Integral of 1/(1-x)

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𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭𝐬
► Integration by parts 👉 • 🧑‍🔧 Integration by parts
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✍🏼 integralsforyou.com - Integral of 1/(1-x) - How to integrate it step by step using the substitution method!
🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Substitution: u=1-x
00:08 Differentiate in both sides
00:17 Substitute 1-x and dx
00:29 Rewrite expression
00:36 Integrate 1/u
00:40 Undo substitution: u in terms of x
00:44 Add integration constant +C
00:50 Final answer!
00:56 See more!
🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐨𝐟 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐬𝐨𝐫𝐭𝐞𝐝 𝐛𝐲 𝐥𝐞𝐯𝐞𝐥 (𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡) 𝐢𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮.𝐜𝐨𝐦:
► Integration by parts 👉 integralsforyou.com/integrati...
► Integration by substitution 👉 integralsforyou.com/integrati...
► Integration by trig substitution 👉 integralsforyou.com/integrati...
► Integration by Weierstrass substitution 👉 integralsforyou.com/integrati...
► Integration by partial fraction decomposition 👉 integralsforyou.com/integrati...
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[@IntegralsForYou]

✍🏼 integralsforyou.com ✍🏼 🔍 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 🙋‍♂ 𝐃𝐨𝐧𝐚𝐭𝐞: ▶ Join the Integrals ForYou community: kzbin.info/door/NLRwiQSPlAn_hiEM2yWIwgjoin

[@fluxite1642]

Iiiiintegraaal ❤ Cute integral ❤ I want to hug this one 😄

[@IntegralsForYou]

😂😊♥

[@gsusmonzon]

Wow, thank you for this resource. Your channel is helping me a lot. Keep posting such a great content 💪

[@IntegralsForYou]

Thanks, I will do! 😊 By the way, I recently opened a new channel for derivatives! Take a look and subscribe to help me grow it! 💪 www.youtube.com/@DerivativesForYou Thank you! ❤

[@ayeshamahvish1725]

It was very easy.

[@IntegralsForYou]

Not for the beginners! 🤭

[@TheTadek2001]

Bukur 😍

[@IntegralsForYou]

Bukur, my friend! How are you? ❤

[@TheTadek2001]

@@IntegralsForYou Not great. The first cycle of Computer Science is coming to an end and honestly CS is terrible. I am going to Electronics for the second cycle, while still dual majoring the real field of interest Quality Science. However, I am uncertain if I get the scholarship and I can end up cleaning rooms.

[@IntegralsForYou]

@@TheTadek2001 Oh, I'm sorry you are in this situation... I wish you the best, I am sure you will end up doing what you like! 💪

[@alexkid1]

Why can't you invert so that it becomes (1-x)^-1 and then integrate?

[@IntegralsForYou]

Hi! Because the next general formula only applies when "n" is different from -1 (if not we would divide by zero...): Integral of f'(x)[f(x)]^n dx = [f(x)]^(n+1)/(n+1) + C To sum up: 1. For "n" different from -1: Integral of (1-x)^n dx = = - Integral of -(1-x)^n dx = = -(1-x)^(n+1)/(n+1) = = (-1/(n+1))*(1-x)^(n+1) + C 2. For n=-1 Integral of (1-x)^n dx = = Integral of (1-x)^(-1) dx = = Integral of 1/(1-x) dx = (watch the video for the details) = -ln|1-x| + C Hope it helped! 💪

[@alexkid1]

@@IntegralsForYou I think I understand. If you have it at -1 and then integrate it would be ^-1+1 and also in the divisor would be -1+1. Thanks for the help boss.

[@IntegralsForYou]

@@alexkid1 My pleasure! Thanks for asking! ❤

[@samruddhikabra797]

I wanted to ask if instead of this it wouldve be int1/(1-x)^2 can we assume it has int(1-x)^-2 and then intergate to get the ans as -(1-x)^-1 +c?

[@IntegralsForYou]

Hi! Not exactly...! Remember that we need the derivative of 1-x multiplying the dx. I did the video here 👉 kzbin.info/www/bejne/pHK6qn1titOcm5I . You can also do it by the substitution u=1-x as I do in the video of the integral of 1/(1-x): Integral of 1/(1-x)^2 dx = Substitution: u = 1-x du = -dx ==> -du = dx = Integral of 1/u^2 (-du) = = - Integral of u^(-2) du = = - u^(-1)/(-1) = = u^(-1) = = 1/u = = 1/(1-x)

[@samruddhikabra797]

@@IntegralsForYou omg yess!! Thank you soo much for replying and clearing my doubt!! Now I get my mistake!! You are such a saviour!!! 🥹🫶

[@IntegralsForYou]

@@samruddhikabra797 my pleasure! enjoy the channel ❤