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# Integration by substitution help watch

1. Integrate 2x/(2x-1)^2 using u=2x-1

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2. (Original post by SDavis123)
Integrate 2x/(2x-1)^2 using u=2x-1
And you have tried ... ... ...
3. (Original post by TenOfThem)
And you have tried ... ... ...
This is what I did:

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4. I suppose its clearer to see if I show the step I skipped

(Integral) x/(2x-1)^2 . 2dx

Then substitute

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5. (Original post by SDavis123)
This is what I did:
Fine until

Then you did nonsense
6. (Original post by TenOfThem)
Fine until

Then you did nonsense
But isn't it (u+1)/2u^2? Or is that the same as what you did brcause the 2 cancels with the du as du=2dx

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7. (Original post by SDavis123)
But isn't it (u+1)/2u^2? Or is that the same as what you did brcause the 2 cancels with the du as du=2dx
yep

but then you still did nonsense
8. (Original post by TenOfThem)
yep

but then you still did nonsense
but what's wrong with the canceling part?

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9. (Original post by SDavis123)
but what's wrong with the canceling part?

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Seriously?

Check this out

That is what you did
10. (Original post by TenOfThem)
Seriously?

Check this out

That is what you did
Argh I have no idea what to do

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11. (Original post by SDavis123)
Argh I have no idea what to do

12. (Original post by TenOfThem)

Wow I feel thick

Thanks for your help though

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13. (Original post by SDavis123)
Wow I feel thick

Thanks for your help though
np

sadly it is an error that I see time and time again
14. (Original post by TenOfThem)
np

sadly it is an error that I see time and time again
Just another question, am I correct up to here? I'm unsure if I might have made the same mistake

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15. you have multiplied by 2x rather than dividing by 2x when substituting for dx
16. (Original post by TenOfThem)
you have multiplied by 2x rather than dividing by 2x when substituting for dx
I'm not sure, my thinking was:

If I multiply by 2x I obtain 2x^4
I know du=2xdx
Therefore all I have to do is find x^3 in terms of u which would be (u-3/4)^3/2

Then I obtain an integral in terms of u:
(Integral) ((u-3/4)^3/2)/u^1/2 du

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17. (Original post by SDavis123)
I'm not sure, my thinking was:

If I multiply by 2x I obtain 2x^4
I know du=2xdx
Therefore all I have to do is find x^3 in terms of u which would be (u-3/4)^3/2

Then I obtain an integral in terms of u:
(Integral) ((u-3/4)^3/2)/u^1/2 du

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I do not really understand any of that

18. (Original post by SDavis123)
I'm not sure, my thinking was:

If I multiply by 2x I obtain 2x^4
I know du=2xdx
Therefore all I have to do is find x^3 in terms of u which would be (u-3/4)^3/2

Then I obtain an integral in terms of u:
(Integral) ((u-3/4)^3/2)/u^1/2 du

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dx=du/2x. You cant decide to multiply by 2x Thus its x^3/2x say. Which is 1/2(x^2). So take 1/2 out of the integral, leaving you with

Thank god
19. This is a pretty similar question, except here I made dx the subject and just substituted, is that ok to do?

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20. (Original post by SDavis123)
This is a pretty similar question, except here I made dx the subject and just substituted, is that ok to do?
TBH I do not know what you were doing previously

You want dx as the subject as that is what you are trying to replace

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