Integral of (x^3)cos(x^2) (substitution + by parts)

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Integral of (x^3)cos(x^2) - How to integrate it step by step using the substitution method and integration by parts!

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: t=x^2
00:16 Differentiate in both sides
00:27 Substitute x^2 and x*dx
00:40 Rewrite expression
00:50 Parts: Integral of u dv = uv - Integral of v du
01:00 Choose u and dv
01:08 Differentiate u to get du
01:12 Integrate dv to get v
01:20 Substitute u, v and du
01:39 Integrate sin(t)
01:55 Rewrite expression
02:10 Undo substitution: t in terms of x
02:27 Add integration constant +C
02:35 Final answer!

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๐ˆ๐ง๐ญ๐ž๐ ๐ซ๐š๐ญ๐ข๐จ๐ง ๐ฆ๐ž๐ญ๐ก๐จ๐๐ฌ ๐ฉ๐ฅ๐š๐ฒ๐ฅ๐ข๐ฌ๐ญ
โ–บ Integration by parts

โ–บ Integration by substitution

โ–บ Integration by trig substitution

โ–บ Integration by Weierstrass substitution

โ–บ Integration by partial fraction decomposition

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

#integralsforyou #integrationbyparts #integrationbysubstitution
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ะะฒั‚ะพั€

๐Ÿ‘‹ Follow @integralsforyou for a daily integral ๐Ÿ˜‰

๐ˆ๐ง๐ญ๐ž๐ ๐ซ๐š๐ญ๐ข๐จ๐ง ๐ฆ๐ž๐ญ๐ก๐จ๐๐ฌ ๐ฉ๐ฅ๐š๐ฒ๐ฅ๐ข๐ฌ๐ญ
โ–บ Integration by parts

โ–บ Integration by substitution

โ–บ Integration by trig substitution

โ–บ Integration by Weierstrass substitution

โ–บ Integration by partial fraction decomposition


๐…๐จ๐ฅ๐ฅ๐จ๐ฐ ๐ˆ๐ง๐ญ๐ž๐ ๐ซ๐š๐ฅ๐ฌ ๐…๐จ๐ซ๐˜๐จ๐ฎ
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IntegralsForYou
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omg man i got stuck on this one for a while kept going in circles, i finally let my pride go and looked this up and immediately was like WOW what a wonderfully simply way to solve this. thx man <3

christopherbarker
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Probably the best integration person on YouTube ๐Ÿ˜Œthanks

CxC_Maths
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Thanks a lot sir ... โค ..this question takes a lot of time

SurenderKumar-kldh
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Oh, thank you sooo much sir, this was one of my assignment questions, thanks a ton โœ”

abdulhafeezahmed
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Integral with more examples


Thank you

MathematicswithAviGarg
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bonsoir maรฎtre merci beaucoup pour cet exercice, il faut donner la rรจgle gรฉnรฉrale pour ce genre d'intรฉgrale, afin qu'elle soit claire
et bonne continuitรฉ

syphaxjuba
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hello sir.. please can you make a video to this integral.. ( integral of exp(-t^3 /3)

safwanahmad
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Try this integration by parts xยฒ cos (xยฒ) dx thankyouu.

alpasirlendit
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I have some differentiation questions can you differentiate ?

siddharthchauhan
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Sir I could not understand -
Integration udv = uv - integration vdu

sandippan
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Mi ejercicio es al revรฉs, integral de xยฒ cos xยณ dx = Sen xยณ/3 + C...
Y la verdad yo esperaba que su procedimiento me ayudara a hacer el mรญo, y para ser sincera no entendรญ nada
๐Ÿ˜ญ๐Ÿ‘‰๐Ÿ‘ˆ

NeMHALSoo
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I'm the only one checkin out the dope pen though

enyioma
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Sir Aapke you ka intergration Kya Hoga๐Ÿคฃ

seema