integral of 1/(2+cos(x)) , Weierstrass substitution

integral of 1/(2+cos(x)) by Weierstrass substitution.
This is a great way to integrate a rational expression that involves sin(x) and cos(x).

[jimd]

I remember doing loads of these integrals in my engineering degree. Very long and challenging to do but in the end very rewarding. Love how the t=tan(x/2) brings all of the trig functions together. Very beautiful.

[JaydentheMathGuy]

There has to be a movie where the victim says "we're in the t world now".

[martinepstein]

I'd never heard of Weierstrass substitution, that's awesome!

[markjackson]

You and Dr. Peyam are one of the best math teacher in YouTube!!! : )

[hugoarteaga]

1:32 whem u think its over, but it wasn´t even starting

[skwbusaidi]

I did this by multiplying top and bottom by 2-cosx and replace cos^2 x by 1-sin^2 x and split into 2 integerals
One on them has cosx in the top easy to do and the other we can multiply top and bottom by sec^2 x to get sec^x in the bottom and function in term of tan x in the bottom

[Grundini]

∫ 1/(u^2+a^2) du = (1/a)arctan(u/a) + c

[Jack-ilck]

I think this could've been done a bit simpler. After Weierstrass substitution, instead of factoring out a 3 from the denominator, you could've just used substitution where t=sqrt(3), and then factor out a 3.

[kruksog]

This was so good. I'm an undergrad senior (fair warning, who has largely focused on discrete and abstract math since being free of calculus.) But this was something I'd never seen before. This vid is awesome (with the video on the substitutions themselves too).

[etakly]

I enjoy this question, thank you very much

[massimot.]

Fantastic video, you saved my life, greetings from Spain.

[joshsmit]

There are thousands of integrals. Maybe start a higher math playlist like linear algebra ?

[kylerachman]

At 1:55, why can't you just instantaneously integrate that to 2/√3 arctan(t/√3), by using a^2 = 3 and the 1/(a^2+u^2) du formula?

[leonardosoto]

Some + signs are pretty equal yo some t letters...

[ravaladitya]

I think this method is not taught with the standard of the sum. Replacing 2 and cosx by submultiple angles.

[norihambujang]

I want to integrate the same equation from 0-2pi....if I am using maple, Matlab and symbolab, I will get when I use calculator, I will get zero (radian mode) and 2.0957 (degree mode), and if I use the final solution given in this video, I also get zero.

[XKAMILX]

Thank you very much - that was very helpful for me :D Greetings from Poland

[TrisCalangi]

In the integral of 2 / 3 + T^2 DT. Why not put the 2 outside and you'll be left with DT/ 3 + T^2, find values of U and DU, and the final answer will be Ln | u | + C?

[theoleblanc]

I din't know this sub but I had already done with euler sub after sub cosx by u.
My result is (2/√3)tan^-1[(2/√3)(((sinx+1)/cosx)+1/2))], by diffentiation it works also!

[blazep]

That's an awesome way to integrate!!
Thank you for the introduction.

PS. Am I the only one, who at first glance read it as - 'weirdass'? XD