Integral of 1/(x^2-9) (partial fraction decomposition)

[@IntegralsForYou]

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► Integration by parts
ruclips.net/p/PLpfQkODxXi4-GdH-W7YvTuKmK_mFNxW_h
► Integration by substitution
ruclips.net/p/PLpfQkODxXi4-7Nc5OlXc0zs81dgwnQQc4
► Integration by trig substitution
ruclips.net/p/PLpfQkODxXi49OUGvTetsTW61kUs6wHnzT
► Integration by Weierstrass substitution
ruclips.net/p/PLpfQkODxXi4-8kbKt63rs1xwo6e3yAage
► Integration by partial fraction decomposition
ruclips.net/p/PLpfQkODxXi4-9Ts0IMGxzI5ssWNBT9aXJ
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[@Yifus]

Thanks for the help! Lo aprecio mucho mi hermano

[@IntegralsForYou]

My pleasure! Disfruta del canal! 😊

[@lacjiki]

Thanks, you helped me a lot!!! Nice video

[@IntegralsForYou]

Thank you Daniela :-D

[@agf6446]

Thank you!! Nice video

[@IntegralsForYou]

Thanks, Amy! Enjoy the channel! 😊😊

[@sakshi6455]

Can you please solve it using substitution method?...and thanks for the video

[@IntegralsForYou]

Hi! Which substitution would you use?

[@FredlynDickson]

❤

[@IntegralsForYou]

😊

[@Quadrillions_quotes2301]

Can I i use this formula - 1/2a log|x-a/x-b| +c

[@Quadrillions_quotes2301]

Please reply

[@IntegralsForYou]

@Rounak Verma Hi! In my opinion we shouldn't use certain formulas such this one but if your teacher allows you to use it then it is ok for me! 😉

[@j.t.6417]

Nice

[@IntegralsForYou]

Thanks! 😀😊

[@akashkhedkar2579]

Sound dude..... without sound kuch b nai samaj mai aa raya

[@dildobaggins2759]

Why cant you use trig sub?

[@IntegralsForYou]

Hi! We use trig substitution when we have sqrt(a^2-x^2), sqrt(x^2-a^2) or sqrt(a^2+x^2). In this case you can use it but it becomes very long and the solution doesn't contain trig functions...

[@dildobaggins2759]

@@IntegralsForYou yes but cant there be multiple solutions sometimes...?

[@generator2883]

Can’t you use natural log properties to simplify it

[@IntegralsForYou]

Yes you can 😉:
Integral of 1/(x^2-9) dx =
= (1/6)ln|x-3| - (1/6)ln|x+3| + C =
= (1/6)( ln|x-3| - ln|x+3| ) + C =
= (1/6)ln|(x-3)/(x+3)| + C

[@ablite4795]

can we use tri substitution for solving this problem?

[@IntegralsForYou]

Theoretically yes, but it will be moooooore much longer than using partial fraction decomposition

[@dildobaggins2759]

@@IntegralsForYou It gives a different answer with trig sub is that fine because i know there can be multiple answers..

[@IntegralsForYou]

@@dildobaggins2759 The answers can be written differently, but their derivative must be the same. Which answer did you get?

[@dildobaggins2759]

@@IntegralsForYou So when i done via trig sub i got -InIcsc +cotxI +C?

[@IntegralsForYou]

@@dildobaggins2759 Hi! The derivative of -ln|csc(x) + cot(x)| is csc(x) and not 1/(x^2-9)...

[@angginit.ananti2841]

you writed it too small

[@IntegralsForYou]

Sorry, Anggini Ananti, if there is something you can't see I can write it here if you want.

[@sanjuranichowdhury8129]

But the answer is not matching with the given answer in ncert

[@IntegralsForYou]

Hi! Can you tell me the answer you have? Thanks!

[@bigpoo8808]

@@IntegralsForYou PMT gave -1/3 ln2 as the answer