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

1. .Sam. Group Title

you can't factor that

2. .Sam. Group Title

best approach is to complete the square and then trig substitution

3. wasiqss Group Title

yehh, it will have complex factors

4. traile Group Title

yup

5. shivam_bhalla Group Title

@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 Group Title

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

7. shivam_bhalla Group Title

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

8. traile Group Title

@shivam_bhalla she said partial fraction

9. TuringTest Group Title

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

10. wasiqss Group Title

traile , it willl become very complex then

11. lilMissMindset Group Title

yeah, im supposed to use that, partial fraction

12. shivam_bhalla Group Title

@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 Group Title

lil miss it will only have complex factors

14. TuringTest Group Title

there is either a typo, or it's impossible

15. shivam_bhalla Group Title

*why

16. TuringTest Group Title

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

17. lilMissMindset Group Title

what am i going to do about this problem then?

18. shivam_bhalla Group Title

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

19. TuringTest Group Title

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 Group Title

do you think quadratic factors can be use

21. shivam_bhalla Group Title

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

22. shivam_bhalla Group Title

*partial

23. TuringTest Group Title

like I said then, it's just redundant

24. TuringTest Group Title

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

25. wasiqss Group Title

you fail turing xD lol jk

26. TuringTest Group Title

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

27. lilMissMindset Group Title

yea. im quite sure i typed it right.

28. lilMissMindset Group Title

let's ignore the partial fraction thingy then.

29. TuringTest Group Title

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

30. lilMissMindset Group Title

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

31. TuringTest Group Title

welcome!