微积分公式大全
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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 x1Dx sin-1 ()= 22aaxx cos-1 ()= axatan-1 ()=2 aax2xcot-1 ()= a 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 dx = x sin-1 x+1x2+C cos-1 x dx = x cos-1 x-1x2+C tan-1 x dx = x tan-1 x-½ln (1+x2)+C cot-1 x dx = x cot-1 x+½ln (1+x2)+C sec-1 x dx = x sec-1 x- ln |x+x21|+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 xsinh-1 ()= ln (x+a2x2) xR axcosh-1 ()=ln (x+x2a2) x≧1 ax1axtanh-1 ()=ln () |x| <1 axa2a1xa-1xcoth ()=ln () |x| >1 -1-12xaa2a csc x dx = x csc x+ ln |x+x1|+C xasec-1 ()= axx2a2csc-1 (x/a)= 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 x11x2sech()=ln(+)0≦x≦1 xax2-1x11x2csch ()=ln(+) |x| >0 2axxduv = udv + vdu -1 duv = uv = udv + vdu → udv = uv - vdu cos2θ-sin2θ=cos2θ cos2θ+ sin2θ=1 cosh2θ-sinh2θ=1 cosh2θ+sinh2θ=cosh2θ sech x = -sech x tanh x sech x dx = -2tan-1 (e-x) + C csch x = -csch x coth x 1ex csch x dx = 2 ln || + C 2x1exDx sinh()= a-11ax1xa222 sinh-1 x dx = x sinh-1 x-1x2+ C cosh-1 x dx = x cosh-1 x-x21+ C sin 3θ=3sinθ-4sin3θ cos3θ=4cos3θ-3cosθ →sin3θ= ¼ (3sinθ-sin3θ) →cos3θ=¼(3cosθ+cos3θ) xcosh()= a-12xatanh-1()= 2 aax2xcoth()= a-1 tanh-1 x dx = x tanh-1 x+ ½ ln | 1-x2|+ C ejxejxejxejxsin x = cos x = 2 coth-1 x dx = x coth-1 x- ½ ln | 1-x2|+ C 2jexexexexsinh x = cosh x = 22abc正弦定理:= ==2R sinsinsin sech-1 x dx = x sech-1 x- sin-1 x + C csch-1 x dx = x csch-1 x+ sinh-1 x + C xa γ sech-1()= 22a axax R b csch-1(x/a)=axax22 β α c 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+β) 2 sin α sin β = cos (α-β) - cos (α+β) x2x3xne=1+x+++…++ … 2!3!n!xsin α + sin β = 2 sin ½(α+β) cos ½(α-β) sin α - sin β = 2 cos ½(α+β) sin ½(α-β) cos α + cos β = 2 cos ½(α+β) cos ½(α-β) cos α - cos β = -2 sin ½(α+β) sin ½(α-β) tan (α±β)=tantancotcot, cot (α±β)= tantancotcot1= n i1nnx3x5x7(1)nx2n1sin x = x-+-+…++ … 3!5!7!(2n1)!x2x4x6(1)nx2ncos x = 1-+-+…++ … 2!4!6!(2n)!x2x3x4(1)nxn1ln (1+x) = x-+-+…++ … 234(n1)!i= ½n (n+1) i1ni2= i1n1 n (n+1)(2n+1) 6ii13= [½n (n+1)]2 2x3x5x7(1)nx2n1tan x = x-+-+…++ … 357(2n1)-1r Γ(x) = tx-1e-t dt = 2t2x-1etdt = 0001(ln)x-1 dt tr(r1)2r(r1)(r2)31m-1n-1(1+x)=1+rx+x+x+… -1β(m, n) =x(1-x) dx=22sin2m-1x cos2n-1x dx
002!3!
=
希腊字母
大写
Α Β Γ Δ
小写 α β γ δ
读音 alpha beta gamma delta
大写 Ι Κ Λ Μ
小写 ι κ λ μ
读音 iota kappa lambda mu
大写 Ρ Σ Τ Υ
0
xm1
dx mn
(1x)
小写 ρ σ, ς τ υ
读音 rho sigma tau upsilon
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