I've been stuck on this question for a while.

Can someone show me how to do this one, thanks.

Question is actually

∫1/((x+9)(x^2+4))

- Mar 2nd 2009, 08:37 PMKitizhiEvaluate the definite integral ∫1/((x+9)(x62+4)) , x from -3 to 2
I've been stuck on this question for a while.

Can someone show me how to do this one, thanks.

Question is actually

∫1/((x+9)(x^2+4)) - Mar 2nd 2009, 08:57 PMtreetheta
Try partial subsitiuation

solve for A and B and then integrate it will be much easier. - Mar 2nd 2009, 09:44 PMmollymcf2009
Partial Fractions:

Get a common denominator:

* THis is equal to the bottom of your original integral

So,

Now FOIL the right side and collect like terms:

Now you can solve for A B & C * Remember that since your numerator in your original integral was 1, you will only put 4A + 9C = 1. You always put your like terms equal to the coefficient of the like term in the numerator of your original integral, so in this case since there are no or terms in the numerator of your integral, the other two will be = 0.

1 = 4A + 9C

0 = A + B

0 = 9B + C

So,

C = -9B

A = -B

then

1 = 4(-B) + 9(-9B)

1 = -4B - 81B

1 = -85B

Then you can solve for the others.

When you get your A B & C, just plug them back into

and this is your new integral!

Whew, these are usually pretty long and time consuming! Hope this helps! - Mar 2nd 2009, 09:51 PMKitizhi
Thanks alot mollymcf2009,

I think I can manage from here on