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6 Cards in this Set
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antiderivative (sin^m x cos^n x) cos is odd sin is even
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save one cos factor and use cos^2 x = 1 - sin^2 x
substitute u= sinx |
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antiderivative (sin^m x cos^n x) sin is odd cos is even |
save one sin factor and use cos^2 x = 1 - sin^2 x sin^2 x = 1- cos^2 x
substitute u = cosx |
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antiderivative (sin^m x cos^n x) sin is odd cos is odd |
either a factor of sin or cos can be saved and cos^2 x = 1 - sin^2 x can be used |
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antiderivative (sin^m x cos^n x) sin is even cos is even |
use half-angle identities: sin^2x = 1/2 (1-cos2x) or cos^2x = 1/2 (1+cos2x)
it might be useful to use the identity: sinxcosx = 1/2 (sin2x) |
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antiderivative (tan^m x sec^n x) sec is even
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save a factor of sec^2x use sec^2x = 1 + tan^2 x
u = tanx |
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antiderivative (tan^m x sec^n x) tan is odd |
save a factor of secxtanx use sec^2x = 1 + tan^2 x tan^2x = sec^2x - 1
u = secx |