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

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ะŸะพะบะฐะทะฐั‚ัŒ ะพะฟะธัะฐะฝะธะต
Integral of (x^3)sin(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

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๐Ÿšถ ๐’๐ญ๐ž๐ฉ๐ฌ
00:00 Rewrite expression
00:11 Substitution: t=x^2
00:16 Differentiate in both sides
00:26 Substitute x^2 and x*dx
00:39 Rewrite expression
00:48 Parts: Integral of u dv = uv - Integral of v du
01:01 Choose u and dv
01:10 Differentiate u to get du
01:14 Integrate dv to get v
01:25 Substitute u, v and du
01:45 Rewrite expression
02:00 Integrate cos(t)
02:14 Undo substitution: t in terms of x
02:31 Add integration constant +C
02:40 Final answer!

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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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
ะะฒั‚ะพั€

Thankyou so much.i love the format of your videos

BridgetMariaTapia
ะะฒั‚ะพั€

Can we do by parts first only then substitution??

tayzhiying
ะะฒั‚ะพั€

Great sir
Sir can you help me to solve this integration of (1-x^2/x)^1/2

swarnims
ะะฒั‚ะพั€

Please integrate x^2 sin(3x) dx. Regards.

pashupatinathdutta
ะะฒั‚ะพั€

There's a mistake I think u wrote x^3 then solved for x^2. Sorry if I'm wrong

bakaneko
ะะฒั‚ะพั€

me podrรญas dar una manita con esta integral :O u...u \int acรก siguiendo tus vรญdeos :)

Melek_OK.