微积分公式大全23643

dx sin x=cos xsin x dx = -cos x + csin -1 (-x) = -sin -1 xcos x = -sin xcos x dx = sin x + ccos -1 (-x) =- cos -1 xtan x = sec 2 xtan x dx = ln |sec x | + ctan -1 (-x) = -tan -1 xcot x = -csc 2 xcot x dx = ln |sin x | + ccot -1 (-x) =- cot -1 xsec x = sec x tan xsec x dx = ln |sec x + tan x | + csec -1 (-x) =- sec -1 xcsc x = -csc x cot xcsc x dx = ln |csc xcot x | + ccsc -1 (-x) = - csc -1 xdx sin -1 ( x )=acos -1 ( x )=a1a 2x2sin -1 x dx = x sin -1 x+1cos -1 x dx = x cos -1 x-x 2x2+csinh -1 ( x )= ln (x+ acosh -1 ( x )=ln (x+a2x 2) xr1+cx2a 2) x1tan -1 ( x )=acot -1 ( x )=aa 2ax2tan -1 x dx = x tan -1 x-? ln (1+x 2 )+c cot -1 x dx = x cot -1 x+? ln (1+x 2)+csec -1 x dx = x sec -1 x- lnatanh -1 ( x )= 1ln ( aa2aa|x+x21 |+ccoth -1 ( x )=1 ln ( xa2axx ) |x| 1 a2sec()= a-1xacsc -1 x dx = x csc -1 x+ lnxx 2a 2|x+x21 |+csech -1 ( x )=ln(a1 +x1xx2)0x1csch -1 ()=ln(ax1x+1x 2x 2) |x| 0csc -1 (x/a)=微积分公式精品资料dx sinh x = cosh x cosh x = sinh x tanh x = sech 2 x coth x = -csch 2 xsech x = -sech x tanhsinh x dx = cosh x + c cosh x dx = sinh x + c tanh x dx = ln | cosh x |+ c coth x dx = ln | sinh x | + csech x dx = -2tan-1 (e-x) + cduv = udv + vdud uv = uv =udv +vdu udv = uv -vdu cos 2 -sin 2 =cos2 cos 2 + sin 2=1xcsch x = -csch x cothcsch x dx = 2 ln |1e x1e 2x| + ccosh 2-sinh 2=1cosh 2+sinh 2=cosh2 xdx sinh-1 ( x )=a1a 2x2sinh -1x dx = x sinh-1 x-1 x2 + csin 3 =3sin -4sin 3cosh-1( x )=a1x2a 2cosh -1x dx = x cosh-1 x-x 21 + ccos3 =4cos3 -3cos tanh-1 ()=a22xaaxtanh -1x dx = x tanh-1 x+?ln | 1-x2 |+ sin3= ? (3sin -sin3 )coth-1 ()=cxacos3 =? (3cos +cos3 )secha2x-1()=a2coth -1cx dx = x coth-1 x-?ln | 1-x2|+jxjxsin x =ee 2 je jxe jxcos x =xax2exe xcsch -1(x/a)=sech -1 x dx = x sech -1 x- sin -1 x + csinh x =cosh x =2axa 2x2csch -1 x dx = x csch -1 x+ sinh -1 x + cexe x2a正弦定理 :a=sinb=sinc=2rsinrb余弦定理 : a 2=b 2+c 2-2bc cos cb2=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 ( -)sin + sin = 2 sin? (+) cos? (-) sin - sin = 2 cos ? (+) sin? (-) cos + cos = 2 cos? (+) cos? (-)cos - cos = -2 sin? (+) sin? (-)2 cos cos = cos ( -) + cos ( +)2 sin sin = cos ( -) - cos ( +)tan ( )=tantantan tan, cot ( )=cot cotcot cotex=1+x+xx 3xn2+2!3!n!x3x5x 7(1)n x2 n 1n1 = ni 1nsin x = x-+-+3!5!7!( 2n+1)!i =? n (n+1)i 1cos x = 1-xx 4x62+-2!4!6!+ (1)n x 2 n+( 2n)!ni 2 =i 11n (n+1)(2 n+1)6ln (1+x) = x-xx3x 42+-+ (1) n xn 1+ni 3 = ? n (n+1) 22234(n1)!i 1tan-1 x = x-35x+ x-7x+ (n2 n 11)x+(x) =t x-1 e-t dt = 2t 2x-1 etdt =(ln 1)x-1 dt357( 2n1)000t(1+x) r =1+ rx+r( r1) x2 + r ( r1)( r2) x3 +(m, n) =1x m-1(1-x) n-1 dx=22 sin 2m-1 x cos 2n-1 x2!3!00m 1-1x1dx =xdx0(1x) m 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alphaiotarhobetakappa, ?sigmagammalambdatau精品资料deltamuupsilonepsilonnuphizetaxikhietaomicronpsithetapiomega倒数关系 : sin csc =1; tan cot =1; cos sec =1精品资料商数关系 : tan =sin; cot =coscos sin平方关系 : cos 2+ sin 2=1; tan 2+ 1= sec 2; 1+ cot 2= csc 2順位高;顺位高 d 顺位低;順位低0*=1*= 0* 1=000=e0();0=e0; 1=e 0顺位二:多项函数 ; 幂函数顺位三:指数; 三角(双曲)00顺位一: 对数; 反三角(反双曲)算术平均数 (arithmetic mean)xx 1x 2.x nn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)gn x1x 2. xn调和平均数 (harmonic mean)h1 ( 1nx111.1 )x2xn平均差 (average deviatoin)n| x ix |1n变异数 (variance)n( x ix ) 2n( x ix ) 21or1nn1标准差 (standard deviation)n( xix ) 2n(x ix ) 21or1nn1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)discrete11 (n+1)1 (n2 +1)1 et (1ent )n212n1etuniform continuous uniform11ba2(a+b)1 (b-a)212ebt (be ata)tbernoullipxq1- x(x=0, 1)ppqq+petbinomialnpxqn-xnpnpq(q+ pet )nxnegative binomialkx1 pkqxkqxpkq2p(1pkqet ) kmultinomialf(x1, x2, xm-1 )=npinpi(1- pi)三项x1 ! xn!2!. xm !xp11p2xx2m. pm(p1 et1 +p2et2 + p3 )n1qpet2geometricpqx-1pp1qethypergeometrknkknxnxnnnnnkn1nicnxpoissonex!e(et1)normalbeta1 x21()e221x1 (1x)12t12 t2e2gammaexponentb(,()(x)1 ex)ex(1)()22t112tnchi-squared =f(2)e( 2)= nv(2 )=2n(12t)22weibull=n (1n2 221 en 122 ) 2e 2x1112212111 000 000 000 000 000 000 000 000 1024 yotta y1 000 000 000 000 000 000 000 1021 zetta z1 000 000 000 000 000 000 1018 exa e1 000 000 000 000 000 1015 peta p1 000 000 000 000 1012 tera t兆1 000 000 000 109 giga g十亿1 000 000 106 mega m百万1 000 10 3 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 1