Integral of sin^3(2x) (substitution)

Integral of sin^3(2x) - How to integrate it step by step using the substitution method!
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[@IntegralsForYou]

👋 Follow @integralsforyou for a daily integral 😉 📸 instagram.com/integralsforyou/ 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭 ► Integration by parts kzbin.info/aero/PLpfQkODxXi4-GdH-W7YvTuKmK_mFNxW_h ► Integration by substitution kzbin.info/aero/PLpfQkODxXi4-7Nc5OlXc0zs81dgwnQQc4 ► Integration by trig substitution kzbin.info/aero/PLpfQkODxXi49OUGvTetsTW61kUs6wHnzT ► Integration by Weierstrass substitution kzbin.info/aero/PLpfQkODxXi4-8kbKt63rs1xwo6e3yAage ► Integration by partial fraction decomposition kzbin.info/aero/PLpfQkODxXi4-9Ts0IMGxzI5ssWNBT9aXJ 𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮 ▶️ KZbin kzbin.info 📸 Instagram instagram.com/integralsforyou/ 👍 Facebook facebook.com/IntegralsForYou 𝐃𝐨𝐧𝐚𝐭𝐞 🙋‍♂️ Patreon www.patreon.com/integralsforyou

[@alexminsky1]

I’m a mathematician, I’m just here for the ASMR!

[@mathematicssinging]

😀😂😂😂😂😂👌

[@IntegralsForYou]

hahahaha never thought my videos as ASMR videos 😂😂😂😂 👉 🙊

[@alexminsky1]

Integrals ForYou, you should! I always watch when I’m about to sleep.

[@IntegralsForYou]

@@alexminsky1 I am wondering if you would you appreciate a 1-hour (or more) video of silent integrals. What do you think?

[@alexminsky1]

Integrals ForYou, well, I definitely would and that’s an interesting path to explore, but I’m not so sure about other fellows. I guess a lot of people relate to ASMR videos through sounds or soothing voices. So, I think if you want to cater that to a broader audience, you should consider talking smoothly and describing the process gently. However, even a silent one will attract nerds like me!

[@KnockerTheExtraordinaire]

I respect math Good job❤❤👌👌👌

[@IntegralsForYou]

Thanks! Enjoy the channel! 😉

[@syphaxjuba8420]

bonsoir , j’apprécie votre retour , afin d'illuminer les esprits mathématiques

[@IntegralsForYou]

Merci, syphax juba!! Désolé pour vous répondre si tard, j'étais en vacances juste après publier cette vidéo...! Merci beaucoup de vos commentaires sur toutes mes vidéos! Merci!

[@Mathstoon]

good explanation

[@IntegralsForYou]

Thanks! 😊

[@revm3gtr982]

Could you integrate x^4/1+x^8 please

[@mamadetaslimtorabally7363]

Nice BIC pen. You seem to like BIC pen a lot. Thanks for the integral though. That was nicely done by you. Take care.

[@IntegralsForYou]

hehe thank you! Yes, I always use it for my videos hehe Thanks for your comment! 💪

[@ZyloSol99]

What is the name of that pen you're using?

[@IntegralsForYou]

Hi! It is a bic black pen 😉

[@asanchezmCAFE]

Vaya makina ! El boss de las matemáticas 😎😎 ojalá entendiera algo de todo eso 😆😆

[@IntegralsForYou]

jeje gracias!! cuando le encuentras el sentido, las integrales se vuelven muy fáciles e interesantes! Pero cuando no se le ve el sentido puede ser un infierno... 😞 Un saludo, y gracias por tu comentario!

[@sahanozkan5885]

Hi I have 2 questions, can you solve it if I send it to you

[@sahanozkan5885]

very important and urgent please

[@thiswasamistake8077]

Thanks a lot!

[@IntegralsForYou]

You're welcome! 😊

[@thiswasamistake8077]

@@IntegralsForYou ❤️❤️❤️

[@IntegralsForYou]

@this was a mistake hehe enjoy the channel! 😉

[@thiswasamistake8077]

@@IntegralsForYou thanks again haha❤️

[@IntegralsForYou]

@this was a mistake 😀👍

[@TheTadek2001]

Bukur 😍

[@IntegralsForYou]

Hi, EPEJSÓDION! How's my bukur man? 😊

[@pashupatinathdutta4648]

Sir, Please integrate cos^3(2x).Regards.

[@IntegralsForYou]

Of course, here you have the solution: Integral of cos^3(2x) dx = Substitution: u = 2x du = 2 dx ==> du/2 = dx = Integral of cos^3(u) du/2 = = (1/2)Integral of cos^3(u) du = = (1/2)Integral of cos^2(u)cos(u) du = = (1/2)Integral of (1-sin^2(u)) cos(u) du = Substitution: t = sin(u) dt = cos(u) du = (1/2)Integral of (1-t^2) dt = = (1/2)(t - t^3/3) = = (t/6)(3 - t^2) = = (sin(u)/6)(3 - sin^2(u)) = = (sin(2x)/6)(3 - sin^2(2x)) + C

[@srijangautam7369]

mannn how you hold your pen while writing😑😑

[@anitashukla3144]

Pls solve the integral of {4x+3/(x-2)³} by substitution

[@IntegralsForYou]

Hi! Here you have the solution: Integral of (4x+3)/(x-2)^3 dx = Substitution: u = x-2 ==> u+2 = x du = dx = Integral of (4(u+2)+3)/u^3 du = = Integral of (4u+8+3)/u^3 du = = Integral of ( 4u/u^3 + 11/u^3 ) du = = Integral of ( 4u^(-2) + 11u^(-3) ) du = = 4u^(-2+1)/(-2+1) + 11u^(-3+1)/(-3+1) = = 4u^(-1)/(-1) + 11u^(-2)/(-2) = = -4/u - 11/2u^2 = = -4/(x-2) - 11/2(x-2)^2 + C

[@anitashukla3144]

@@IntegralsForYou thank u so much

[@IntegralsForYou]

@Anita Shukla You're welcome! 😉

[@oguzhantopaloglu9442]

come on man do something hard that has special named functions like integral of sinx/x etc.

[@IntegralsForYou]

In this channel I do indefinite elementary integrals. The next video will be harder 😉