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# Integration question... ?

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1. Integration question... ?
Hi there,

Just have a quick question on integration...

Why is it that when solving this question... y-3/y(y-1), it would not be possible to take the natural log (aside from the fact that the denominator can be spilt to 2 fractions)...while y/y-1 can be solved by taking the natural log ro make y ln |y-1| ?

If it was say y/y(y-1) could the natural log then be taken?

Would really appreciate some clarification as I seem to most of the time think to take the natural logs as soon as I see something over something, though this is obviously not correct.

Thank you so much
2. Re: Integration question... ?
woops have posted this on the wrong section, would appreciate a mod moving it to maths please
3. Re: Integration question... ?
(Original post by Jasmine_777)
Hi there,

Just have a quick question on integration...

Why is it that when solving this question... y-3/y(y-1), it would not be possible to take the natural log (aside from the fact that the denominator can be spilt to 2 fractions)...while y/y-1 can be solved by taking the natural log ro make y ln |y-1| ?

If it was say y/y(y-1) could the natural log then be taken?

Would really appreciate some clarification as I seem to most of the time think to take the natural logs as soon as I see something over something, though this is obviously not correct.

Thank you so much
I'm quite unsure of what you're asking. You can't just 'take a natural log' of an integral.

If you mean the result of an integral is a natural log, then that's only true if you have the integral of the derivative of a function divided by the function.

Written mathematically:

Last edited by Intriguing Alias; 14-04-2012 at 23:42.
4. Re: Integration question... ?
(Original post by Jasmine_777)
Hi there,

Just have a quick question on integration...

Why is it that when solving this question... y-3/y(y-1), it would not be possible to take the natural log (aside from the fact that the denominator can be spilt to 2 fractions)...while y/y-1 can be solved by taking the natural log ro make y ln |y-1| ?

If it was say y/y(y-1) could the natural log then be taken?

Would really appreciate some clarification as I seem to most of the time think to take the natural logs as soon as I see something over something, though this is obviously not correct.

Thank you so much
can't be integrated by just taking the natural log.

First convert it into a form, which can be integrated.

For your second question,

Now this can be integrated by using natural log.
5. Re: Integration question... ?
(Original post by Jasmine_777)
Hi there,

Just have a quick question on integration...

Why is it that when solving this question... y-3/y(y-1), it would not be possible to take the natural log (aside from the fact that the denominator can be spilt to 2 fractions)...while y/y-1 can be solved by taking the natural log ro make y ln |y-1| ?
Your question will be integrated in the following way,

Convert into partial fractions.

Then it will be simple to solve it.
6. Re: Integration question... ?
(Original post by raheem94)
can't be integrated by just taking the natural log.

First convert it into a form, which can be integrated.

For your second question,

Now this can be integrated by using natural log.
Hey, thanks for replying, the working out really helps!

Wondering why you did y-1+1 ... where did the 1s come from when converted it to a form that can be integrated?

So okay, I see now that the numerator of the equation needs to be the differentiated form of the denominator before it can be integrating (by doing ln|....| ) ... is that right?
7. Re: Integration question... ?
(Original post by hassi94)
I'm quite unsure of what you're asking. You can't just 'take a natural log' of an integral.

If you mean the result of an integral is a natural log, then that's only true if you have the integral of the derivative of a function divided by the function.

Written mathematically:

Thanks for pointing that out ! I don't recall my teacher ever telling us that so thanks! to confirm, that means you can only integrate something by taking the natural logs when the numerator is in the differentiated form of the denominator of the equation ?
8. Re: Integration question... ?
(Original post by Jasmine_777)
Hey, thanks for replying, the working out really helps!

Wondering why you did y-1+1 ... where did the 1s come from when converted it to a form that can be integrated?

So okay, I see now that the numerator of the equation needs to be the differentiated form of the denominator before it can be integrating (by doing ln|....| ) ... is that right?
couldn't have been integrated until i hadn't simplified it.

This is an improper fraction, you need to make it proper. Alternatively i could have used long division but this was the easiest method.

For the second question,
Integrating 1/x gives lnx, integrating gives ln(x-1), but some expressions are in the form , they can by integrated to

You need to practice more, then you will easily be able to recognize the method.
9. Re: Integration question... ?
(Original post by Jasmine_777)
Thanks for pointing that out ! I don't recall my teacher ever telling us that so thanks! to confirm, that means you can only integrate something by taking the natural logs when the numerator is in the differentiated form of the denominator of the equation ?
That's right. That's why Raheem did what he did with

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