Advertisement Remove all ads

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

Sum

Evaluate the following.

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

Advertisement Remove all ads

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 '(x) = `(-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

Notes

[Note: Answer in the textbook is incorrect.]

  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×