【#第一文档网# 导语】以下是®第一文档网的小编为您整理的《微积分公式大全》,欢迎阅读!
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 xx1Dx sin-1 ()= sinh-1 ()= ln (x+a2x2) xR sin-1 x dx = x sin-1 x+1x2+C aaa2x2 cos-1 x dx = x cos-1 x-1x2+C -1x1-1xcosh ()=ln (x+x2a2) x≧1 cos ()= aaa2x2 tan-1 x dx = x tan-1 x-½ln (1+x2)+C 1ax-1xatanh ()=ln () |x| <1 -1x-1-12tan ()=2 a2aax cot x dx = x cot x+½ln (1+x)+C aax21xa-1x-1-12acoth ()=ln () |x| >1 -1x sec x dx = x sec x- ln |x+x1|+C cot ()=2 a2axa2aax csc-1 x dx = x csc-1 x+ ln |x+x21|+C 11x2-1xa-1xsech()=ln(+)0≦x≦1 sec ()= 222axxaxxa 2x11x-1xacsch ()=ln(+) |x| >0 csc-1 ()= 2axxaxx2a2Dx 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 1ex csch x dx = 2 ln || + C 2x1e-1-12duv = udv + vdu duv = uv = udv + vdu →udv = uv - vdu cos2θ-sin2θ=cos2θ cos2θ+ sin2θ=1 cosh2θ-sinh2θ=1 cosh2θ+sinh2θ=cosh2θ 3sin 3θ=3sinθ-4sinθ sinh x dx = x sinh x-1x+ C cos3θ=4cos3θ-3cosθ -1-12 cosh x dx = x cosh x-x1+ C →sin3θ= ¼ (3sinθ-sin3θ) -1-12 tanh x dx = x tanh x+ ½ ln | 1-x|+ C →cos3θ=¼(3cosθ+cos3θ) -1-12 coth x dx = x coth x- ½ ln | 1-x|+ C ejxejxejxejx-1-1-1sin x = cos x = sech x dx = x sech x- sin x + C 22j csch-1 x dx = x csch-1 x+ sinh-1 x + C exexexex sinh x = cosh x = γ 22R a b abcα 正弦定理:===2R sinsinsinc 余弦定理: a2=b2+c2-2bc cosα b2=a2+c2-2ac cosβ β c2=a2+b2-2ab cosγ sin (α±β)=sin α cos β± cos α sin β sin α + sin β = 2 sin ½(α+β) cos ½(α-β) cos (α±β)=cos α cos β sin α sin β sin α - sin β = 2 cos ½(α+β) sin ½(α-β) 2 sin α cos β = sin (α+β) + sin (α-β) cos α + cos β = 2 cos ½(α+β) cos ½(α-β) 2 cos α sin β = sin (α+β) - sin (α-β) cos α - cos β = -2 sin ½(α+β) sin ½(α-β) 2 cos α cos β = cos (α-β) + cos (α+β) x1Dx sinh()= 22aaxx1cosh-1()= 22axaaxtanh-1()= 2 2aaxaxcoth-1()=2 aax2xasech-1()= 22axaxxacsch-1()= 22axax-12 sin α sin β = cos (α-β) - cos (α+β) x2x3xne=1+x+++…++ … 2!3!n!x3x5x7(1)nx2n1sin x = x-+-+…++ … 3!5!7!(2n1)!xtan (α±β)=tantancotcot, cot (α±β)= tantancotcot1= n ni= ½n (n+1) 12= n (n+1)(2n+1) i6i1i1nni1nx2x4x6(1)nx2ncos x = 1-+-+…++ … 2!4!6!(2n)!x2x3x4(1)nxn1ln (1+x) = x-+-+…++ … 234(n1)!-1ii13= [½n (n+1)]2 1x-1x-1-t2x-1t2x3x5x7(1)nx2n1(lnΓ(x) = e dt = 2dt = ttetan x = x-+-+…++ … 0t) dt 00357(2n1)1m-1n-1r(r1)r(r1)(r2)β(m, n) =x(1-x) dx=22sin2m-1x cos2n-1x dx r23(1+x)=1+rx+x+x+… -100
2!3!m1
x= dx 0(1x)mn
本文来源:https://www.dywdw.cn/21ed5e570622192e453610661ed9ad51f11d543b.html