1、微积分公式Dx sin x=cos xcos x = -sin xtan x = sec2 xcot x = -csc2 xsec x = sec x tan xcsc 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 | + Csin-1(-x) = -sin-1 xcos-1(-x) = -
2、cos-1 xtan-1(-x) = -tan-1 xcot-1(-x) = - cot-1 xsec-1(-x) = - sec-1 xcsc-1(-x) = - csc-1 xDx sin-1 ( )=a21cos-1 ( )= xtan-1 ( )=a2cot-1 ( )= xsec-1 ( )=a2acsc-1 ( )=x2 sin-1 x dx = x sin-1 x+ +C21 cos-1 x dx = x cos-1 x- +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
3、x dx = x sec-1 x- ln |x+ |+C1x csc-1 x dx = x csc-1 x+ ln |x+ |+C2sinh-1 ( )= ln (x+ ) x Ra2cosh-1 ( )=ln (x+ ) x1atanh-1 ( )= ln ( ) |x| 1axsech-1( )=ln( + )0x1ax12csch-1 ( )=ln( + ) |x| 0Dx sinh x = cosh xcosh x = sinh xtanh x = sech2 xcoth x = -csch2 xsech x = -sech x tanh xcsch x = -csch x coth
4、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 | | + Cx21duv = udv + vdu duv = uv = udv + vdu udv = uv - vducos2-sin 2=cos2cos2+ sin 2 =1cosh2 -sinh2=1cosh2 +sinh2=cosh2Dx sinh-1( )= a21cosh-1(
5、 )= xtanh-1( )= a2coth-1( )= xsech-1( )= a2csch-1( )=x2x sinh-1 x dx = x sinh-1 x- + C cosh-1 x dx = x cosh-1 x- + C2x 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 + Csin 3 =3sin-4sin 3cos3 =4
6、cos3-3cossin 3 = (3sin-sin3)cos 3 =(3cos+cos3 )sin x = cos x = jejj22jxjesinh x = cosh x = x正弦定理: = = =2Rsinaibsinc余弦定理: a 2=b2+c2-2bc cosb2=a2+c2-2ac cosc2=a2+b2-2ab cosa bcRsin ()=sin cos cos sin cos ()=cos cos sin sin 2 sin cos = sin (+) + sin (-)2 cos sin = sin (+) - sin (-)2 cos cos = cos (-) +
7、 cos (+)2 sin sin = cos (-) - cos (+)sin + sin = 2 sin (+) cos (-)sin - sin = 2 cos (+) sin (-)cos + cos = 2 cos (+) cos (-)cos - cos = -2 sin (+) sin (-)tan ()= , cot ()=tantcottex=1+x+ + + + !23x!nsin x = x- + - + + 57)!12(xncos x = 1- + - + + !24x!6ln (1+x) = x- + - + + 34)!1(nxtan-1 x = x- + - +
8、 + 57x2(1+x)r =1+rx+ x2+ x3+ -1x1!)1(!)(r= ni1= n (n+1)i= n (n+1)(2n+1)i126= n (n+1)2ni3(x) = x-1e-t dt = 2 2x-1 dt = x-1 dt0t02e0)1(ln(m, n ) = m-1(1-x)n-1 dx=2 2m-1x cos2n-1x dx 10x0si= dx1)(n希腊字母 (Greek Alphabets)大写 小写 读音 大写 小写 读音 大写 小写 读音 alpha iota rho beta kappa , sigma gamma lambda tau delta
9、mu upsilon epsilon nu phi zeta xi khi eta omicron psi theta pi omega倒数关系: sincsc =1; tancot=1; cos sec=1商数关系: tan= ; cot= cosinsinco平方关系: cos 2+ sin 2=1; tan 2+ 1= sec2; 1+ cot 2= csc 2; 顺位高 d 顺位低 ; 順 位 低順 位 高0* = * = = 0* = 101= ; = ; = 0)(e0e0顺位一: 对数; 反三角(反双曲)顺位二: 多项函数; 幂函数顺位三: 指数; 三角(双曲)算术平均数(Ari
10、thmetic mean) nXXn.21中位数(Median) 取排序后中间的那位数字众数(Mode) 次数出现最多的数值几何平均数(Geometric mean) nnXG.21调和平均数(Harmonic mean) ).(21nxxH平均差(Average Deviatoin) Xni|1变异数(Variance) or nni21)(1)(2nni标准差(Standard Deviation) or Xi21)()(21Xi分配 机率函数 f(x) 期望值 E(x) 变异数 V(x) 动差母函数 m(t)Discrete Uniform n1(n+1)21(n2+1)1tne1Con
11、tinuous Uniform ab(a+b) (b-a)2 tabt)(Bernoulli pxq1-x(x=0, 1) p pq q+petBinomial pxqn-xnp npq (q+ pet)nNegative Binomial pkqx1pkq2pkqktqep)1(Multinomialf(x1, x2, , xm-1)= mxn.!.21npi npi(1-pi)三项(p1et1+ p2et2+ p3)nGeometric pqx-1 p12qtqHypergeometric nNxkn Nkn1NkPoisson !xe )1(teNormal2)(1 2 2 ttBeta
12、 11)(),(xB2)(1(Gamma xe1)( 2tExponent x121tChi-Squared 2=f( 2)= 122ennE( 2)=n V( 2)=2n 2)1(ntWeibull xe 1111221 000 000 000 000 000 000 000 000 1024 yotta Y 1 000 000 000 000 000 000 000 1021 zetta Z 1 000 000 000 000 000 000 1018 exa E 1 000 000 000 000 000 1015 peta P 1 000 000 000 000 1012 tera T
13、 兆 1 000 000 000 109 giga G 十亿 1 000 000 106 mega M 百万1 000 103 kilo K 千 100 102 hecto H 百 10 101 deca D 十 0.1 10-1 deci d 分，十分之一 0.01 10-2 centi c 厘（或写作厘 ） ，百分之一 0.001 10-3 milli m 毫，千分之一 0.000 001 10-6 micro ? 微，百万分之一 0.000 000 001 10-9 nano n 奈，十亿分之一 0.000 000 000 001 10-12 pico p 皮，兆分之一 0.000 000 000 000 001 10-15 femto f 飞（或作 费 ） ，千兆分之一 0.000 000 000 000 000 001 10-18 atto a 阿 0.000 000 000 000 000 000 001 10-21 zepto z 0.000 000 000 000 000 000 000 001 10-24 yocto y
