【数学】高中数学微积分公式大全

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2、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 Dx sin-1 (ax)= 221xacos-1 (ax)= tan-1 (ax)=22xaacot-1 (ax)= sec-1 (ax)=22axxacsc-1 (x/a)= sin-1 x dx = x sin-1 x+21x+C cos-1 x dx = x cos-1 x-21x+C tan-1 x dx = x tan-1 x-? ln (1+x2)+C cot-

3、1 x dx = x cot-1 x+? ln (1+x2)+C sec-1 x dx = x sec-1 x- ln |x+12x|+C csc-1 x dx = x csc-1 x+ ln |x+12x|+C sinh-1 (ax)= ln (x+22xa) xR cosh-1 (ax)=ln (x+22ax) x1 tanh-1 (ax)=a21ln (xaxa) |x| 1 sech-1(ax)=ln(x1+221xx)0 x1csch-1 (ax)=ln(x1+221xx) |x| 0 Dx sinh x = cosh x cosh x = sinh x tanh x = sech2

4、 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 csch x dx = 2 ln |xxee211| + C duv = udv + vdu duv = uv = udv + vdu udv = uv - vducos2-sin2=cos2

5、cos2+ sin2=1 cosh2-sinh2=1 cosh2+sinh2=cosh2精品学习资料可选择p d f - - - - - - - - - - - - - - 第 1 页，共 5 页 - - - - - - - - -学习好资料欢迎下载Dx sinh-1(ax)= 221xacosh-1(ax)= 221axtanh-1(ax)= 22xaacoth-1(ax)= sech-1(ax)= 22xaxacsch-1(x/a)=22xaxa sinh-1 x dx = x sinh-1 x-21x+ C cosh-1 x dx = x cosh-1 x-12x+ C tanh-1

6、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 sin 3=3sin-4sin3cos3=4cos3-3cossin3= ? (3sin -sin3)cos3=?(3cos+cos3) sin x = jeejxjx2cos x = 2jxjxeesinh x = 2xxeecosh x = 2xxee正弦定理 :sina= sinb=sin

7、c=2R 餘弦定理 : a2=b2+c2-2bc cos b2=a2+c2-2ac cos c2=a2+b2-2ab cos sin ( )=sin cos cos sin cos ( )=cos cos sin sin 2 sin cos = sin ( + ) + sin ( - ) 2 cos sin = sin ( + ) - sin ( - ) 2 cos cos = cos ( - ) + cos ( + ) 2 sin sin = cos ( - ) - cos ( + ) sin + sin = 2 sin ? ( + ) cos ? ( - ) sin - sin = 2 c

8、os ? ( + ) sin ? ( - ) cos + cos = 2 cos ? ( + ) cos ? ( - ) cos - cos = -2 sin ? ( + ) sin ? ( - ) tan ( )=tantantantan, cot ( )=cotcotcotcotex=1+x+! 22x+! 33x+!nxn+ sin x = x-! 33x+! 55x-! 77x+)!12() 1(12nxnn+ cos x = 1-! 22x+! 44x-! 66x+)!2()1(2nxnn+ ln (1+x) = x-22x+33x-44x+)!1() 1(1nxnn+ ni 11=

9、 nnii1= ? n (n+1) nii12= 61n (n+1)(2n+1) nii13= ? n (n+1)2a b c R 精品学习资料可选择p d f - - - - - - - - - - - - - - 第 2 页，共 5 页 - - - - - - - - -学习好资料欢迎下载tan-1 x = x-33x+55x-77x+)12() 1(12nxnn+ (1+x)r=1+rx+! 2)1(rrx2+! 3)2)(1(rrrx3+ -1x1 (x) = 0tx-1e-t dt = 20t2x-12tedt = 0)1(lntx-1 dt(m, n) =10 xm-1(1-x)

10、n-1 dx=220sin2m-1x cos2n-1x dx = 01)1(nmmxxdx希臘字母(Greek Alphabets) 大寫小寫讀音大寫小寫讀音大寫小寫讀音alpha iota rho beta kappa , ?sigma gamma lambda tau delta mu upsilon epsilon nu phi zeta xi khi eta omicron psi theta pi omega 倒數關係 : sincsc=1; tancot=1; cossec=1 商數關係 : tan= cossin; cot= sincos平方關係 : cos2+ sin2=1;

11、tan2+ 1= sec2; 1+ cot2= csc2順位低順位高; 順位高 d 順位低 ; 0* = 1* = = 0*01= 0000= )(0e; 0= 0e; 1= 0e順位一 : 對數; 反三角 (反雙曲 ) 順位二 : 多項函數 ; 冪函數順位三 : 指數; 三角(雙曲) 精品学习资料可选择p d f - - - - - - - - - - - - - - 第 3 页，共 5 页 - - - - - - - - -学习好资料欢迎下载算術平均數 (Arithmetic mean) nXXXXn.21中位數 (Median) 取排序後中間的那位數字眾數(Mode) 次數出現最多的數

12、值幾何平均數 (Geometric mean) nnXXXG.21調和平均數 (Harmonic mean) )1.11(1121nxxxnH平均差 (Average Deviatoin) nXXni|1變異數 (Variance) nXXni21)(or 1)(21nXXni標準差 (Standard Deviation) nXXni21)(or 1)(21nXXni分配機率函數 f(x) 期望值 E(x) 變異數 V(x) 動差母函數m(t) Discrete Uniform n121(n+1) 121(n2+1) tntteeen1)1(1Continuous Uniform ab121

13、(a+b) 121(b-a)2tabeeatbt)(Bernoulli pxq1-x(x=0, 1) p pq q+petBinomial xnpxqn-xnp npq (q+ pet)nNegative Binomial xxk1pkqxpkq2pkqktkqep)1(Multinomial f(x1, x2, , xm-1)= mxmxxmpppxxxn.!.!212121npinpi(1-pi)三項(p1et1+p2et2+ p3)n精品学习资料可选择p d f - - - - - - - - - - - - - - 第 4 页，共 5 页 - - - - - - - - -学习好资料

14、欢迎下载Geometric pqx-1p12pqttqepe1Hypergeometric nNxnkNxknNk1NnNnNkPoisson ! xex)1(teeNormal 2)(2121xe22221tteBeta 11)1(),(1xxB2)(1(Gamma xex1)()(2tExponent xe121tChi-Squared 2=f(2) =212222)(221ennnE(2)=nV(2)=2n2)21 (ntWeibull xe1111111222精品学习资料可选择p d f - - - - - - - - - - - - - - 第 5 页，共 5 页 - - - - - - - - -

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