Integral of x*arctan(2x) (by parts)

Опубликовано: 23 Август 2026
на канале: Integrals ForYou

2,229

💥 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 Parts: Integral of u dv = uv - Integral of v du
00:11 Choose u and dv
00:23 Differentiate u to get du
00:44 Integrate dv to get v
00:50 Substitute u, v and du
01:16 Simplify expression
01:44 Multiply and divide by 4 and add +1-1 on the numerator
02:21 Split into two integrals
03:00 Simplify and multiply and divide by 2
03:45 Integrate 1 and 2/(1+(2x)^2)
04:08 Rewrite expression
04:29 Add integration constant +C
04:41 Final answer!
04:46 See more!

#integralsforyou #integrals #integration