook is incorrect.

  Is there an error in this question or solution?
Chapter 5: Integration - EXERCISE 5.5 [Page 133]
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