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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 xDx sin-1 ()= a?1a2?x2? 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 2 ? sin-1 x dx = x sin-1 x+1?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 x cos-1 ()= ax?atan-1 ()=2 aa?x2xcot-1 ()= a? cos-1 x dx = x cos-1 x-1?x2+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+x2?1|+C ? csc-1 x dx = x csc-1 x+ ln xsinh-1 ()= ln (x+a2?x2) x?R axcosh-1 ()=ln (x+x2?a2) x≧1 ax1a?xtanh-1 ()=ln () |x| <1 a2aa?xx1x?acoth-1 ()=ln () |x| >1 a2ax?a2x?11?xsech-1()=ln(+)0≦x≦1 2axx2x11?xcsch-1 ()=ln(+) |x| >0 axx2x?asec-1 ()= 22axx?a|x+x2?1|+C csc-1 (x/a)= 精品资料
______________________________________________________________________________________________________________ Dx sinh x = cosh x cosh x = sinh x tanh x = sech2 x coth x = -csch2 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 duv = udv + vdu ? duv = uv = ? udv + ? vdu →? udv = uv - ? vdu cos2θ-sin2θ=cos2θ cos2θ+ sin2θ=1 cosh2θ-sinh2θ=1 cosh2θ+sinh2θ=cosh2θ sech x = -sech x tanh ? sech x dx = -2tan-1 (e-x) + C x csch x = -csch x coth x xDx sinh-1()= axcosh-1()= a1a?x1x?a222? csch x dx = 2 ln |1?e?x1?e?2x| + C ? sinh-1 x dx = x sinh-1 x-1?x2+ C sin 3θ=3sinθ-4sin3θ 2 ? cosh-1 x dx = x cosh-1 x-x2?1+ C cos3θ=4cos3θ-3cosθ ? tanh-1 x dx = x tanh-1 x+ ? ln | 1-x2|+ →sin3θ= ? (3sinθ-sin3θ) C →cos3θ=?(3cosθ+cos3θ) x?atanh-1()= 2 aa?x2xcoth-1()= axsech-1()= a?a 22xa?xcsch-1(x/a)=ejx?e?jx cos x = ? coth-1 x dx = x coth-1 x- ? ln | 1-x2|+ sin x = 2jC β ejx?e?jx 2ex?e?xsinh x = cosh x = 2? sech-1 x dx = x sech-1 x- sin-1 x + C ?axa?x22 x?xe?e ? csch-1 x dx = x csch-1 x+ sinh-1 x + C 2 R a γ 正弦定理:b bca= ==2R sin?sin?sin?α 餘弦定理: a2=b2+c2-2bc cosα b2=a2+c2-2ac cosβ c2=a2+b2-2ab cosγ c 精品资料
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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+β) 2 sin α sin β = cos (α-β) - cos (α+β) 23nxxxex=1+x+++…++ … 2!3!n!sin α + sin β = 2 sin ?(α+β) cos ?(α-β) sin α - sin β = 2 cos ?(α+β) sin ?(α-β) cos α + cos β = 2 cos ?(α+β) cos ?(α-β) cos α - cos β = -2 sin ?(α+β) sin ?(α-β) tan (α±β)=tan??tan??cot?cot?, cot (α±β)= ?tan?tan?cot??cot??1= n i?1nn(?1)nx2n?1x3x5x7sin x = x-+-+…++ … (2n?1)!3!5!7!(?1)nx2nx2x4x6cos x = 1-+-+…++ … (2n)!2!4!6!(?1)nxn?1x2x3x4ln (1+x) = x-+-+…++ … (n?1)!234n2n?1357(?1)xxxxtan-1 x = x-+-+…++ … (2n?1)357?i= ?n (n+1) i?1n2i?= i?1n1 n (n+1)(2n+1) 6?ii?13= [?n (n+1)]2 ?Γ(x) = ?t0x-1e-t dt = 21?t0?2x-1e?t2dt = 2??01(ln)x-1 dt t(1+x)r =1+rx+-1 ??0xm?1dx (1?x)m?n大寫 Α Β Γ 小寫 讀音 alpha beta gamma 大寫 Ι Κ Λ 小寫 讀音 iota kappa lambda 精品资料 大寫 Ρ Σ Τ 小寫 讀音 rho α β γ ι κ λ ρ σ, ? sigma τ tau
微积分公式大全
