Question

int. dx/ (x^2 +2x+10) using partial fraction. please.

Answer 1

you can't factor that

Answer 2

best approach is to complete the square and then trig substitution

Answer 3

yehh, it will have complex factors

Answer 4

yup

Answer 5

@lilMissMindset To complete the square

x^2 +2x+10= x^2+2x+1+9 = (x+1)^2 +3^2

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

Now complete the rest

Answer 6

Remember

\[\int\limits_{}^{}\frac{dt}{x^2+a^2} = \frac{1}{a} \tan^{-1}(\frac{x}{a})\]

Answer 7

You can eaily prove the above by substituting x = atan(theta)

Answer 8

@shivam_bhalla she said partial fraction

Answer 9

but it cannot be done with partial fraction if it cannot be factored

Answer 10

traile , it willl become very complex then

Answer 11

yeah, im supposed to use that, partial fraction

Answer 12

@LOL, whjy do you want to complicate things when there is a aeasier method available. If you still insist on partial fraction, then it is fine

Answer 13

lil miss it will only have complex factors

Answer 14

there is either a typo, or it's impossible

Answer 15

*why

Answer 16

I mean that using partial fractions is impossible... or at least redundant

Answer 17

what am i going to do about this problem then?

Answer 18

Take x+1 = t
dx=dt



You still get the same thing with partial fractions too

Answer 19

how would you do this with partial fractions?
I don't see it... perhaps I am wrong though, it wouldn't be the first time :P

Answer 20

do you think quadratic factors can be use

Answer 21

\[\frac{1}{t^2+9} = \frac{At+B}{t^2+9}\]

we see a = 0, B=1

We again get back the same thing. So partail fraction approach should be useless

Answer 22

*partial

Answer 23

like I said then, it's just redundant

Answer 24

by impossible, I meant that the operation is useless, as you just said

Answer 25

you fail turing xD lol jk

Answer 26

@lilMissMindset are you \(sure\) there isn't a typo in your post?

Answer 27

yea. im quite sure i typed it right.

Answer 28

let's ignore the partial fraction thingy then.

Answer 29

then shivam bhalla has shown you the right way
do you know trig substitution integrals?

Answer 30

yeah. i'm sorry, i'll do it using trig substitution. thank you so much.

Answer 31

welcome!