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Urgent help needed on CORE 4 Integration...

Hey guys,

I am stuck on this question and have tried everything, but I can't seem to solve it.

Say I is the integral... therfore I 2x divided by (2x-1)^2
With the substitution U= 2X-1

My workings out;
if U= 2X-1
DU/DX = 2
therefore DX = DU/2

U^2= (2x-1)^2
and finally U+1=2X

Then the integral is I U+1 divided by 2U^2
But then thats worst then the original... What do I do now?
Original post by J DOT A
Hey guys,

I am stuck on this question and have tried everything, but I can't seem to solve it.

Say I is the integral... therfore I 2x divided by (2x-1)^2
With the substitution U= 2X-1

My workings out;
if U= 2X-1
DU/DX = 2
therefore DX = DU/2

U^2= (2x-1)^2
and finally U+1=2X

Then the integral is I U+1 divided by 2U^2
But then thats worst then the original... What do I do now?


That's right. Divide each term by u^2 and integrate term by term.
Reply 2
Avatar for J DOT A
J DOT A
OP
Original post by Mr M
That's right. Divide each term by u^2 and integrate term by term.


Sorry what does that mean:s-smilie:... How do I do that?
u+12u2=u−12+u−22\frac{u+1}{2u^2} = \frac{u^{-1}}{2} + \frac{u^{-2}}{2}
Reply 4
Avatar for J DOT A
J DOT A
OP
Original post by Mr M
Unparseable latex formula:

\frac{u+1}{2u^2} = \frac{u^{-1}{2} + \frac{u^-2}{2}



aah the latex failed:/
Original post by J DOT A
aah the latex failed:/


blimey impatient soul - I fixed it
Reply 6
Avatar for J DOT A
J DOT A
OP
Original post by Mr M
u+12u2=u−12+u−22\frac{u+1}{2u^2} = \frac{u^{-1}}{2} + \frac{u^{-2}}{2}


AAHHHH I see! So you divded the U by 2U^2 and the +1 by 2U^2?

Absolute Legend! Thank you so much:smile:
Original post by J DOT A
AAHHHH I see! So you divded the U by 2U^2 and the +1 by 2U^2?

Absolute Legend! Thank you so much:smile:


You are welcome.
Reply 8
Avatar for Quadratic
Quadratic
9
It might also make it easier to take a factor of a half out of the integral too :P? But that's not necessary, just makes it a tad simpler ^^
Reply 9
Avatar for therealOG
therealOG
2
c4 is a bitch
Reply 10
Avatar for J DOT A
J DOT A
OP
Original post by Quadratic
It might also make it easier to take a factor of a half out of the integral too :P? But that's not necessary, just makes it a tad simpler ^^


just a quick question... if U=e^x, then what would e^-x become?

And yeah it is now you mention it:P
Reply 11
Avatar for Quadratic
Quadratic
9
Original post by J DOT A
just a quick question... if U=e^x, then what would e^-x become?

And yeah it is now you mention it:P


I could just tell you the answer but that wont help you. Just try thinking about another way to write e^-x so it has e^x in it :smile:

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