Question

Partial fractions problem

Answer 1

\[\int\limits_{}^{} \frac{ x^2 + x + 3 }{ x^4 + 6x^2 + 9 }dx\]

Answer 2

hmm repeated quadratics...

Answer 3

I think it goes
\[\frac{ Ax+B }{ x ^{2} +3} + \frac{ Cx+D }{(x ^{2} +3)^2}\]

Answer 4

ok that makes sense, you factor and then do the same process as always since the degree must be 1 less on the numerator it is Ax + B and Cx + D?

Answer 5

working it out...

Answer 6

hmm, I don't think that works actually...

Answer 7

damn haha

Answer 8

hmm it does work... now to figure out how..

Answer 9

heh got it.. dumb mistake..

Answer 10

what is it?

Answer 11

whoops I changed the letters

Answer 12

Ax^3 + Bx^2 + 3Ax + 3B + Cx +D

Answer 13

what if I did this?

Answer 14

or am i not allowed to do that?

Answer 15

close

Answer 16

\[\frac{ x^2 + 3 +x }{ (x^2+3)^{2} }= \frac{ x^2 + 3 }{ (x^2+3)^{2} } +\frac{ x }{ (x^2+3)^{2} } =\frac{ 1 }{ (x^2+3)^{} } + \frac{ x }{ (x^2+3)^{2} }\]

Answer 17

so then I could do two separate partial fraction integrals?

Answer 18

you mean do an expansion on
\[\frac{x }{ (x^2+3)^{2} }\]
?

Answer 19

doesn't look like it

Answer 20

wouldn't need to anyway, pretty easy to integrate as is...

Answer 21

arctan for
\[\frac{ 1 }{ x^2+3 }\]

Answer 22

ok?

Answer 23

yup :)