## lilMissMindset 3 years ago int. dx/ (x^2 +2x+10) using partial fraction. please.

1. .Sam.

you can't factor that

2. .Sam.

best approach is to complete the square and then trig substitution

3. wasiqss

yehh, it will have complex factors

4. traile

yup

5. shivam_bhalla

@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

6. shivam_bhalla

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

7. shivam_bhalla

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

8. traile

@shivam_bhalla she said partial fraction

9. TuringTest

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

10. wasiqss

traile , it willl become very complex then

11. lilMissMindset

yeah, im supposed to use that, partial fraction

12. shivam_bhalla

@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

13. wasiqss

lil miss it will only have complex factors

14. TuringTest

there is either a typo, or it's impossible

15. shivam_bhalla

*why

16. TuringTest

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

17. lilMissMindset

18. shivam_bhalla

Take x+1 = t dx=dt You still get the same thing with partial fractions too

19. TuringTest

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

20. traile

do you think quadratic factors can be use

21. shivam_bhalla

$\frac{1}{t^2+9} = \frac{At+B}{t^2+9}$ we see a = 0, B=1 We again get back the same thing. So partail fraction approach should be useless

22. shivam_bhalla

*partial

23. TuringTest

like I said then, it's just redundant

24. TuringTest

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

25. wasiqss

you fail turing xD lol jk

26. TuringTest

@lilMissMindset are you $$sure$$ there isn't a typo in your post?

27. lilMissMindset

yea. im quite sure i typed it right.

28. lilMissMindset

let's ignore the partial fraction thingy then.

29. TuringTest

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

30. lilMissMindset

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

31. TuringTest

welcome!