Integral of sqrt(x^n-1)/x (substitution)
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🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Multiply by x^(n-1)/x^(n-1)
00:15 Rewrite expression
00:27 Substitution: u=sqrt(x^n - 1)
00:35 Differentiate in both sides
01:13 Substitute sqrt(x^n - 1), x^n and (x^(n-1))dx
01:54 Rewrite expression
02:05 Add +1-1 and split into two integrals
02:36 Integrate 1 and 1/(1+u^2)
02:54 Undo substitution: u in terms of x
03:13 Add integration constant +C
03:25 Final answer!
🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫:
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🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡 𝐥𝐞𝐯𝐞𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐡𝐞𝐫𝐞:
► Integration by parts 👉https://integralsforyou.com/integration-methods/integration-by-parts
► Integration by substitution 👉https://integralsforyou.com/integration-methods/integration-by-substitution
► Integration by trig substitution 👉https://integralsforyou.com/integration-methods/integration-by-trig-substitution
► Integration by Weierstrass substitution 👉https://integralsforyou.com/integration-methods/integration-by-weierstrass-substitution
► Integration by partial fraction decomposition 👉https://integralsforyou.com/integration-methods/integration-by-partial-fraction-decomposition
👋 𝐅𝐨𝐥𝐥𝐨𝐰 @𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮 𝐟𝐨𝐫 𝐚 𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥! 😉
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Видео Integral of sqrt(x^n-1)/x (substitution) канала Integrals ForYou
🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Multiply by x^(n-1)/x^(n-1)
00:15 Rewrite expression
00:27 Substitution: u=sqrt(x^n - 1)
00:35 Differentiate in both sides
01:13 Substitute sqrt(x^n - 1), x^n and (x^(n-1))dx
01:54 Rewrite expression
02:05 Add +1-1 and split into two integrals
02:36 Integrate 1 and 1/(1+u^2)
02:54 Undo substitution: u in terms of x
03:13 Add integration constant +C
03:25 Final answer!
🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫:
► Integral searcher 👉https://integralsforyou.com/integral-searcher
🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡 𝐥𝐞𝐯𝐞𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐡𝐞𝐫𝐞:
► Integration by parts 👉https://integralsforyou.com/integration-methods/integration-by-parts
► Integration by substitution 👉https://integralsforyou.com/integration-methods/integration-by-substitution
► Integration by trig substitution 👉https://integralsforyou.com/integration-methods/integration-by-trig-substitution
► Integration by Weierstrass substitution 👉https://integralsforyou.com/integration-methods/integration-by-weierstrass-substitution
► Integration by partial fraction decomposition 👉https://integralsforyou.com/integration-methods/integration-by-partial-fraction-decomposition
👋 𝐅𝐨𝐥𝐥𝐨𝐰 @𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮 𝐟𝐨𝐫 𝐚 𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥! 😉
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𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮
▶️ Youtube: https://www.youtube.com/integralsforyou?sub_confirmation=1
📸 Instagram: https://www.instagram.com/integralsforyou/
👍 Facebook: https://www.facebook.com/IntegralsForYou
𝐃𝐨𝐧𝐚𝐭𝐞
🙋♂️ Patreon: https://www.patreon.com/integralsforyou
#integralsforyou #integrals #integrationbysubstitution
Видео Integral of sqrt(x^n-1)/x (substitution) канала Integrals ForYou
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