微积分公式大全

微积分公式大全

Newly compiled on November 23, 2020

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 ?1xDx sin-1 ()= 22aa?xx cos-1 ()= ax?atan-1 ()=2 2aa?xxcot-1 ()= ax?asec-1 ()= 22axx?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) = -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+a2?x2) x?R ax cos-1 x dx = x cos-1 x-1?x2+C cosh-1 ()=ln (x+x2?a2) x≧1 a tan-1 x dx = x tan-1 x-ln (1+x2)+C 1a?x-1xtanh ()=ln () |x| <1 -1-12a?xa2a cot x dx = x cot x+ln (1+x)+C 1x?a-1x2-1-1coth ()=ln () |x| >1 sec x dx = x sec x- ln |x+x?1|+C x?aa2a csc-1 x dx = x csc-1 x+ ln |x+x2?1|+C ?11?x2-1xsech()=ln(+)0≦x≦1 2xax sin-1 x dx = x sin-1 x+1?x2+C x11?x2csch ()=ln(+) |x| >0 axx2duv = udv + vdu duv = uv = udv + vdu → udv = uv - vdu cos2θ-sin2θ=cos2θ cos2θ+ sin2θ=1 cosh2θ-sinh2θ=1 cosh2θ+sinh2θ=cosh2θ -1csc-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 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 1?e?x csch x dx = 2 ln || + C ?2x1?e sinh-1 x dx = x sinh-1 x-1?x2+ C cosh-1 x dx = x cosh-1 x-x2?1+ 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 γ a R b α 1xDx sinh()= 22aa?x1xcosh-1()= 22ax?ax?atanh-1()= 2 aa?x2xcoth-1()= a?axsech-1()= 22axa?x?acsch-1(x/a)= 22xa?x-1sin 3θ=3sinθ-4sin3θ cos3θ=4cos3θ-3cosθ →sin3θ= (3sinθ-sin3θ) →cos3θ=(3cosθ+cos3θ) ejx?e?jxejx?e?jxsin x = cos x = 2j2c β ex?e?xex?e?xsinh x = cosh x = 22bca正弦定理:= ==2R sin?sin?sin?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) 2n3xxxex=1+x+++…++ … 2!3!n!(?1)nx2n?1x3x5x7sin x = x-+-+…++ … (2n?1)!3!5!7!(?1)nx2nx2x4x6cos x = 1-+-+…++ … (2n)!2!4!6!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??tan??cot?cot?tan (α±β)=, cot (α±β)= ?tan?tan?cot??cot??1= n i?1nn?i= n (n+1) i?1?ii?1nn21= n (n+1)(2n+1) 6(?1)nxn?1x2x3x4ln (1+x) = x-+-+…++ … (n?1)!234-1?ii?13= [n (n+1)]2 ???1x-1x-1-t2x-1?t2(?1)nx2n?1x3x5x7ettΓ(x) = e dt = 2dt = (ln) dt ?0?0tan x = x-+-+…++ … ?0t(2n?1)357?12m-1n-12m-12n-1r(r?1)2r(r?1)(r?2)3xβ(m, n) =(1-x) dx=2x cosx dx sinr ?0?0(1+x)=1+rx+x+x+… -1

大写 Α Β Γ Δ Ε Ζ Η Θ 小写 α β γ δ ε ζ η θ 读音 alpha beta gamma delta epsilon zeta eta theta 大写 Ι Κ Λ Μ Ν Ξ Ο Π 小写 ι κ λ μ ν ξ ο π 读音 iota kappa lambda mu nu xi omicron pi 大写 Ρ Σ Τ Υ Φ Χ Ψ Ω 小写 ρ σ, sigma tau τ υ upsilon phi φ khi χ psi ψ ω omega 读音 rho 倒数关系: sinθcscθ=1; tanθcotθ=1; cosθsecθ=1 商数关系: tanθ=

sin?cos?; cotθ= cos?sin?平方关系: cos2θ+ sin2θ=1; tan2θ+ 1= sec2θ; 1+ cot2θ= csc2θ

順位高; 顺位高d 顺位低 ;

順位低1?10顺位一: 对数; 反三角(反双曲) * = = 0* = 顺位二: 多项函数; 幂函数 ??00顺位三: 指数; 三角(双曲) 00 = e0(??) ; ?0 = e0?? ; 1? = e0?? 算术平均数(Arithmetic mean) 中位数(Median) 取排序后中间的那位数字 0* =