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Integral of sqrt(tan(x))/sin(2x) (substitution)
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Integral of sqrt(tan(x))/sin(2x) - How to integrate it step by step using the substitution method!
๐ถ ๐๐ญ๐๐ฉ๐ฌ
00:00 Use the sin(2x)=2sin(x)cos(x) trig identity
00:27 Multiply by cos(x)/cos(x) on the denominator
00:55 Write sin(x)/cos(x) as tan(x) and cos(x)cos(x) as cos^2(x)
01:25 Simplify expression
01:40 Substitution: u=tan(x)
01:47 Differentiate in both sides
01:53 Substitute tan(x) and (1/cos^2(x))dx
02:04 Integrate 1/2sqrt(u)
02:07 Undo substitution: u in terms of x
02:12 Add integration constant +C
02:18 Final answer!
๐ Follow @integralsforyou on Instagram for a daily integral ๐
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
๐ถ ๐๐ญ๐๐ฉ๐ฌ
00:00 Use the sin(2x)=2sin(x)cos(x) trig identity
00:27 Multiply by cos(x)/cos(x) on the denominator
00:55 Write sin(x)/cos(x) as tan(x) and cos(x)cos(x) as cos^2(x)
01:25 Simplify expression
01:40 Substitution: u=tan(x)
01:47 Differentiate in both sides
01:53 Substitute tan(x) and (1/cos^2(x))dx
02:04 Integrate 1/2sqrt(u)
02:07 Undo substitution: u in terms of x
02:12 Add integration constant +C
02:18 Final answer!
๐ Follow @integralsforyou on Instagram for a daily integral ๐
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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