Integral of (x-arctan(x))/(1+x^2) (substitution)
💥 𝐃𝐞𝐫𝐢𝐯𝐚𝐭𝐢𝐯𝐞𝐬 𝐅𝐨𝐫𝐘𝐨𝐮
/ @derivativesforyou
🍏 𝐀𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐚 𝐝𝐚𝐲 𝐤𝐞𝐞𝐩𝐬 𝐭𝐡𝐞 𝐝𝐨𝐜𝐭𝐨𝐫 𝐚𝐰𝐚𝐲
/ integralsforyou
/ integralsforyou
🎓 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭𝐬
• 🧑🔧 Integration by parts
• 🧑🔧 Integration by substitution
• 🧑🔧 Integration by trig substitution
• 🧑🔧 Integration by Weierstrass substitution
• 🧑🔧 Integration by partial fraction decomp...
✍🏼 𝐖𝐞𝐛𝐬𝐢𝐭𝐞
https://integralsforyou.com
💪 𝐇𝐨𝐰 𝐭𝐨 𝐜𝐨𝐥𝐥𝐚𝐛𝐨𝐫𝐚𝐭𝐞
Subscribe to Integrals ForYou
Watch, like and share the videos
Use SuperThanks in the videos
Join the community: / @integralsforyou
🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Split into two integrals
00:22 Rewrite expression
00:46 Substitution: u = 1+x^2
00:54 Differentiate in both sides
00:59 Substitute 1+x^2 and 2x*dx
01:16 Substitution: t = arctan(x)
01:23 Differentiate in both sides
01:30 Substitute arctan(x) and (1/(1+x^2))*dx
01:43 Integrate 1/u
01:51 Integrate t
01:56 Undo substitution: u in terms of x
02:06 Undo substitution: t in terms of x
02:15 Add integration constant +C
02:26 Final answer!
02:32 See more!
#integralsforyou #integrals #integration