I have attempted to solve this integration problem by parts but I have not been able to arrive at the final answer. Can anyone help?

Problem: integration of dx/[(1-2x)^2*(3-x)]

Answer: 1/[5*(1-2x)] + (1/25)*Ln[(2x-1)/(x-3)]

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- Mar 17th 2009, 12:03 AMgnameniIntegration of dx/[(1-2x)^2*(3-x)]
I have attempted to solve this integration problem by parts but I have not been able to arrive at the final answer. Can anyone help?

Problem: integration of dx/[(1-2x)^2*(3-x)]

Answer: 1/[5*(1-2x)] + (1/25)*Ln[(2x-1)/(x-3)] - Mar 17th 2009, 12:21 AMADARSH
- Mar 17th 2009, 01:14 AMgnameni
I do not think that

dx/(1-2x)^2 equals -1/4(dx/(x-1/2)^2) - Mar 17th 2009, 01:20 AMADARSH
- Mar 17th 2009, 01:30 AMgnameni
Yes- but that is what you wrote.

I think that the correct expression for the integration of dx/[(1-2x)^2*(3-x)]

is -1/2*integral(dx/[(x-1/2)^2*(x-3)])

How would one go about solving: integral of A/(X-1/2)^2 + integral of B/(x-3)? - Mar 17th 2009, 01:53 AMADARSH
If you are trying to say that

than I am sorry sun will not rise from left(Giggle),try again

(Music) Twinkle Twinkle Little Star..

Quote:

How would one go about solving: integral of A/(X-1/2)^2 + integral of B/(x-3)?

but just for an example I will give A= 1 & B = 1

Put (x-1/2) = t

dx =dt

Hence integral becomes

doing the same for second integral

- Mar 17th 2009, 05:21 AMSoroban
Hllo, gnameni!

Let's take it from the top . . .

Quote:

We have: .

Then: .

Let .[1]

Let .[2]

Let

. . Substitute [1] and [2]: .

Hence, we have: .

Integrate: .

. . . . . . . .

. . . . . . . .

. . . . . . . .