Integral of x/(1+4x^4) (substitution)
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🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Rewrite expression
00:14 Substitution: u=2x^2
00:21 Differentiate in both sides
00:36 Substitute 2x^2 and x*dx
00:52 Take 1/4 outside the integral
01:02 Integrate 1/(1+u^2)
01:10 Undo substitution: u in terms of x
01:18 Add integration constant +C
01:27 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 x/(1+4x^4) (substitution) канала Integrals ForYou
🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Rewrite expression
00:14 Substitution: u=2x^2
00:21 Differentiate in both sides
00:36 Substitute 2x^2 and x*dx
00:52 Take 1/4 outside the integral
01:02 Integrate 1/(1+u^2)
01:10 Undo substitution: u in terms of x
01:18 Add integration constant +C
01:27 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:
▶️ Join the Integrals ForYou community: https://www.youtube.com/channel/UCNLRwiQSPlAn_hiEM2yWIwg/join
#integralsforyou #integrals #integration
Видео Integral of x/(1+4x^4) (substitution) канала Integrals ForYou
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