# Help! P3 Integration Q (Maths)

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#1
Hey, please could someone have a quick go at this Q because I only get half of the answer

Integrate (ln x)/(x^3) between limits e and 0

Now the answer is supposedly 1/4 - 3/(4e^2)
but I only get the -3/(4e^2) bit. I can't get the 1/4, I keep getting all these ln 0 and /0 which don't work so can someone see if they get this answer? Thanksssssss
0
17 years ago
#2
I get 3/16e^4
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17 years ago
#3
Wait ive done it wrong
0
17 years ago
#4
I get -1/3e^2(1-1/4e)
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17 years ago
#5
Wait Ive done it wrong again.
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17 years ago
#6
3/4e^2 I get
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#7
(Original post by confusedguy234)
3/4e^2 I get
same as i get but apparently there's still a 1/4 missing?? did u get ln 0 's and things/0 as well?
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17 years ago
#8
Yeh, just did it yet again and I got -1/4e^2. This is really confusing me now.
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17 years ago
#9
-3/4e^2. There we go..
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17 years ago
#10
(Original post by Sugaray)
Hey, please could someone have a quick go at this Q because I only get half of the answer

Integrate (ln x)/(x^3) between limits e and 0

Now the answer is supposedly 1/4 - 3/(4e^2)
but I only get the -3/(4e^2) bit. I can't get the 1/4, I keep getting all these ln 0 and /0 which don't work so can someone see if they get this answer? Thanksssssss
I think you mean e and 1.

Parts gives:

[-1/2 (ln(x))/x^2)] + 1/2 integral of 1/x^3. = -1/2e^2 + 1/4 - 1/4e^2 = 1/4 - 3/4e^2 = 1/4(1-3/e^2)
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#11
(Original post by theone)
I think you mean e and 1.

Parts gives:

[-1/2 (ln(x))/x^2)] + 1/2 integral of 1/x^3. = -1/2e^2 + 1/4 - 1/4e^2 = 1/4 - 3/4e^2 = 1/4(1-3/e^2)
Well the book says 0 so I assume it's wrong. They've already made 2 printing errors on the same page stupid OCR >.< lol thanks
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17 years ago
#12
(Original post by Sugaray)
Well the book says 0 so I assume it's wrong. They've already made 2 printing errors on the same page stupid OCR >.< lol thanks
For any k>0, the integral from k to e is

(e^2 - 3k^2 + 2e^2 ln(k))/(4e^2 k^2).

Call that I(k). Then I(1) = 1/4 - 3/(4e^2). Also, I(k) tends to -infinity as k tends to 0 from above. So the integral from 0 to e doesn't exist (the area under the curve is infinite).
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