Thread: Integration problem (partial fractions)

Integrate:



Now I used partial fractions:



and after a lot of working out got the following equations:









Now I tried gauss reducing it, but it was rather long and tedious which gave me:









In my final answer I got:



which was of that right form (due to the logs and arctan) but obviously the values were wrong.

So I was wondering, is there a more efficient way to do this question and solve for A, B, D and E without using gauss reduction?

Well, I don't know if you can use that, but I use some sort of inspection to get the values of A and B.



Take the fraction:



Now, what value do you have to assign to x so that one denominator becomes 0?

We put x = 3.

So, you find this:



And put x = 3, to get 1/36. This is the value of A.

From this, take x = -3 now:



Evaluate and you get -1/36, which is the value of B.

Now, you are left with:



There are only two constants to find now

Originally Posted by Unknown008

Now, what value do you have to assign to x so that one denominator becomes 0?

We put x = 3.

So, you find this:



And put x = 3, to get 1/36. This is the value of A.

but then if you let x = 3, then wouldnt the whole of the LHS = 0? How would this get you a value for A, if you saying ?

look at it this way:




So,

..............................(I)


Now first put x=-3 in equation (I) to find A.

then put x=3 in equation (I) to find B..

Then work on to find D and E

Yes, that's the same concept, but I find it faster as you don't have to write the full expansion before finding the values of A and B.

Originally Posted by Unknown008

Yes, that's the same concept, but I find it faster as you don't have to write the full expansion before finding the values of A and B.

Thats right! I thought the OP wasn't able to figure out the expansion before finding the values of A and B. So I wrote it down!!