微积分基本公式.docVIP

微积分基本公式 微积分基本公式 PAGE 微积分基本公式 微积分公式 Dx sin x=cos x cos x = -sin x tan x = sec2 x cot x = -csc2 x sec x = sec x tan x csc x = -csc x cot x ? sin x dx = -cos x + C ? cos x dx = sin x + C ? tan x dx = ln |sec x | + C ? cot x dx = ln |sin x | + C ? sec x dx = ln |sec x + tan x | + C ? csc x dx = ln |csc x – cot x | + C sin-1(-x) = -sin-1 x cos-1(-x) = ? - cos-1 x tan-1(-x) = -tan-1 x cot-1(-x) = ? - cot-1 x sec-1(-x) = ? - sec-1 x csc-1(-x) = - csc-1 x Dx sin-1 ()= cos-1 ()= tan-1 ()= cot-1 ()= sec-1 ()= csc-1 ()= ? sin-1 x dx = x sin-1 x++C ? cos-1 x dx = x cos-1 x-+C ? tan-1 x dx = x tan-1 x-?ln (1+x2)+C ? cot-1 x dx = x cot-1 x+?ln (1+x2)+C ? sec-1 x dx = x sec-1 x- ln |x+|+C ? csc-1 x dx = x csc-1 x+ ln |x+|+C sinh-1 ()= ln (x+) xR cosh-1 ()=ln (x+) x≧1 tanh-1 ()=ln () |x| 1 coth-1 ()=ln () |x| 1 sech-1()=ln(+)0≦x≦1 csch-1 ()=ln(+) |x| 0 Dx sinh x = cosh x cosh x = sinh x tanh x = sech2 x coth x = -csch2 x sech x = -sech x tanh x csch x = -csch x coth x ? sinh x dx = cosh x + C ? cosh x dx = sinh x + C ? tanh x dx = ln | cosh x |+ C ? coth x dx = ln | sinh x | + C ? sech x dx = -2tan-1 (e-x) + C ? csch x dx = 2 ln || + C duv = udv + vdu ? duv = uv = ? udv + ? vdu →? udv = uv - ? vdu cos2θ-sin2θ=cos2θ cos2θ+ sin2θ=1 cosh2θ-sinh2θ=1 cosh2θ+sinh2θ=cosh2θ Dx sinh-1()= cosh-1()= tanh-1()= coth-1()= sech-1()= csch-1()= ? sinh-1 x dx = x sinh-1 x-+ C ? cosh-1 x dx = x cosh-1 x-+ C ? tanh-1 x dx = x tanh-1 x+ ? ln | 1-x2|+ C ? coth-1 x dx = x coth-1 x- ? ln | 1-x2|+ C ? sech-1 x dx = x sech-1 x- sin-1 x + C ? csch-1 x dx = x csch-1 x+ sinh-1 x + C aγ a γ Rαβcb R α β c b sin 3θ=3sinθ-4sin3θ cos3θ=4cos3θ-3cosθ →sin3θ= ? (3sinθ-sin3θ) →cos3θ=?(3cosθ+cos3θ) sin x = cos x = sinh x = cosh x = 正弦定理:= ==2R 余弦定理: a2=b2+c2-2bc cosα b2=a2+c2-2ac cosβ c2=a2+b2-2ab cosγ sin (α±β)=sin α cos β ± cos α sin β cos (α±β)=cos α cos β sin α sin β 2 sin α cos β = sin (α+β) + sin (α-β) 2 cos α sin β = sin (α+β) - sin (α-β) 2 cos α cos β = cos (α-β) + cos (α+