Maths C4 Integration - tricky question needing help

Hi there,

I'm having trouble with the following question:

Unparseable latex formula:

\[\textup{Show that }\int_{1}^{e}\frac{1}{x^2}\textup{ln}\textup{ }\textup{dx}=1-\frac{2}{e}\]\]

(^ I don't know why there's a "p" in there, please ignore it...)

I think I've got the answer of the intergration (by parts):

Unparseable latex formula:

\left [\frac{1}{3}x^{-3} \right ]_{1}^{e}\]

Which means when I put the limits in I get:

\frac{1}{3e^{3}}-\frac{1}{3}

I have no idea how to turn this into what they want. I might have got the integration wrong but have been over that many times.

Any help much appreciated, cheers!

Reply 1

Cephalus

You've integrated incorrectly.

Integrate by parts again

Reply 2

jhex6

Aggghhh, turns out I thought the integral of lnx was 1/x and not the other way round, so used the wrong parts.

Many thanks, Cephalus!

Reply 3

Cephalus

Original post by jhex6

Aggghhh, turns out I thought the integral of lnx was 1/x and not the other way round, so used the wrong parts.

Many thanks, Cephalus!

Lol its no problem. It happens sometimes :tongue:

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Maths C4 Integration - tricky question needing help

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