- #1

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## Homework Statement

Integrate (8-16x)/(8x^2-4x+1) dx

Q

## Homework Equations

I separate it first 8/(8x^2-4x+1)dx -16x/(8x^2-4x+1)dx

Then I have no idea what to do next.

## The Attempt at a Solution

none ;(

- Thread starter Jude075
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- #1

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Integrate (8-16x)/(8x^2-4x+1) dx

Q

I separate it first 8/(8x^2-4x+1)dx -16x/(8x^2-4x+1)dx

Then I have no idea what to do next.

none ;(

- #2

SteamKing

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Look at the numerator. Isn't that expression close to the derivative of the denominator? See if you can work out the integral based on this line.

- #3

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Based on my calculator, I need to use trig substitution. But I have no clue:(

- #4

Ray Vickson

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Put away the calculator; it may be hurting you more than helping.Based on my calculator, I need to use trig substitution. But I have no clue:(

Here is a little hint: write ##8 - 16x = 4 + (4 - 16x)##; this will give you two separate terms that need to be integrated. For one of the terms, use the hint provided by the previous responder; for the other term, use partial fractions.

BTW: writing things as above is just a matter of practice and experience. After you have done lots of questions like this one, it will become second nature to you---but ONLY if you put away the calculator!

- #5

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Put away the calculator; it may be hurting you more than helping.

Here is a little hint: write ##8 - 16x = 4 + (4 - 16x)##; this will give you two separate terms that need to be integrated. For one of the terms, use the hint provided by the previous responder; for the other term, use partial fractions.

BTW: writing things as above is just a matter of practice and experience. After you have done lots of questions like this one, it will become second nature to you---but ONLY if you put away the calculator!

Thank you! With your help, I got -ln|8x^2-4x+1| +8arctan(x-1/4)+C by using separation , completing the square and trig substitution.Put away the calculator; it may be hurting you more than helping.

Here is a little hint: write ##8 - 16x = 4 + (4 - 16x)##; this will give you two separate terms that need to be integrated. For one of the terms, use the hint provided by the previous responder; for the other term, use partial fractions.

BTW: writing things as above is just a matter of practice and experience. After you have done lots of questions like this one, it will become second nature to you---but ONLY if you put away the calculator!

Hope this is the right answer:)

- #6

Dick

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No, I don't think the arctan part is correct. Can you show your work?Thank you! With your help, I got -ln|8x^2-4x+1| +8arctan(x-1/4)+C by using separation , completing the square and trig substitution.

Hope this is the right answer:)

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