Integral of sqrt(1-x)/(x+sqrt(x)) (substitution + substitution)
✍🏼 https://integralsforyou.com - Integral of sqrt(1-x)/(x+sqrt(x)) - How to integrate it step by step using the substitution method!
🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Rewrite expression
00:31 Substitution: u=sqrt(x)
00:37 Differentiate in both sides
00:43 Substitute sqrt(x), x and (1/2sqrt(x))dx
01:14 Substitution: u=sin(t)
01:24 Differentiate in both sides
01:32 Substitute u, u^2 and du
01:57 Apply 1=sin^2(t)+cos^2(t)
02:42 Simplify expression
03:01 Apply 1=sin^2(t)+cos^2(t)
03:19 Apply a^2-b^2 = (a+b)(a-b)
03:57 Simplify expression
04:15 Integrate 1 and sin(t)
04:28 Undo substitution: t in terms of u
04:52 Simplify expression
05:16 Undo substitution: u in terms of x
05:27 Add integration constant +C
05:37 Final answer!
05:41 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! 😉
📸 / integralsforyou
𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮
▶️ Youtube: https://www.youtube.com/integralsfory...
📸 Instagram: / integralsforyou
👍 Facebook: / integralsforyou
🙋♂️ 𝐃𝐨𝐧𝐚𝐭𝐞:
▶️ Join the Integrals ForYou community: / @integralsforyou
#integralsforyou #integrals #integration