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1、微积分公式sin x=cos xsin x dx =-cos x + Csin-1(-x)=-sin -1 xcos x 二=-sin xcos x dx ：=sin x + Ccos-1 (-x)=-1=- cosxtan x =2:sec xtan x dx =In |sec x | + Ctan-1(-x)=-tan-1 xcot x =-csc2 xcot x dx =In |sin x | + Ccot-1(-x)=-1- cotxsec x 二=sec x tan xsecx dx ：=In |sec x + tan x | + Csec-1(-x)=-1- secxcsc x =
2、-cscx cot xcscx dx 二=In |csc x - cot x | + Ccsc-1(-x)=- csc-1 xDxc -1 / x、Dx sin (一)= asin-1 x dx = x sin-1 x+cos-1 x dx = x cos-1 x-cos-1 (x)=atan-1 (x)=aa=2x-1 cot(x)=a-1 sec(x)=a-1 csc(x/a)=Dx sinh x = cosh x cosh x = sinh x tanh x = sec斤 x coth x = -csch2 x sech x = -sech x tanh x csch x = -csch
3、 x coth xDx sinh-1(x)=cosh-1 (x)=a1 a212xx2a2tanh-1( x)=acoth-1 (x)=asech-1 (x)=acsch-1 (x/a)=aI / 22x a x1 x2 +C,1 x2 +Ctan-1 x dx = x tan-1 x-?ln (1+x2)+Ccot-1 x dx = x cot-1 x+?ln (1+x2)+C-112sec x dx = x sec x- In |x+ x 1 |+C-112csc x dx = x csc x+ In |x+ v x 1 |+Csinh x dx = cosh x + C cosh x d
4、x = sinh x + C tanh x dx = In | cosh x |+ C coth x dx = In | sinh x | + C sech x dx = -2tarj1 (e-x) + C.，1 ex ,八 csch x dx = 2 In | | + C2x1 esinh-1 x dx = x sinh-1 x- .1 x2 + C.-1-12cosh x dx = x cosh x- . x 1 + Ctanh- coth-sech-1csch-1x dx = x tanh-1 x+ ? In | 1-x2|+ C x dx = x coth-1 x- ? In | 1-
5、x2|+ Cx dx =x dx =-1 x22_sinh ( )= In (x+ . a x ) x R acosh”tanh-1coth-1()=ln (x+ x x2a2 ) x= 1a(-)=a2aa x、ln () |x| 1sechi1( )=ln( + a xcsch-1 ()=ln( +1 x22x1 x22x)0三x1)|x| 0duv = udv + vduduv = uv = udv + vdu-udv = uv - vdu cos2 0 -sin2 0 =cos2 0 cos2 0 + sin2 0 =1 cosh2 0 -sinh2 0 =1 cosh2 0 +sin
6、h2 0 =cosh2 0 sin 3 0 =3sin 0 -4sin3 0 cos3 0 =4cos3 0 -3cos 0 fsin3 0 = ? (3sin 0 -sin3 0) 一cos3 0 =?(3cos 0 +cos3 0)cjxa jxe esin x =2jx x e e sinh x =2J a jx e e cos x =2cosh x =正弦定理：a sinsin sinc =2R余弦定理:a2=b2+c2-2bc cosa b2=a2 +c2-2ac cos。 c2=a2+b2-2ab cossin ()=sincos (工 B )=cos2 sinacos2 cosa
7、sin2 cosacos2 sinasina cos cos a sinBa cos sina sinB3 = sin ( a +?+ sin ( a3 = sin-(sin (a 邢 0)3 =-cos + cos ( a + B )3 = coscos (x a + B )sin a + sin sin - sin 0 cos a + cos cos - cos f tan (% B )=:3 -2antan3 =?2 sin+ B ) cos - B )c cos a + B ) s?( - B )3 = 2(cos+ B ) co?( - B )sin ?( a + B ) sM( -
8、 B )tan, , n x cot cot,cot( f )=tancot cot23nex=1+x+ + 2!3!n!357，,、n 2n 1x x x ,. ( 1) x ,sin x = x+ + +3!5! 7!(2n 1)!246，,、n 2n.xxx ,. ( 1) x,cos x = 1+ + 2!4!6!(2n)!234,n n 11 /、x x x, ( 1) xln (1+x) = x+ 234(n 1)!357,、n 2n 1 -1x x x ( 1) xtan x = x-+ - + +357(2n 1)dr(r 1) 2 r(r 1)(r 2)(1+x) =1+rx
9、+ x + x一2!3!+3+ - -1x1n1 = ni 1 ni = ?n(n+1)i 1i2 = - n (n+1)(2n+1)i 16ni3 = ?n (n+1)2i 1r(x) =tx-1e-tdt = 2 t2x-1 e t2 dt =(ln1)x-1dt-000 tB (m, n) = ；x m-1(1-x)n-1 dx=2 0 2sin2m-1x cos2n-1x dxm 1x.=m n dx0 (1 x)m n希腊字母(Greek Alphabets)大写小写坟日大写小写坟日大写小写坟日sinecos 6AaalphaIiiotaPPrhoBBbetaK降kappaE2sig
10、mar丫gammaA入lambdaTTtauwAsdeltaMmuYUupsilonEepsilonNVnuphizzetaS工xiXXkhiH刀eta00omicron6psisec 8esc H00thetan兀piQ3omega倒数关系:sin 0 cscO =1; tan 0 cot 0 =1; cos 0 secO =1商数关系:tan 0 = in ; cot 8 = coscossin平方关系：cos2 0 + sin2 0 =1; tan2 0 + 1= sec 0 ; 1+ cot2 0 = csc 00*=1 * =八* 10=0* =00顺位一：对数；反三角(反双曲)顺位
11、二:多项函数；幕函数00 二0()0=e；二0/0=e ; 1= e顺位三:指数；三角(双曲)顺位高d顺位低JIH位高JIM立低算术平均数(Arithmetic mean)X-Xi X2. XnXn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)GnX X2 . Xn调和平均数(Harmonic mean)H111117.一) nx1x2xn平均差(Average Deviatoin)n|Xi X|1n变异数(Variance)nn2 2(Xi X)(Xi X)21cr 1or nn 1标准差(Standard Devia
12、tion)1n_1n_(Xi X)2(Xi X)2ll 1cr 11nn0、n 1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)DiscreteUniform1 n1如+1)112(n2+1)1 et (1 ent) n 1etContinuousUniform1 b a9(a+b)(b-a)212btate e(b a)tBernoullipxq1-x(x=0, 1)Ppqq+petBinomialn pxqn-x xnpnpq(q+ pet)nNegativeBinomialk x 1 k 丫xpkqxkq p幽2 pkp/Atk(1 qe)Multinomialf(x1, x2,xm-1)=npinpi(1-pi)三项(p1et1 +n!x1x2xm-Pi p2 .pmp2et2+ p3)nx1!x2!.xmGeometricx-1 pqx11pq -2 Ptpe1 qetHypergeometrickxN k n xk n NNnkN 1NNnPoissonx e入入e(et 1)x!Normal11()22 22 (Tt12t2V2
