Try partial subsitiuation
solve for A and B and then integrate it will be much easier.
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))
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!