Integral of 1/(x^6+1) without partial fractions! 

Can someone help me with integral 1/sqrt(a + bsinx)

blackpenredpen But, isn’t coth^-1 equal to tanh?

@@axelcastillo7432 No. it is not reciprocal. It's an inverse function.

Your note is totally wrong. .. Use their standerd FORMULA

GAZALI SAMEER 2(a+bsin(x))^1/2+C

You can see my channle for JEE integrals. I have already solve this integral few months ago. See: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eugIOsqaI8Q.html

Cauchy Riemann I am a JEE aspirant too BTW

@@arjavgarg5801 Oh, all the best for jee, I'm a first year student at bits.

Cauchy Riemann did you sit for it? What rank?

@@arjavgarg5801 A useless 10k+ doesn't get you anything in IITs. Anyway, let's not dig the past :-P

Yay!

Bapolino 1:30 for me, lol

Ikr I have been up all night, 6am watching this right now

@@ricardomahfoud DUDE ME TOO

Yes!!!🥂

You would take a lifetime

That's my way..

Anudeep CVS it takes 10 minutes.. So if you are done with all questions.. U can do that

I know but you will loss time if a small mistake happen. Differentiate the same answer and get question you cannot simplify

Not in mains

Microwave Burrito you should check out the essence of calculus by 3blue1brown

DragonKidPlaysMC Ok thanks I’ll see. I’m only in grade 8 so I’ll probably start learning it next year but thanks for the video. It might give me a head start next year.

It’s how I fell in love with math.. became an engineer. Just a curiosity.

Artorias Thugz Oh cool. Hope you have a great life.

4 years back i was just like u

BlackpenRedpenBluepenGreenpen. It's going to be a Rainbowpen

NOW THERE ARE TWO OF THEM

If you make a tweet asking me to integrate 1/(x^8+1) and the tweet gets 2019 likes, then I will. : )

That's a great idea lol

@@blackpenredpen You will be asked soon to the 1/(x^10+1) integral hahaha

Can be done by contour integration or just break it to a^2- b^2 using complex numbers.

This would make me cry of happiness, like if you like super insane af integrals!

I wonder is there a recursive formula to derive the above integral.

@@rayandy2460 I was wondering the same thing, but I don't think there is.

Obi Wan Yup

@@blackpenredpen Who would come up with such a convoluted solution and HOW?? I hope you can PLEASE respond for once, please. It would mean alot.

@@leif1075 well, x+1/x is a standard strategy in a competitive integral environment and the other integrals are standard textbook. The partial fraction in the beginning was also a logical first step. It's all about recognising which technique to be applied where.

@@bigbrain296 i don't see how it could be standard..and if you've never seen it before..would anyone ever think of it? I doubt it.

@@leif1075 I think there are just some people in the right place at the right time, and have a knack for clever puzzles and stuff, and creating problems which have smart solutions. They might not even understand why some rules or tricks are in place, or why they work, but they love using them in smart ways regardless of context. Those tricks are shared, and after that its one of those things, where after you see it once or twice or thrice, you kind of get the idea. There is not really a world between not knowing the trick and knowing it.

Awww thank you! I am very happy to hear it! Best of luck and enjoy calc 2!

Feels awesome your integration tables know about hyperbolic tangent, not you lol.

But does it say what hyperbolic tangent really is? :)

I don't think so. The derivative of ln {(u-a)(u+a) } = 2u/(u^2 -a^2)

This is the approach used on wolfram, yes. Nice observation

Don't know about the indefinite but it's actually generalized for definite integral with limits ranging from 0 to infinity

I remember doing a reduction formula for this its pretty easy to prove

For definite integral with limits 0 to infinity, it becomes the beta function

Ahhhh, I forgot to check the min. of (x+1/x)/sqrt(3) You are right, I should have used arcoth, thank you!!!

For anyone who's interested, check out the derivative of arctanh vs. arcoth ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-GPvN5UWJlmE.html

@@blackpenredpen oh no problem, in fact thank you for these fabulous math videos:-)👌👍

Your note is not complet you forget u' in the top

I liked this comment to just look smart.

You can see my vedies. Such: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eugIOsqaI8Q.html

ronjamac Making RU-vid videos : )

Or find the general formula of indefinite integral of 1/(1+x^n)

I think it will b a reduction integral

I've done in in the complex world.

@@123pok456ey nth root of unity.. ?? De moivres

wc k Residues?

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-GPvN5UWJlmE.html

@@GhostyOcean thx

Most useless things to do in life

No way. Don't drag him into that mess. This channel is for math enthusiasts not math exam enthusiasts

You're wrong cause you change the integral into a completely different one which isn't the same anymore.

Oon Han it is!!

Is this a k-pop reference?

How? This isn't a definite integral. There are no bounds.

Thuis cannot be solved in a simple wat but it can be done by complex numbers.

Yay!!