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微積分公式
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 ()= a-1 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+1?x2+C 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 |x+x2?1|+C 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 |sin-1(-x) = -sin-1 x cos-1(-x) = - cos-1 x tan-1(-x) = -tan-1 x cot-1(-x) = sec-1(-x) = - cot-1 x - sec-1 x csc-1(-x) = - csc-1 x 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?ax?11?x2sech()=ln(+)0≦x≦1 2xax-1?1a?x22x cos-1 ()= ax?atan-1 ()=2 2aa?xxcot-1 ()= ax?asec-1 ()= 22axx?acsc-1 (x/a)= 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 x11?x2csch ()=ln(+) |x| >0 axx2-1duv = udv + vdu duv = uv = → udv = uv - udv + vdu vdu cos2θ-sin2θ=cos2θ cos2θ+ sin2θ=1 1?e?x1?e?2x| + C cosh2θ-sinh2θ=1 cosh2θ+sinh2θ=cosh2θ 精品
. xDx sinh()= a-11a?x1x?a2222 sinh-1 x dx = x sinh-1 x-1?x2+ C cosh-1 x dx = x cosh-1 x-x2?1+ C sin 3θ=3sinθ-4sin3θ cos3θ=4cos3θ-3cosθ xcosh-1()= a C tanh-1 x dx = x tanh-1 x+ ? ln | 1-x2|+ →sin3θ= ? (3sinθ-sin3θ) →cos3θ=?(3cosθ+cos3θ) coth-1 x dx = x coth-1 x- ? ln | 1-x2|+ ejx?e?jxejx?e?jxsin x = cos x = 22jx?a)= 2 aa?x2xcoth-1()= atanh-1(?axC sech-1()= axa2?x2 sech-1 x dx = x sech-1 x- sin-1 x + C csch-1 x dx = x csch-1 x+ sinh-1 x + C β csch-1(x/a)=?axa?x22ex?e?xex?e?xsinh x = cosh x = 22 正弦定理:bca= ==2R sin?sin?sin?R a c γ α b 餘弦定理: 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 ?(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?1nnx3x5x7(?1)nx2n?1sin x = x-+-+…++ … 3!5!7!(2n?1)!x2x4x6(?1)nx2ncos x = 1-+-+…++ … 2!4!6!(2n)!?i= ?n (n+1) i?1n?i2= i?11 n (n+1)(2n+1) 6精品
. x2x3x4(?1)nxn?1ln (1+x) = x-+-+…++ … 234(n?1)!?ii?1n3= [?n (n+1)]2 ??2xxx(?1)xtan x = x-+-+…++ … 357(2n?1)-1357n2n?1Γ(x) = ?tx-1e-t dt = 2?t2x-1e?tdt = 00??01(ln)x-1 dt t(1+x)r =1+rx+r(r?1)2r(r?1)(r?2)3x+x+… -1 希臘字母 (Greek Alphabets) 大寫 Α Β Γ Δ Ε Ζ Η Θ 倒數關係: sinθcscθ=1; tanθcotθ=1; cosθsecθ=1 商數關係: tanθ= sin?cos?; cotθ= cos?sin??0xm?1dx (1?x)m?n小寫 讀音 alpha beta gamma delta epsilon zeta eta theta 大寫 Ι Κ Λ Μ Ν Ξ Ο Π 小寫 讀音 iota kappa lambda mu nu xi omicron pi 大寫 Ρ Σ Τ Υ Φ Χ Ψ Ω 小寫 讀音 rho sigma tau upsilon phi khi psi omega α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ, ? τ υ φ χ ψ ω 平方關係: cos2θ+ sin2θ=1; tan2θ+ 1= sec2θ; 1+ cot2θ= csc2θ 順位高; 順位低 順位高d 順位低 ; = ?10 = 0* = 00?0* = 1 *?順位一: 對數; 反三角(反雙曲) 精品
高中数学微积分公式大全
