Integral of 1/cosx

Integral of 1/cosx
Integral of 1/e^x+1: • Integral of 1/(e^x-1)

[@DipsAndPushups]

Thank you. Straight to the point and easy to understand.

[@wrathcs]

glad i found this channel, expect so many likes lol, also remove the sound and put some music over just some piano i'd say

[@ប្រទេសកម្ពុជារបស់ខ្ញុំ]

Yeah lemme try😊 thanks for being here🙏✅

[@blackblue1515]

Where are you from

[@martipalacios8334]

THANK YOU SO MUCH :)

[@erchguyj1234]

When you integrate 1/1-u², why can't you just apply the 1/2aln(a+x/a-x) formula?

[@jesusangelMD]

It was not easier to convert 1/cos(x) to sec(x) and obtain the direct integral which is ln(sec(x) + tan(x) + c

[@aubreymsipha7059]

hie please cross check I think there is an error denominator should be 1-sinx and NOT sinx-1....double check the working again

[@ប្រទេសកម្ពុជារបស់ខ្ញុំ]

Absolutely friend. Note that In integrated function, the answers show in different forms but they are exactly the same in their properties and graphs.☘️ Especially, here I use absolute value bars in the natural logarithm, so |1-sinx|=|sinx-1| .☘️

[@aubreymsipha7059]

@@ប្រទេសកម្ពុជារបស់ខ្ញុំ thanks very much I understand now thank you 👍

[@ezu8501]

this is really cool

[@mamadetaslimtorabally7363]

Fantastic🎉

[@Infinity-tg7sd]

du/(u²+1) it's the table integral already, why did you make its solution harder

[@ប្រទេសកម្ពុជារបស់ខ្ញុំ]

Oh brother, in case for those who are new here and don’t know where it comes from.
And thank you for advice.

[@etienneduhoux]

There is no du/(u^2 +1) on the video

[@omarhmidani6063]

Can you use your brain 🧠?

[@tracyasiimire7]

but du/u^2+1 is not anywhere

[@ernestschoenmakers8181]

The other solution is lnItan(x)+sec(x)I +c.

[@ប្រទេសកម្ពុជារបស់ខ្ញុំ]

Absolutely right!

[@ernestschoenmakers8181]

@@ប្រទេសកម្ពុជារបស់ខ្ញុំ Here are the steps:
I = int of dx/cos(x), now multiply and divide by sec(x)+tan(x):
I = int of (sec(x)+tan(x))*dx/[cos(x)*(sec(x)+tan(x))]
Let 1/cos(x)=sec(x):
I = int of sec(x)*(sec(x)+tan(x))*dx/(sec(x)+tan(x))
I = int of (sec^2(x)+sec(x)*tan(x))*dx/(sec(x)+tan(x))
Let sec(x)+tan(x)=u
(sec(x)*tan(x)+sec^2(x))*dx=du
I = int of du/u = lnIuI + C so the final solution is:
I = lnIsec(x)+tan(x)I + C.

[@ernestschoenmakers8181]

Note: (1+sin(x))/(1-sin(x)) = (sec(x)+tan(x))^2
1+sin(x) = (1-sin(x))*(sec(x)+tan(x))^2, multiply both sides by sec(x):
sec(x)+tan(x) = (sec(x)-tan(x))*(sec(x)+tan(x))^2
1 = (sec(x)-tan(x))*(sec(x)+tan(x))=sec^2(x)-tan^2(x), this
proves that: sec^2(x)=1+tan^2(x).

[@ប្រទេសកម្ពុជារបស់ខ្ញុំ]

@@ernestschoenmakers8181 yes bro, but anyway our friends can use the method they think it's easier for them☘️💐

[@ernestschoenmakers8181]

@@ប្រទេសកម្ពុជារបស់ខ្ញុំ True but it's always educational to know in how many ways one can solve an integral and to see how anything is related.

[@IamJacksColon4]

replacing x=2arctant is much easier

[@ytho8025]

can i integrate the answer ?

[@user-amenoiru]

谢谢，这是一个十分有用的视频!

[@creator8101]

Yeah I think I should consider dropping engineering

[@patrikbede8950]

Lmao

[@JessyP-u6q]

Why should environment engineer study maths for the entire graduation .....
Maths is again incorporated for the first year of post graduate ......and ........studying civil engineering has become useless .....as even computer students rely on environment science ?!

[@ohong7032]

Good❤

[@stevejustin670]

YES THANK U

[@ប្រទេសកម្ពុជារបស់ខ្ញុំ]

yes😀

[@Timetravel005]

integral √cosx-cosx^3dx = ? Please

[@ប្រទេសកម្ពុជារបស់ខ្ញុំ]

Is it cosx^3 OR cos^3x ?

[@edislam1666]

Why 1/2

[@patrikbede8950]

What do you mean

[@abdulbaseerabbasi3443]

😮😮😮😮😮😮

[@jeanbaptistedebret]

Ê o barulho do inferno

[@vidyavidya5410]

X/cosx

[@СнежныйБарс-х8ь]

406

[@StryKeZ69]

1/cosx = secx

[@ប្រទេសកម្ពុជារបស់ខ្ញុំ]

Yeah

[@gravyy14]

horrible