How to Solve: The integral of (x-6) / (x^2 + 6x + 10) dx

[@laggyclip]

Thanks for teaching this. Also I’m pretty sure what you did was allowed but couldn’t it also be arccot?

[@Dablue5]

You are right about that, I forgot about arccot 💀

[@emre-rt1xz]

nice 👍

[@Raphael_Rodrigues]

i did it a little different. I think it's a simpler way.
(x-6)(x^2+6x+10)^-1
(x-6)[(x+3+j)(x+3-j)]^-1
x-6 = a(x+3-j) + b(x+3+j)
(+j)(-j) = (+j) (-j)
1/2(1-9j) = a
1/2(1+9j) = b
integral(a(x+3+j)^(-1)+b(x+3-j)^(-1))dx
aln(x+3+j)+bln(x+3-j)+cte //

[@Dablue5]

@@Raphael_Rodrigues true this does seem much simpler and faster, do you mind telling me what this method is called so that I can learn it?

[@Raphael_Rodrigues]

@@Dablue5 it's called partial fraction decomposition