Integral of 1/(ax^2+bx+c) (ALL CASES 💪)

✍🏼 Integral of 1/(ax^2+bx+c) - How to integrate it step by step!

🚶 𝐂𝐚𝐬𝐞𝐬
00:00 Case b^2-4ac = ZERO
04:01 Case b^2-4ac = NEGATIVE
12:12 Case b^2-4ac = POSITIVE
21:27 Integral of (mx+n)/(ax^2+bx+c)

🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫:

🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡 𝐥𝐞𝐯𝐞𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐡𝐞𝐫𝐞:

👋 𝐅𝐨𝐥𝐥𝐨𝐰 @𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮 𝐟𝐨𝐫 𝐚 𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥! 😉

𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮

𝐃𝐨𝐧𝐚𝐭𝐞

#integralsforyou #integrals #integration

[IntegralsForYou]

Hope you enjoy the longest video I've ever made 😊

0:01 Integral of 1/(ax^2+bx+c) dx => b^2-4ac = 0
4:01 Integral of 1/(ax^2+bx+c) dx => b^2-4ac < 0
12:12 Integral of 1/(ax^2+bx+c) dx => b^2-4ac > 0
21:28 Integral of (mx+n)/(ax^2+bx+c) dx (all cases)

👇Examples of integrals of (mx+n)/(ax^2+bx+c) dx in this playlist👇

Bukur 😉

[せんとくん-vp]

Thank you for your useful formulas!
I often calculate the 2nd case integlation in my research.

[thusharaditya]

Sir ur just amazing
Making sound less explanation can make mind more power
Sir hats off to u and your work...

[rayandy]

OMG amazing! Thank you I love it a lot!

[arvasugupta]

Respected Sir, This is very helpful as in extension as dx/(n+sinx) and dx/(n+cosx) and where n is any number, as in sinx and cosx can be converted into (2tany/(1+tan^2y) and cosx into (1-tan^2y)/(1+tan^2y) where y is x/2 and hence a generalised result like in this video, THANK YOU VERY MUCH in opening a new door for me.

[Gabs]

heyy thank you for this, this one was pretty challenging but super interesting to do! interesting how different the results are for all case scenarios :)

[noway]

For the first one (where b^2=4ac), I wouldn't include the c in the completing the square. Instead, I'd leave it out, and when you subtract (b/(2a))^2, you divide it by a (since it is leaving the bracket) giving you b^2/(4a), which is equal to c. Hence, c - b^2/(4a) = 0, and the quadratic can be expressed as a linear term squared.

[jorgemedeiros]

This video helped me a lot! Thank you very much!

[marshmelloalanwalker]

Wow..That's Incredible Very Very Good 👍🏻💥💥💥

[ayoubabadou]

Thanks for your helpful solution. I have a question regarding the solution 12:12 Integral of 1/(ax^2+bx+c) dx if b^2-4ac > 0.
How can the expression of x be retrieved?
Thanks

[amberheard]

For second case you don't need to bash your mind by doing insane u substitution. There is trigonometric formula for antiderivative of 1/(c^2+x^2) where c is constant. Or you can derive it from a triangle with base x height c and hyp of sqrt(x^2+c^2) using trigonometry definition.

[karthiksmanian]

Can't we use completing square for all quadratic integral occur in denominator?

[nourb]

I Love your channel and how it's specified, your videos push us to interact with the solutions actively and anticipate! Good job! 👍💎👏💫
Really if only YouTube had more channels like this for different maths topics like Differential Equations, Proofs, problems with Σ and Π, vectorial spaces ....etc

[keirobangs]

Thank you very much. love your channel.

[colt]

You are great, could do with reducing how much you cover up as you write though!

[pashupatinathdutta]

Sir, integration of (ax^2+bx+c)dx is a/3*x^3+b/2*x^2+cx+c.This same process is for integration of sqrt(ax^2+bx+c)dx or some different.Please sir.Regards.

[adnanbnj]

Are those cases useful if signs of polynomial function like
1/(ax^2-bx+c) or

[colt]

I have a question how does it work with -A*x^2+B*x+C...ie the A coefficient is negative and do you use that negative for the b^2-4AC criteria

[pashupatinathdutta]

Sir, can we integrate this(ax^2+bx+c)^-1.if yes, how.if not why.I have to learn more and more from you.pl.guide me.. Regards.

[justaperson]

Hi i didnt see any questions around this topic so if your not busy could you explain how you would obtain the gen solution of
8/(10x+3) dy/dx =e^4y
using the separation of variables method iknow that its a 1st order equation etc