Integral of 1/(1+cos(x) vs integral of sqrt(1+cos(x))

Integral of 1/(1+cos(x)), Integral of sqrt(1+cos(x)),

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[blackpenredpen]

Comment more uncommon trig identities!

[ananyapathak]

A video a day keeps my math professor away.

[agentplatipus]

These questions used to be tricky in 1990s, these days even a 16 year old can solve these with no issues. competition has escalated to new level .

[gabest]

As noted, second one smells wrong without the abs value. Square root of something is always positive under the curve, but if you use the sin function, it may give a negative result.

[x-warrior]

your channel helps me a lot to keep in touch with mathematics all the time .Namaste🙏👩‍👦‍👦

[Gold]

I love tricks like this. Trying out double and half angle identities is hard to remember to do when you just have functions of x

[dudewaldo]

Something something absolute value for the second one

[maxchatterji]

Hey there I did the Oxford MAT exam yesterday. I just wanted to thank you for creating really interesting content. It has invigorated my passion for maths whilst I have been preparing for it.

[wahidhanif]

proud to be a subscriber.
very useful and helpful channel...

[astudyofeverything]

being in India and being a student preparing for jee....we learn this formula in very first stage of trigonometry and this type of integrals in very very preliminary trust me its the one of the most easiest problems in integrals and if you are in india then there are lots of questions in maths which will give you a heart

[holyshit]

2. f(x)=2*sin(x)/sqrt(1+cos(x))
with Euler substitution twice and Ostogradski isolation of rational part
1. Euler substitution once should give nice result

[rajrajeswaribag]

I like your applied are eligible make clear idea

[nelsonwalker]

When you cancel the square root with the (cos(x))^2, does it not become modulus(cos(x))?

[blue_blue-]

Tricky Integral! Especially the second one.
Some "+/-„-signs obviously were abandoned 🤨.
Graphing recommended, to see what happens.

[tomyao]

you should have called the video trig or treat. Now you'll have to regret it forever

[amirparsi]

Wouldn’t be halloween without cosine integrals

[pritamseth]

This is way easier than JEE level problems

[milos_radovanovic]

Without a very specific boundaries the second one is wrong!
A primitive function of a nonnegative function must be monotonic!
True result is a piecewise comprised of a sin+c and -sin+c segments with constants ajusted to form a continius monotonicaly increasing staircase.

[Rubikorigami]

Doesn’t the second integral simplify to the integral of sqrt(2)abs(cos(x/2)) since you take the root of a square which is always positive?

[tomasmolinamorbiducci]

N^2 = (N_x)^2 + (N_y)^2 + (N_z)^2
N, N_x, N_y, N_z integers...
How can I know the amount of combinations(degeneracy) for a given N?