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Integral of sin^3(x)cos^4(x) (substitution)
ะะพะบะฐะทะฐัั ะพะฟะธัะฐะฝะธะต
Integral of sin^3(x)cos^4(x) - How to integrate it step by step using the substitution method!
โ ๐๐๐ซ๐ข๐ฏ๐๐ญ๐ข๐ฏ๐ ๐ญ๐จ ๐๐ก๐๐๐ค ๐ญ๐ก๐ ๐ฌ๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง
๐ Follow @integralsforyou on Instagram for a daily integral ๐
๐ถ ๐๐ญ๐๐ฉ๐ฌ
00:00 Rewrite expression
00:15 Use the 1=sin^2(x)+cos^2(x) identity
00:51 Substitution: u=cos(x)
00:57 Differentiate in both sides
01:10 Substitute cos(x) and sin(x)dx
01:33 Rewrite expression
02:05 Integrate u^6 and u^4
02:15 Undo substitution: u in terms of x
02:26 Add integration constant +C
02:33 Final answer!
๐๐ง๐ญ๐๐ ๐ซ๐๐ญ๐ข๐จ๐ง ๐ฆ๐๐ญ๐ก๐จ๐๐ฌ ๐ฉ๐ฅ๐๐ฒ๐ฅ๐ข๐ฌ๐ญ
โบ Integration by parts
โบ Integration by substitution
โบ Integration by trig substitution
โบ Integration by Weierstrass substitution
โบ Integration by partial fraction decomposition
๐ ๐จ๐ฅ๐ฅ๐จ๐ฐ ๐๐ง๐ญ๐๐ ๐ซ๐๐ฅ๐ฌ ๐ ๐จ๐ซ๐๐จ๐ฎ
๐๐จ๐ง๐๐ญ๐
#integralsforyou #integrals #integrationbysubstitution
โ ๐๐๐ซ๐ข๐ฏ๐๐ญ๐ข๐ฏ๐ ๐ญ๐จ ๐๐ก๐๐๐ค ๐ญ๐ก๐ ๐ฌ๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง
๐ Follow @integralsforyou on Instagram for a daily integral ๐
๐ถ ๐๐ญ๐๐ฉ๐ฌ
00:00 Rewrite expression
00:15 Use the 1=sin^2(x)+cos^2(x) identity
00:51 Substitution: u=cos(x)
00:57 Differentiate in both sides
01:10 Substitute cos(x) and sin(x)dx
01:33 Rewrite expression
02:05 Integrate u^6 and u^4
02:15 Undo substitution: u in terms of x
02:26 Add integration constant +C
02:33 Final answer!
๐๐ง๐ญ๐๐ ๐ซ๐๐ญ๐ข๐จ๐ง ๐ฆ๐๐ญ๐ก๐จ๐๐ฌ ๐ฉ๐ฅ๐๐ฒ๐ฅ๐ข๐ฌ๐ญ
โบ Integration by parts
โบ Integration by substitution
โบ Integration by trig substitution
โบ Integration by Weierstrass substitution
โบ Integration by partial fraction decomposition
๐ ๐จ๐ฅ๐ฅ๐จ๐ฐ ๐๐ง๐ญ๐๐ ๐ซ๐๐ฅ๐ฌ ๐ ๐จ๐ซ๐๐จ๐ฎ
๐๐จ๐ง๐๐ญ๐
#integralsforyou #integrals #integrationbysubstitution
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