Integration help

[grizzled compass]

Hey guys, do any of you guys know how to integrate this?

[gray jay]

you can write it as
1/(x³sqrt(x+4)sqrt(x-4))
then split it into 3 fractions and integrate each of them individually

[grizzled compass]

so something like this?:

(1/x^3)(1/sqrt(x+4))(1/sqrt(x-4))

and integrate all of this individually

[gray jay]

no
I mean write it in the form of
(A/x³) + (B/sqrt(x+4)) + (C/sqrt(x-4))
where A, B, and C are constants
if possible

[grizzled compass]

I did it like you said but I don’t know how to solve for the constants

[gray jay]

should be
A sqrt(x+4) sqrt(x-4) + Bx³sqrt(x-4) + Cx³sqrt(x+4) = 1

[grizzled compass]

Something like this?

[gray jay]

the 1st term should be
A sqrt(x+4) sqrt(x-4)

[grizzled compass]

Alright, so far I managed to solve for C but I’m not sure how to solve for the other constants (A and B)

A and B may be just 1

nevermind no

[gray jay]

for A, set x = 0
for B, set x = -4
it turns out that both A and B are imaginary tho

[grizzled compass]

that's the problem