How to integrate this?

[petesmc]

Hi,

I've an important exam coming up, and just doing some study, but stuck on this problem. I know it's not electronics, but you guys are math geniuses so, how to integrate this:

1 / (x^2 - 4)

I know what the answer is, but i can't seem to figure out how to do it. I even downloaded MuPad to try and get help, but it seems that MuPad just goes straight to the answer and doesn't show any steps.

Thanks in advance,
-Peter

 

[TKS]

rulezz..

searchin google for math rulez and your subject

wasn't it something whit NX^N-1..???

TKS

 

[udi_hakim]

blahhhh

 

[Roff]

You should transform your equation like this:
1/(x^2-4) = 1/(x^2) - (1/ 4) = x^-2 - 0.25
Now you can integrate it (red is the intigration):
-1x^-2+1 - 0.25x = -1x^-1 - 0.25x = -1/x - 1/4x


I also knows physics and bible if you need... 8)

Maybe you should stick to the Bible.
1/(x^2-4) does not equal 1/(x^2) - (1/ 4)

According to my CRC handbook, the integral of dx/(x^2-a^2) is

1/(2*a)*ln[(x-a)/(x+a)] where ln is the natural log operator.
In this case, of course, a=2.

There is equivalent form which involves the inverse hyperbolic cotangent :roll: .

 

[udi_hakim]

Oh ****... to early in the morning or math i guess... thought you ment something else...


1 / (x^2 - 4) = 1 / 4[((x^2) / 4) - 1] = 0.25 * {1 / [((x^2) / 4) -1]} = 0.25 * {1 / ((x/2)^2 - 1)} = - 0.25 * 2 arctg x/2 + c =-0.5arctg(x/2)+c

 

[Roff]

Oh [bleep]... to early in the morning or math i guess... thought you ment something else...


1 / (x^2 - 4) = 1 / 4[((x^2) / 4) - 1] = 0.25 * {1 / [((x^2) / 4) -1]} = 0.25 * {1 / ((x/2)^2 - 1)} = - 0.25 * 2 arctg x/2 + c =-0.5arctg(x/2)+c

Ok, you've convinced me that you are much better at math than I am.
And I'm sure you know the Bible better than I.
How about the integral I posted? Do you know if it is correct?

 

[petesmc]

Ron H,

Your solution was the correct one, but we have not learnt that integral. Does anyone know in simpler terms how to solve it?

-Peter

 

[petesmc]

ok i figured this out, had to split 1/(x^2 - 4) into 1/(x-2)(x+2) and make partial fractions in the form of:

1/(4(x-2)) - 1/(4(x+2))

Then easy to integrate...thanks for the help!