Question

integrate: (x^2+4)/(x^2-4)

Answer 1

first use long division, then factor the remaining numerator and use partial fractions

Answer 2

after long division i got 1 remainder 8

Answer 3

ok, so that would be 8/(x^2-4)
now you can factor the denominator (*oh I said numerator last time, my bad..)
and use partial fractions

Answer 4

factoring gives you (x+2)(x-2)

Answer 5

can you perform partial fractions on that?

Answer 6

no

Answer 7

not familiar with the technique?

Answer 8

there's only one number in the numerator

Answer 9

i've done it before but don't remember much

Answer 10

\[{8\over(x-2)(x+2)}={A\over x-2}+{B\over x+2}\]looking familiar yet?

Answer 11

\[{8\over(x-2)(x+2)}={A\over x-2}+{B\over x+2}\implies A(x+2)+B(x-2)=8\]now we choose some values for x that will let us know what A and B are

Answer 12

ok let me try to work this. i remember now

Answer 13

thank you

Answer 14

welcome :)

Answer 15

2 nd -2 will make it zero

Answer 16

so
A=?
B=?

Answer 17

B=-2 and A=2

Answer 18

yep :)
so our integral is now...?

Answer 19

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

Answer 20

yes, and you can integrate that, I'm pretty sure
good job !

Answer 21

2ln(x-2/x+2) +x

Answer 22

i forgot my constant and of course +C