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How do I integrate this function?

Hi,

How do I integrate this?



I put the function on an online calculator with step-by-step instructions and saw they rearranged the function like this (after taking the 0.6 constant in the numerator out), making it much easier to integrate:



How do you do that?
(edited 9 years ago)
Reply 1
Avatar for davros
davros
16
Original post by leosco1995
Hi,

How do I integrate this?



I put the function on an online calculator with step-by-step instructions and saw they rearranged the function like this (after taking the 0.6 constant in the numerator out), making it much easier to integrate:



How do you do that?


It's just rewriting the fraction in the same way that you can write

xx+1=x+1−1x+1=1−1x+1\displaystyle \dfrac{x}{x+1} = \dfrac{x + 1 - 1}{x + 1} = 1 - \dfrac{1}{x + 1}
Reply 2
Avatar for leosco1995
leosco1995
OP
2
How exactly do you rewrite it like that? Like where does the -1.667 and 6.667 come from? Your example is a bit easier because the value of x is the same in the numerator and denominator, but that's not the case with mine so I'm finding it a little confusing.

Thanks in advance.
Reply 3
Avatar for simon0
simon0
13
Notice the polynomial on both the numerator and denominator are of the same degree. As with top heavy fractions, we need to rewrite the function as a proper polynomial fraction form. We divide the numerator by the denominator. To do this, we could:
1) Rewrite and function as stated in the second post in this thread
2) Perform Long division

Also, in your example, we can simplify the function but factorising "0.6" by both the numerator and denominator.

Which online calculator did you use to rewrite the function as the re-written form does not make sense?
(edited 9 years ago)
Reply 4
Avatar for davros
davros
16
Original post by leosco1995
How exactly do you rewrite it like that? Like where does the -1.667 and 6.667 come from? Your example is a bit easier because the value of x is the same in the numerator and denominator, but that's not the case with mine so I'm finding it a little confusing.

Thanks in advance.


The weird 0.667 bits come from the fact that in the paragraph where you say "let's rewrite the integrand" you've divided by 0.6. This doesn't actually achieve anything - in fact, it makes things look more complicated!

To compare with my example earlier, just note that

0.6x = -(-0.6x) = -(-0.6x + 2.4 - 2.4) = -(2.4 - 0.6x) - (-2.4) = 2.4 - (2.4 - 0.6x)

and now you should be able to see how to reduce your original to 2 simpler integrands.
Reply 5
Avatar for BabyMaths
BabyMaths
Original post by leosco1995
Hi,

How do I integrate this?



I put the function on an online calculator with step-by-step instructions and saw they rearranged the function like this (after taking the 0.6 constant in the numerator out), making it much easier to integrate:



How do you do that?


This ^ is horrible.

0.6x2.4−0.6x=x4−x=x−4+44−x=−1+44−x\displaystyle \dfrac{0.6x}{2.4-0.6x}=\dfrac{x}{4-x}=\dfrac{x-4+4}{4-x}=-1+\dfrac{4}{4-x}
Reply 6
Avatar for leosco1995
leosco1995
OP
2
Thanks. That was very clear. :smile:

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