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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 sinM x·cosN 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 tanM x ·secN x dx 1)N is even: u=tanx; du=sec²x sec²x=1+tan²x 2)M is odd: u=secx: du=secxtanxdx tan²x=sec²x-1