微积分基本公式复习进程

1、此文档仅供收集于网络，如有侵权请联系网站删除微积分公式Dx sin x=cos xcos x = -s in x tan x = seE x cot x = -csC2 x sec x = sec x tan x csc x = -csc x cot xsin x dx = -cos x + C cos x dx = sin x + C tan x dx = In |sec x | + C cot x dx = In |sin x | + C sec x dx = In |sec x + tan x | + C csc x dx = In |csc x -cot x | + C -1 / -1

2、sin (-x) = -sin x cos (-x) =- cos xtan-1(-x) = -ta n-1 x cot-1(-x) =- cot-1 xsec (-x) =- sec xcsc (-x) = - csc xc/ X、1Dx sin ()= ”aJaxcos-1 (x)= ,1 a 丿122aVaxtan ( )= 22a a x円/ xacot ()= 22a a xsec-1 ( x )=J2ax & a2csc ( )=*ax Vx2 a2sin-1 x dx = x sin-1 x+訥 x2 +C11J2cos x dx = x cos x-寸1 x +C112tan

3、1 x dx = x tan 1 x-? In (1+x2)+C-1-12cot x dx = x cot x+? ln (1+x )+Csec-1 x dx = x sec-1 x- ln |x+ G x21 |+C11r2csc x dx = x csc x+ ln |x+Yx1 |+Csinh-1 ( )= ln (x+ Ja2 x2 ) x R acosh1 ( )=ln (x+ J x2a2 ) x = 1atanh-1 (?)二丄 In (- ) |x| 1a2ax a冲 x111x2secf()=ln(+、2)0 三 x 三 1ax xcsch1 ( ) ln( +J 2) |x

4、| 0ax 4 xDx sinh x = cosh x cosh x = sinh x tanh x = secF x coth x = -csch2 x sech x = -sech x tanh x csch x = -csch x coth xsi nh x dx = cosh x + C cosh x dx = sinh x + C tanh x dx = ln | cosh x |+ C coth x dx = ln | si nh x | + C sech x dx = -2tari1 (e_x) + C1 e xcsch x dx = 2 ln | | + C12x 1v1 ed

5、uv = udv + vduduv = uv = udv + vdu f udv = uv - vdu cos2 0 -sin2 0 =cos2 0 cos2 0 + sin2 0 =1 cosh? 0 -sinh2 0 =1 cosn 0 +sinh2 0 =cosh2 0只供学习与交流Dx sin h-1 (x)= acosh-1 (x)= a12 2 a x12 2x asin h-1 x dx = x sin h-1 x- 1x2 + C11i1 2cosh x dx = x cosh x-、x 1 + Ctanh-1( x)= acoth-1( x)= atanh-1coth-1se

6、ch1csch112x dx = x tanh x+ ? ln | 1-x |+ C12x dx = x coth 1 x- ? In | 1-x2|+ C x dx = x sech-1 x- sin-1 x + Cx dx =sechl x)= aar22x、a xcsch-1 (x)= asin (a=sin a cos B cos asin B cos (aB=cos a cos B sin a sin B 2 sin a cos B = sin (o+ B + sin ( a B 2 cos asin B = sin (o+ B - sin (a- B2 cos acos B= co

7、s (a + COS (a+ B2 sin asin B= cos (a B) - cos (o+ Bsin 3 0 =3sin 0 -4sin3 03cos30 =4cos 0 -3cos0sin3 0 = ? (3sin 0 -sin3 0)cos3 0 =?(3cos 0 +cos3 0)x a jxe esin x =2jxxe esinh x =2xa jxe ecos x =2xx. e ecosh x =2b = c =2R sin sin正弦定理：asin余弦定理:a2=b2+c2-2bc cosa b2=a2 +c2-2ac cosB c2=a2+b2-2ab cos 丫=2

8、 sin ? ( a+ B cos ? ( a B sin a- sin B= 2 cos ? ( a+ B sin ? (a- B cos a+ cos B= 2 cos ? ( a+ B cos ? ( a B cos a- cos B = -2 sin ? ( a+ B sin ? ( a B tan tan, cot cottan ( a)=, cot ( aB=tan tancot cot23nx ,X Xxex=1+x+ +2!3! n!357n 2n 1x x x( 1) xsin x = x- 一+ 一- 一 + + 3!5! 7!(2n 1)!2 46，八 n 2n.xxx(

9、 1) xcos x = 1- + - + 2!4!6!(2n)!234，八 n n 1x x x( 1) xIn (1+x) = x- 一 + 一 - 一 + + 234(n 1)!357n 2n 11X x X 丄丄(1)xtan x = x- 一 + 一 - 一 + + 3 57(2n1)r 彳 r(r 1) 2 r(r 1)(r2) 3(1+x) =1+rx+x +12!x + -1x+1)1 et (1 ent) n 1etCon ti nu ousUn iform1 b a丄(a+b)2丄(b-a)212btate e(b a)tBerno ullipxq1-x(x=0, 1)pp

10、qq+petBi nomial；pxqn-xnpnpq(q+ pet)nNegative Bi nomialk x 1 k x pkqx xkqpkq2 pkp(1 qet)kMulti no mialf(X1, X2,xm-1)=n!X1X2Xmnnnnpi叩 i(1-Pi)三项(p1et1 + p2et2+ p3)n.r1 r2Pmx1!x2!.xm!Geometricpqx-11 pq 2 ptpe1 qetHypergeometrickNkxn xNnk n NN nkn N 1NPoiss onX ex!入入(e1 1) eNormal1l(x )2.e 2v22CTt2t2e 2B

11、eta1x1(1x)1x (1 X)B(,)2( 1)( )Gamma(X) e ()2tExp onente x11tChi-Squared% 2=f( %2)= _1 ( 2)21e22 一n ()en 2-222E(% 2)=nV( % 2)=2nn(1 2t)：WeibullX1 e1 1 11-2 2 1 一 1 一 11 000 000 000 000 000 000 000 000 1024 yotta Y1 000 000 000 000 000 000 000 1021 zetta Z1 000 000 000 000 000 000 1018 exa E此文档仅供收集于网络

12、，如有侵权请联系网站删除1 000 000 000 000 000 10 15 peta P1 000 000 000 000 10 12 tera T 兆1 000 000 000 10 9 giga G 十 亿1 000 000 10 6 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 10 -12 pico p 皮，兆 分之