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31 Cards in this Set

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d/dx (sin-¹x)
1/sqrt(1-x²)
d/dx (sin-¹u)
1/ (1-u²) du/dx
d/dx (tan-¹x)
1/ (1+x²)
d/dx (tan-¹u)
1/(1+u²) du/dx
d/dx (sec-¹x)
1/x[sqrt(x²-1)]
d/dx(sec-¹u)
1/[u(sqrt u²-1)]
sin(x+y)
sinxcosy+cosxsiny
sin(x-y)
sinxcosy-cosxsiny
cos(x+y)
cosxcosy-sinxsiny
cos(x-y)
cosxcosy+sinxsiny
tan(x+y)
tanx+tany/1-tanxtany
sin²x
1-cos2x/2
tan(x-y)
tanx-tany/1+tanxtany
sin2x
2sinxcosx
cos2x
cos²x-sin²x
tan2x
2tanx/1-tan²x
sin²x
1-cos2x/2
cos²x
1+cos2x/2
tan²x
1-cos2x/1+cos2x
sin u/2
±sqrt(1-cosu/2)
cos u/2
±sqrt(1+cosu/2)
integral dx/[sqrt(1-x²)]
sin-¹x + c
integral du/[sqrt(a²-u²)]
sin-¹u/a + c
integral dx/(1+x²)
tan-¹x + c
integral du/(a²+u²)
1/a tan-¹(u/a) + c
integral dx/x[sqrt x²-1]
sec-¹x + c
integral du/u[sqrt u²-a²]
1/a sec-¹ u/a + c
shell
V=2¶ integral x · f(x)dx
revolves around y
disk
V=¶ integral [f(x)]²dx
revolves around x axis
integral of sinˆM x·cosˆN x dx
1)N is odd: u=sinx; du=cosxdx
cos²x=1-sin²x

2)M is odd: u=cosx; du=-sinxdx
sin²x=1-cos²x

3)M and N are even:
sin²x=1-cos2x/2
cos²x=1+cos2x/2
integral tanˆM x ·secˆN x dx
1)N is even: u=tanx; du=sec²x
sec²x=1+tan²x

2)M is odd: u=secx: du=secxtanxdx
tan²x=sec²x-1