Question

integration of rational functions: Evaluate I=integral of (2x^2+3x+4)/(x^2+6x+10)dx

Answer 1

\[\int\limits_{}^{} \frac{ (2x^2+3x+4)/(x^2+6x+10) }dx\]

Answer 2

most likely your gonna have to use partial fractions to split this up into do-able sums

Answer 3

is there any special formula??

Answer 4

like a magic trick? no

but i do notice that the bottom poly appears to be prime; try to do division on it first to see how that plays out

Answer 5

ax+b[d/dx(x)}+constant

Answer 6

i'm doing correspondance cuorse sir, pls hlp

Answer 7

i am helping, but i will not do it FOR you.

what does the long division give us?

Answer 8

if need be, try using the wolf to simplify it or dbl chk your results

Answer 9

long divisin method?

Answer 10

can we expand (x^2+6x+10)= (x+3)^2+1

Answer 11

yes, but that will be more useful to us after we split this thing up into a more usable form.

Answer 12

we can try to split it apart into individual sums as is and see how that plays out

Answer 13

long divisn = 1+ (x^2-3x-6)/x^2+6x+10

Answer 14

is ths correct?

Answer 15

\[\frac{(2x^2+3x+4)}{(x^2+6x+10)}=\frac{2x^2}{(x+3)^2+1}+\frac{3x}{(x+3)^2+1}+\frac{4}{(x+3)^2+1}\]

Answer 16

your long division seems off to me

Answer 17

2
----------------
x^2+6x+10 ( 2x^2+3x+4
(2x^2+12x+20)
--------------
-9x-16
\[2-\frac{9x+16}{(x+3)^2+1}\]

Answer 18

\[\int 2-\frac{9x}{(x+3)^2+1}-\frac{16}{(x+3)^2+1}\ dx\]

the first term is simple enough, the middle term looks by partable, and the last is an arctan

Answer 19

2x-9/2 tan^{-1} (x+3)-16 (tan^{-1}(x+3)+c

Answer 20

is ths correct?

Answer 21

first terms is good

the middle and last term i think need more work

Answer 22

last term is fine

Answer 23

2x-9/2 x^{2} tan^{-1} (x+3)-16 tan^{-1}(x+3) +c

Answer 24

-9/2 x^{2} tan^{-1} (x+3) this part is giving you troubles

Answer 25

is ths correct

Answer 26

thank you sooooo much sir

Answer 27

\[\int \frac{9x}{(x+3)^2+1}dx =\frac{9}{2}ln((x+3)^2+1)-6tan^{-1}(x+3)\]

Answer 28

but integral of 1/ (1+x^{2})= tan {-1} x

Answer 29

http://www.wolframalpha.com/input/?i=integrate+%282x%5E2%2B3x%2B4%29%2F%28x%5E2%2B6x%2B10%29

all in all, it should get to this

Answer 30

thank you sir