Integral of (sin(x) - cos(x))/(sin(x) + cos(x)) (substitution)

✍🏼 integralsforyo... - Integral of (sin(x) - cos(x))/(sin(x) + cos(x)) - How to integrate it step by step using the substitution method!
✅ 𝐃𝐞𝐫𝐢𝐯𝐚𝐭𝐢𝐯𝐞 𝐭𝐨 𝐜𝐡𝐞𝐜𝐤 𝐭𝐡𝐞 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧
Derivative of -ln(sin(x)+cos(x)) = • Derivative of -ln(sin(...
🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫:
► Integral searcher 👉integralsforyo...
🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡 𝐥𝐞𝐯𝐞𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐡𝐞𝐫𝐞:
► Integration by parts 👉integralsforyo...
► Integration by substitution 👉integralsforyo...
► Integration by trig substitution 👉integralsforyo...
► Integration by Weierstrass substitution 👉integralsforyo...
► Integration by partial fraction decomposition 👉integralsforyo...
👋 𝐅𝐨𝐥𝐥𝐨𝐰 @𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮 𝐟𝐨𝐫 𝐚 𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥! 😉
📸 / integralsforyou
𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮
▶️ KZbin: www.youtube.co...
📸 Instagram: / integralsforyou
👍 Facebook: / integralsforyou
𝐃𝐨𝐧𝐚𝐭𝐞
🙋‍♂️ Patreon: / integralsforyou
#integralsforyou #integrals #integrationbysubstitution

[@IntegralsForYou]

🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫: ► Integral searcher 👉integralsforyou.com/integral-searcher 🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡 𝐥𝐞𝐯𝐞𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐡𝐞𝐫𝐞: ► Integration by parts 👉integralsforyou.com/integration-methods/integration-by-parts ► Integration by substitution 👉integralsforyou.com/integration-methods/integration-by-substitution ► Integration by trig substitution 👉integralsforyou.com/integration-methods/integration-by-trig-substitution ► Integration by Weierstrass substitution 👉integralsforyou.com/integration-methods/integration-by-weierstrass-substitution ► Integration by partial fraction decomposition 👉integralsforyou.com/integration-methods/integration-by-partial-fraction-decomposition 👋 𝐅𝐨𝐥𝐥𝐨𝐰 @𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮 𝐟𝐨𝐫 𝐚 𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥! 😉 📸 instagram.com/integralsforyou/

[@AmanKumar-ek9ux]

Physics wallah did it wrong ❌ Thank you for this, now I am confident 😎😉

[@IntegralsForYou]

My pleasure! 😊

[@ertugrulghazi3339]

@Aman Kumar bhai choti moti mistake hoti rhti b

[@AmanKumar-ek9ux]

@@ertugrulghazi3339 ha yrr But i was confused

[@ertugrulghazi3339]

@@AmanKumar-ek9ux koi nhi bhai

[@Studylapse-sf6lg]

Yes

[@dragoscalin4883]

Trigonometrie și primitive de funcții. Frumos, infinit de frumos !!!!! Oricum , vrem nu vrem, suntem înconjurați zi de zi , la infinit de matematică. Frumoasă integrala nedefinită !!!!!

[@IntegralsForYou]

❤

[@dragoscalin4883]

Primitive de funcții, matematica infinitezimală, foarte frumoasă. Tata Leibnitz a fost inteligent, nu glumesc.

[@IntegralsForYou]

❤❤

[@wychan7574]

You can multiply both denominator and numerator by sin x + cos x the the numerator becomes cos 2x something and the denominator becomes sin 2x something, the rest is straightforward.

[@IntegralsForYou]

Oh! Nice approach! Let's see: Integral of (sin(x)-cos(x))/(sin(x)+cos(x)) dx = = Integral of [(sin(x)-cos(x))/(sin(x)+cos(x))]*[(sin(x)+cos(x))/(sin(x)+cos(x))] dx = = Integral of (sin^2(x)-cos^2(x))/(sin^2(x)+2sin(x)cos(x)+cos^2(x)) dx = = Integral of -cos(2x)/(1+sin(2x)) dx = = - Integral of 1/(1+sin(2x)) cos(2x)dx = Substitution: u = 1+sin(2x) du = cos(2x)*2 dx ==> du/2 = cos(2x)dx = - Integral of 1/u du/2 = = (-1/2)*Integral of 1/u du = = (-1/2)*ln|1+sin(2x)| + C Thanks for your comment! ❤

[@ajithkumarnair8785]

How is this correct the answer is not matching to Ur videos answer​@@IntegralsForYou

[@IntegralsForYou]

@@ajithkumarnair8785 Hi! Using trig identities we can see that both solutions are equal or equal except for the constant, which has derivative equal to zero: (-1/2)*ln|1+sin(2x)| + C = { (sin(x)+cos(x))^2 = sin^2(x)+2sin(x)cos(x)+cos^2(x) = 1+sin(2x) } = (-1/2)*ln|(sin(x)+cos(x))^2| + C = { ln(a^n) = n*ln(a) } = (-1/2)*2*ln|sin(x)+cos(x)| + C = = - ln|sin(x)+cos(x)| + C = Another way to check the answer is correct is by deriving the solution: Derivative of (-1/2)*ln|1+sin(2x)| + C = = (-1/2)*[1/(1+sin(2x))]*(0+cos(2x)*2) + 0 = = (-1/2)*[1/(1+sin(2x))]*2cos(2x) = = -[1/(1+sin(2x))]*cos(2x) = = -cos(2x)/(1+sin(2x)) = { cos(2x)=cos^2(x)-sin^2(x) } { 1+sin(2x) = (sin(x)+cos(x))^2 } = -(cos^2(x)-sin^2(x))/(sin(x)+cos(x))^2 = = (sin^2(x)-cos^2(x))/(sin(x)+cos(x))^2 = { a^2-b^2 = (a-b)(a+b) } ==> sin^2(x)-cos^2(x) = (sin(x)-cos(x))(sin(x)+cos(x)) = (sin(x)-cos(x))(sin(x)+cos(x))/(sin(x)+cos(x))^2 = = (sin(x)-cos(x))/(sin(x)+cos(x)) Hope it helped! 💪

[@ajithkumarnair8785]

@@IntegralsForYou thank u sir for Ur comment sir I have a one last question that is in order to master mathematics what all it takes also which course should I take in order to become a mathematician

[@IntegralsForYou]

@@ajithkumarnair8785 Hi! Honestly this is a difficult question... in a sentence I would say that to become "officially" a mathematician you should take a Maths degree in university but you won't never become a true mathematician if you don't enjoy learning maths where "enjoy" doesn't mean necessarily "it has to be easy to learn mathematics". Learning, understanding, practicing, understanding and enjoying maths are, in my opinion, the clue to become a mathematician. But that's my opinion 😉

[@AdZard]

Can we use the substitution method? Please reply with an answer in that method

[@IntegralsForYou]

Hi! Yes, we can use the substitution method and we did so in the video, we did u=sin(x)+cos(x) 😉

[@sadi_supercell2132]

Does the legend still reply?

[@IntegralsForYou]

Hi! I think so! 🤭

[@manasvisaxena04]

Thank you for solution 😊

[@IntegralsForYou]

My pleasure! 😊😊

[@Dc78498]

Hi

[@thinhquoc2255]

I from in Viet Nam

[@IntegralsForYou]

Hi! 😊

[@defensewallahfanclub6803]

my teacher did it wrong that they miss the minus but i have full confidence in my answer so here to verify it thank you sir it is now 4 years but still he is replying wow

[@IntegralsForYou]

You can share this channel with your teacher hehe it is almost five years of Integrals ForYou and it will continue for many years if I can! 💪

[@leehoanggg]

love ur vids. amazing

[@IntegralsForYou]

Thanks! ;-D

[@newkid9807]

I dropped something and it went HOANG!!!!

[@KashmiriJanu]

Aesa kyu krna pda Direct kyu nhi krte plx

[@KashmiriJanu]

Aur ye kese smj aaye ki aesa knha p krna h plz😇🙆🌍

[@IntegralsForYou]

@@KashmiriJanu Hi! I'm sorry but I don't understand...

[@KashmiriJanu]

@@IntegralsForYou sir. Why should we do like this. Why cant do we it directly as we do other qs. How can we understand that we have to change its sign then integrate Plz 😭🌍

[@IntegralsForYou]

@@KashmiriJanu hehe for the integral in the video I confess that you will know it by trying all methods you know... In this case we can think in deriving the numerator and see if the derivative is equal to the numerator or to the "numerator multiplied by a constant"... If we see it before starting, we can manipulate the function by multiplying by a constant in order to have the exact derivative on the numerator

[@gunrattansingh4447]

No need to take minus out. Just assume the denominator.

[@IntegralsForYou]

True 😉

[@unknownhuman4134]

Can you explain me... How?

[@unknownhuman4134]

@@IntegralsForYou Can we multiply (Cosx-Sinx) with -1 so, we can get (Sinx-Cosx). Like this, du/dx= -(Cosx-Sinx) = du= (Sinx-Cosx)dx

[@IntegralsForYou]

@Unknown Human Yes! 😉

[@unknownhuman4134]

@@IntegralsForYou Than answer will come positive. Is it correct?

[@DARK-od4zk]

mera ans sahi thaaaaaaa 🥳🥳🥳🥳

[@hectordiazhuaraca244]

gracias

[@IntegralsForYou]

Un placer! 😊

[@DigitalVPawan]

It is the my question Sinx+cosx/ (Sinx-cosx)^3

[@IntegralsForYou]

Hello, Pawan Kumar! Here you have the answer: Integral of (sin(x)+cos(x))/(sin(x)-cos(x))^3 dx = = Integral of 1/(sin(x)-cos(x))^3 (sin(x)+cos(x))dx = u = sin(x) - cos(x) du = ( cos(x) - (-sin(x)) )dx = (cos(x)+sin(x))dx = (sin(x)+cos(x))dx = Integral of 1/u^3 du = = Integral of u^(-3) du = = u^(-3+1)/(-3+1) = = u^(-2)/(-2) = = -1/(2u^2) = = -1/[2(sin(x)-cos(x))^2] + C ;-D

[@alinasaifi4116]

Thank you 😊

[@IntegralsForYou]

My pleasure! ☺☺

[@pritykumar5483]

😅gadha

[@DivyanshiMishra-tb2sr]

Thank you Sir🙏

[@IntegralsForYou]

You're welcome! 😉

[@HuyenThanh-ck1cz]

Cảm ơn rất nhiều😭🙏🙏

[@IntegralsForYou]

My pleasure! 😎

[@muskankhardu9634]

Thank you sir

[@IntegralsForYou]

My pleasure! 😊😊

[@Jakiasultana-z3b]

Jazakallahu Khoiran!

[@IntegralsForYou]

My pleasure! 😎

[@anjalivinod7448]

thq so much . the video was short and clear . 👍👍

[@IntegralsForYou]

You're welcome, anjalivinod vinod! :-D

[@manishajoshi167]

Short???

[@ranjanvadhel7948]

From where are u @integrals for you Nice solution

[@IntegralsForYou]

Thank you, Arya! I'm from Spain 😊

[@katakurisama898]

Integral of sin (x) is -cos (x ) and integral of cos( x) is +sin (x ),so with minus(-) sign in between them the next integral in next step should be -cos (x ) - sin(x) so why did you wrote -cos(x) + sin (x) in next integral step directly?? 🥲with minus(-)sign in between them( - )gets multiplied by +sin (x) resulting in( -)×(+)=(-) so therefore -sin (x) but you wrote +sin(x)😅🥲🥲why???

[@IntegralsForYou]

Hi! In the first step I looked the denominator and saw that if I do u=sin(x)+cos(x) then du = (cos(x)-sin(x))dx . Then, for the first step I just changed sin(x)-cos(x) into -cos(x)+sin(x) in order to have the same order than (cos(x)-sin(x))dx. Since I have -cos(x)+sin(x) and I want to have cos(x)-sin(x) on the numerator, we multiply by -1 inside and outside the integral and we have the expression we were looking for: Integral of (sin(x)-cos(x))/(sin(x)+cos(x)) dx = = Integral of (-cos(x)+sin(x))/(sin(x)+cos(x)) dx = = - Integral of -(-cos(x)+sin(x))/(sin(x)+cos(x)) dx = = - Integral of (cos(x)-sin(x))/(sin(x)+cos(x)) dx = = - Integral of 1/(sin(x)+cos(x)) (cos(x)-sin(x))dx = Substitution: u = sin(x)+cos(x) du = (cos(x)-sin(x))dx = - Integral of 1/u du = = -ln|u| = = -ln|sin(x)+cos(x)| + C Hope it helped! ;-)

[@katakurisama898]

@@IntegralsForYou 🥺🥺ty

[@tanmayasahoo4326]

du/u ka integration log e |u| nahin hota kya ?

[@smartleka875]

Integrate sinx+cosx/sinx-cosx plz answer it

[@IntegralsForYou]

Hi, Smart Leka, here you have the solution: Integral of (sin(x)+cos(x))/(sin(x)-cos(x)) dx = = Integral of 1/(sin(x)-cos(x)) (sin(x)+cos(x)) dx = Substitution: u = sin(x) - cos(x) du = (cos(x) - (-sin(x))) dx = (cos(x)+sin(x)) dx = (sin(x)+cos(x)) dx = Integral of 1/u du = = ln|u| = = ln|sin(x)-cos(x)| + C ;-D

[@CoolishCrane8ICz]

Am i the only one not listening nothing?

[@IntegralsForYou]

Hi! No, you're not the only one! All my videos are muted 😀. I prefer to let people think why am I doing each step and if they don't understand it they can ask me in a comment. In my opinion, it is the best way to learn to integrate

[@rabinpaudel4401]

how to do sinx/1+tanx dx of its antiderivatives

[@Chayanshijain]

After watching this ..found myself so silly Thank you so much for this

[@IntegralsForYou]

You're welcome, Chayanshi Jain, and don't worry, you are not the only one, it took me a while to find the secret... ;-D

[@СнежныйБарс-г2я]

439

[@IntegralsForYou]

😊

[@aryanvatsaofficial07]

Sir what is meaning of ln in this video

[@IntegralsForYou]

en.wikipedia.org/wiki/Natural_logarithm 😉😉

[@muskankhardu9634]

ln means log

[@davimbarbosadasilva924]

tnank you, you save me...

[@IntegralsForYou]

You're welcome!! ;-D

[@divyanshisingh8071]

u are really good/...

[@IntegralsForYou]

Thanks! ;-D

[@parthgoenka5834]

Thanks a lot

[@IntegralsForYou]

You're welcome! ;-D

[@priteechaudhary9664]

Just

[@IntegralsForYou]

😉

[@kainglay6453]

Very good teacher

[@IntegralsForYou]

Thank you very much!

[@chantha5744]

Good

[@IntegralsForYou]

Thanks, Chan Tha! ;-D

[@shubhamg9495]

Thanks for the Integral for me 😉

[@IntegralsForYou]

My pleasure! 💪

[@TejaswiLaluYadav]

Thanks for solving this problem

[@IntegralsForYou]

You're welcome! 😉

[@nguyenan1433]

You’re great but your handwriting isn’t...

[@IntegralsForYou]

Well... at least I'm great! ;-D

[@leehoanggg]

chữ vậy đc rồi, muốn thế nào nữa. tầm cao bá quát mới đọc đc à. ??

[@divyanshisingh8071]

why bro even his handwriting is great ....

[@sourav6899]

Speak while explaining