(Method 2) Integral of x^3/(x^2+1) (substitution)

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ะŸะพะบะฐะทะฐั‚ัŒ ะพะฟะธัะฐะฝะธะต

๐Ÿ™ˆ ๐’๐š๐ฆ๐ž ๐ข๐ง๐ญ๐ž๐ ๐ซ๐š๐ฅ, ๐๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ ๐ฆ๐ž๐ญ๐ก๐จ๐๐ฌ

โœ… ๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐ญ๐จ ๐œ๐ก๐ž๐œ๐ค ๐ญ๐ก๐ž ๐ฌ๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง

๐Ÿšถ ๐’๐ญ๐ž๐ฉ๐ฌ
00:00 Rewrite expression
00:11 Substitution: u=x^2
00:15 Differentiate in both sides
00:26 Substitute x^2 and x*dx
00:39 Rewrite expression
00:53 Split into two integrals
01:11 Integrate 1 and 1/(u+1)
01:25 Undo substitution: u in terms of x
01:36 Add integration constant +C
01:44 Final answer!

๐Ÿ” ๐€๐ซ๐ž ๐ฒ๐จ๐ฎ ๐ฅ๐จ๐จ๐ค๐ข๐ง๐  ๐Ÿ๐จ๐ซ ๐š ๐ฉ๐š๐ซ๐ญ๐ข๐œ๐ฎ๐ฅ๐š๐ซ ๐ข๐ง๐ญ๐ž๐ ๐ซ๐š๐ฅ? ๐…๐ข๐ง๐ ๐ข๐ญ ๐ฐ๐ข๐ญ๐ก ๐ญ๐ก๐ž ๐ข๐ง๐ญ๐ž๐ ๐ซ๐š๐ฅ ๐ฌ๐ž๐š๐ซ๐œ๐ก๐ž๐ซ:

๐ŸŽ“ ๐‡๐š๐ฏ๐ž ๐ฒ๐จ๐ฎ ๐ฃ๐ฎ๐ฌ๐ญ ๐ฅ๐ž๐š๐ซ๐ง๐ž๐ ๐š๐ง ๐ข๐ง๐ญ๐ž๐ ๐ซ๐š๐ญ๐ข๐จ๐ง ๐ฆ๐ž๐ญ๐ก๐จ๐? ๐…๐ข๐ง๐ ๐ž๐š๐ฌ๐ฒ, ๐ฆ๐ž๐๐ข๐ฎ๐ฆ ๐š๐ง๐ ๐ก๐ข๐ ๐ก ๐ฅ๐ž๐ฏ๐ž๐ฅ ๐ž๐ฑ๐š๐ฆ๐ฉ๐ฅ๐ž๐ฌ ๐ก๐ž๐ซ๐ž:

๐Ÿ‘‹ ๐…๐จ๐ฅ๐ฅ๐จ๐ฐ @๐ข๐ง๐ญ๐ž๐ ๐ซ๐š๐ฅ๐ฌ๐Ÿ๐จ๐ซ๐ฒ๐จ๐ฎ ๐Ÿ๐จ๐ซ ๐š ๐๐š๐ข๐ฅ๐ฒ ๐ข๐ง๐ญ๐ž๐ ๐ซ๐š๐ฅ! ๐Ÿ˜‰

๐…๐จ๐ฅ๐ฅ๐จ๐ฐ ๐ˆ๐ง๐ญ๐ž๐ ๐ซ๐š๐ฅ๐ฌ ๐…๐จ๐ซ๐˜๐จ๐ฎ

๐ƒ๐จ๐ง๐š๐ญ๐ž

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IntegralsForYou
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It is also a very interesting integration by parts, where you integrate 1/(x^2+1) and derivative x^3.

darcash
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That pen looks too good!
Btw thank you.

onlychessbydhanush
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Bukur๐Ÿ˜. First integral calculus test December 21.

TheTadek
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Can you solve it by trigonometric substitution please?

Amfs
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MatematiฤŸin evrensel bi dil olmasฤฑ harika ๐Ÿคฉ

gozdecandan
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By which pen you're writing sir ?

tanishadas
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Hello. Could you explain why right after simplifying (u+1/u+1) it gave 1, but right after putting u?

simassantanaufrpe
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What do you write with? Pen or pencil. What is its company name. Absolutely amazing videos BTW... KEEP ROCKING... from ๐Ÿ‡ฎ๐Ÿ‡ณ

vaikanpeddi
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Same question but with limit 1 to -1 comes means what answet

meerafathima
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hello i have i question if i have integral dx/sqrt X^2+25 so the answer will be ln|x+sqrt X^2 +25 | -ln5 +c can i right it as ln|x+sqrt X^2 +25| + C so i take the ln5 inside the C is these true?

battomisaadi
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why do i get a different answer when i use u as 1+x^2

anupamsai
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Will you ever do a face and voice reveal one day?๐Ÿ˜ pleasee do

mathgeek
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Can you help me to solve these problems :
1) Integral of 1/(1+sqrt(x)+sqrt(x+1))
2) Integral of 4(x-1)/(1+x+sqrt(x^2+1))
3) Integral of (x-1)/[(x+1)sqrt(x^2+1)]
Thanks for helping me a lot.

nguyenhathoang