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

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you can't factor that
best approach is to complete the square and then trig substitution
yehh, it will have complex factors

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@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
Remember \[\int\limits_{}^{}\frac{dt}{x^2+a^2} = \frac{1}{a} \tan^{-1}(\frac{x}{a})\]
You can eaily prove the above by substituting x = atan(theta)
@shivam_bhalla she said partial fraction
but it cannot be done with partial fraction if it cannot be factored
traile , it willl become very complex then
yeah, im supposed to use that, partial fraction
@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
lil miss it will only have complex factors
there is either a typo, or it's impossible
I mean that using partial fractions is impossible... or at least redundant
what am i going to do about this problem then?
Take x+1 = t dx=dt You still get the same thing with partial fractions too
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
do you think quadratic factors can be use
\[\frac{1}{t^2+9} = \frac{At+B}{t^2+9}\] we see a = 0, B=1 We again get back the same thing. So partail fraction approach should be useless
like I said then, it's just redundant
by impossible, I meant that the operation is useless, as you just said
you fail turing xD lol jk
@lilMissMindset are you \(sure\) there isn't a typo in your post?
yea. im quite sure i typed it right.
let's ignore the partial fraction thingy then.
then shivam bhalla has shown you the right way do you know trig substitution integrals?
yeah. i'm sorry, i'll do it using trig substitution. thank you so much.

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