微积分公式合集35348

1、欢迎共阅微积分公式Dxsin x=cosx朗n xdx=-cosx+C-1 -1sin (-x)=-sin xcosx=-s inxXosxdx=s inx+C-1-1cos (-x)= ?-cos xtan x=seCx?tan xdx=ln| secx|+C-1-1tan (-x)=-tan xcotx=-cs£x尢otxdx=l n|si nx|+C-1-1cot (-x)=?-cot xsecx=secxta nx怎ecxdx=ln| secx+ta nx|+C-1 -1sec (-x)= ?-sec x-1 -1csc (-x)=-csc xcscx=-cscxcotx：O

2、scxdx=ln| cscx -cotx|+CDxsin-1( x)=-±1/in-1xdx=xs in -1x+J1 -x2 +Csinh-l()=ln(x+ Ja2 + x2 )x R a' afa2 _ x2*itos-1xdx=xcos-1x- x2 +Ccos ()= a-1 -1 2亶an xdx=xtan x-?ln(1+x )+Ccosh-1()=ln(x+Yx2_a2 )x = 1 atan-1(-)=a 2a a + x-1-12*fcot xdx=xcot x+?ln(1+x )+C丄-1/ x、1 i / a 十 x、|tanh ( )= ln()|x

3、|<1a 2a a - x*-1/ x、 cot ()=a-1-1 : 2%ec xdx=xsec x-ln|x+ #x -1 |+C丄-1/ x、1i, x + a、|“a 2a x - a*tsc xdx=xcsc x+ln|x+ px -1 |+C-1/X、±a,-.z Ii_ _、r- 'sech-1( )=ln(二 + J1 j )0 = x = 1sec (一)=-ax #x2 _a2csc-1 (x/a)=|csch(x)=ln(丄 + J2 )|x|>0 ax Y xDxsin hx=coshxn hxdx=coshx+Cduv=udv+vduco

4、shx=s inhx*toshxdx=s in hx+C?duv=uv= ?udv+ Wdutan hx=seclhx?ta nhxdx=l n|coshx|+Cf ?udv=uv-?vducothx=-csch x%othxdx=l n|si nhx|+C12 2cos 0 -sin 0 =cos2 0sechx=-sechxta nhx-1-x定echxdx=-2tan (e )+C2 2cos 0 +sin 0 =1cschx=-cschxcothx1 +e先schxdx=2ln| j|+C訥-e'x2 2cosh 0 -sinh 0 =12 2cosh 0 +sinh 0 =c

5、osh2 0欢迎共阅3Dxsi nh-1(x)=-一a ,.a2 x2cosh-1 (x)= _ aJx2 a2二 a-x2-1-i2：sinh xdx=xsinh x- 1 x +C:cosh-1xdx=xcosh-1x-1 x2 -1 +Ctan h-1( x)= aa2coth-1( x)= a1 1 2lanh xdx=xtanh x+?ln|1-x |+C1 -1 2:coth xdx=xcoth x-?ln|1-x |+C-1-1-1:sech xdx=xsech x-sin x+Csec(x)= a-ax.a2 - x2-1csch (x/a)=_ax/a2 +x2sin3 0

6、=3sin 0 -4sin 03cos30 =4cos 0-3cos03sin 0 =?(3sin 0 -sin3 0)3cos 0 =?(3cos 0 +cos3 0)jx jx jx jxe - ee + esinx=cosx=2j2x_xx_xe - ee + esinhx=coshx=2 2正弦定理：旦=丄=亠=2R sina sin P sin '<余弦定理：a2=b2+c2-2bccosa2 2 2b =a +c -2accosB2 2 2c =a +b -2abcos丫sin( ± B )=sin a cosc0s a sin B cos( ±

7、B )=cos a cdssjn a sin B 2sin a cos B =sin( a + B-)+sin( a 2cos a sin B =sin( -sirn()2cos a cos B =CosB )+cos( a + B) 2sin a sin B =cos)os( a + B)sin a +sin B =2sin + B)cos- B)sin -sin B =2c(s a + B )?(n - B)/、hcos a +cos B =2?os + B)c(s- B)cos -cos B =sin?( a + B )?(n - B)tan ： - tancot ： cot :tan(

8、±B tatan P 血 ±B GcotPxx+.2!3357xxx+-3!5!7!246xxx+ 一2!4!6!sin x=x-+cosx=1-2 3nx一 +.n!(一 1)nx2n1+(2n1)!n 2n.+ (_1) x +.(2n)!ex=1+x+n' 1=ni总n' i =?n(n+1)iT234，八n n十x x(一1) x ,ln( 1+x)=x-+-+ 234-1 x3 x5 x7tan x=x- 一 + 一-一+357(n 1)!n 2n T(T) x(2n1)(1+x)r=1+rx+ r(r-1) x2+r(一 1)(2)x3i-1vx

9、v12!3!n' i2:i An3ii 41=1 n(n+1)(2 n+1) 62=?n(n +1)2r (x)=:(?x-1e-tdt=2 乍2x-1e<dt= f(lnf)x-1dtB(m,n)= :x m'1(1-x)n-1dx=o 2sin2m_1xcos2n-1xdx=严 xm0 (1 x)m n dx大写小写、七 读曰大写小写、七 读曰大写小写、七 读曰AaalphaIiiotaPPrhoBBbetaKKkappa艺sigmarYgammaA入lambdaTTtauASdeltaMamuYUupsilo n希腊字母(GreekAlphabets)欢迎共阅E&#

10、163;epsil onNVnu©phiZz 1zetauExiXXkhiHneta00omicro nWpsi00thetannPiQ3omega倒数关系：sin 0 cscB =1;tanB cot 0 =1;cosB secB =1商数关系:tan 0 = ;cot 0 = coscos日sin日2 2 2 2 2 2平方关系:cos 0 +sin 0 =1;tan 0 +1=sec 0 ;1+cot 0 =csc 0順位高ltl;:顺位咼d顺位低；顺位一:对数;反三角(反双曲) 顺位二:多项函数;幕函数 顺位三:指数;三角(双曲)順位低1 1 0 0* 二 一* = 一=0*

11、 = 0 0算术平均数(Arithmeticmean)中位数(Media n):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(Geometricmean)调和平均数(Harmonicmean).x X X ”严 X ' :平均差(AverageDeviato in)昇r变异数(Varia nee)nn送(Xi -X)2 送(Xi X)21 or 1ornn-1标准差(Sta ndardDeviatio n)住(Xi-X)2忖(Xi -X)21 1or* 1Vor ynin -10=e ;：-=e ;1 = e分配1机率函数f(X)期望值E(x)变异数V(x)动差母

12、函数m(t)DiscreteU niform111扌(n+1)-(n2+1)12Con ti nu ousU niform寸(a+b)TT (b-a)212Berno ullipXq1-x(x=0,1)ppqq+petBi no mialnx n-x p qnpnpq(q+pet)nNegativeB ino mial"k + x -1" k x 严Multi no mialf(X1 ,X2,Xm>1)=n!X1X2Xmnpi叩i(1-Pi)三项(p1et1+p22+p3)nX1! X2!.Xm!P1 P2 .pmGeometricx-1 pqHypergeometr

13、icnQIN丿(N n、fkini小一1丿IN丿Poiss on入入Normal2CTBetaGammaExp onent2Chi-Squared x=f( x 2)=a2)2 e2 巴22l2丿E( x 2)=nV( x 2)=2 nWeibull10000000000000000000000001024yotta Y10000000000000000000001021 zettaZ10000000000000000001018exaE100000000000000010 15petaP100000000000010 12teraT 兆100000000010 9gigaG 十亿100000010 6megaM 百万100010 3kiloK 千100102hectoH 百10101decaD 十0.110-1decid 分，十分之一0.0110 -2centic厘(或写作厘)，百分之一0.00110 millim 毫，千分之一0.00000110 -6micro?微，百万