Integral of sin(x)/cos^4(x) (substitution)

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๐Ÿšถ ๐’๐ญ๐ž๐ฉ๐ฌ
00:00 Rewrite expression
00:15 Substitution: u=cos(x)
00:21 Differentiate in both sides
00:36 Substitute cos(x) and sin(x)dx
00:50 Rewrite expression
00:56 Integrate u^(-4)
01:05 Rewrite expression
01:18 Undo substitution: u in terms of x
01:25 Add integration constant +C
01:31 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

#integralsforyou #integrals #integrationbysubstitution
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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˜‰

IntegralsForYou
ะะฒั‚ะพั€

Hello. Can you solve this please? from 1 to 7 f(sqrt(4x-3)) =16, from 1 to 5 x.f(x) =?

ayseatl
ะะฒั‚ะพั€

have you done integral of e to the power of x squared? if not, please do!
you saved me so many times man, thabk you so much!!!

ioanab
ะะฒั‚ะพั€

Great! I don't know if it's my computer's problem, but I can't hear the steps.
Anyways, thanks for the video!!
Greetings from Chile

cochayuyo