Integral of 1/(e^x-1)^2 (substitution + partial fraction decomposition)

Integrals ForYou
Integrals ForYou
2.8 هزار بار بازدید - 6 ماه پیش - ✍🏼
✍🏼 https://integralsforyou.com - Integral of x*ln(x+sqrt(1+x^2))/sqrt(1+x^2) - How to integrate it step by step using the substitution method and integration by partial fraction decomposition!

🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Substitution: u=e^x-1
00:10 Differentiate in both sides
00:34 Substitute e^x-1 and dx
00:49 Rewrite expression
01:00 Partial fraction decomposition for 1/((u^2)(u+1))
01:09 Find A, B and C
03:41 1/((u^2)(u+1)) in terms of A, B and C
04:16 Rewrite expression
04:40 Integrate 1/u, u^(-2) and 1/(u+1)
04:59 Undo substitution: u in terms of x
05:20 Simplify expression
05:40 Add integration constant +C
05:50 Final answer!
05:56 See more!

🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫:
► Integral searcher 👉https://integralsforyou.com/integral-...


🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡 𝐥𝐞𝐯𝐞𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐡𝐞𝐫𝐞:
► Integration by parts 👉https://integralsforyou.com/integrati...
► Integration by substitution 👉https://integralsforyou.com/integrati...
► Integration by trig substitution 👉https://integralsforyou.com/integrati...
► Integration by Weierstrass substitution 👉https://integralsforyou.com/integrati...
► Integration by partial fraction decomposition 👉https://integralsforyou.com/integrati...


👋 𝐅𝐨𝐥𝐥𝐨𝐰 @𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮 𝐟𝐨𝐫 𝐚 𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥! 😉
📸 Instagram: integralsforyou


𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮
▶️ Youtube: https://www.youtube.com/integralsfory...
📸 Instagram: Instagram: integralsforyou
👍 Facebook: Facebook: IntegralsForYou


🙋‍♂️ 𝐃𝐨𝐧𝐚𝐭𝐞:
▶️ Join the Integrals ForYou community: @integralsforyou


#integralsforyou #integrals #integrationbyparts
6 ماه پیش در تاریخ 1402/10/25 منتشر شده است.
2,875 بـار بازدید شده
... بیشتر