微积分公式大全

1、名师推荐精心整理学习必备微积分公式sin x=cos xf sin x dx =-cos x + Csin -|(-x)= -1-sin xcos x =-s in xJcos x dx :=sin x + Ccos-1 (-x)=-1=兀-cos xtan x =2 :sec xf ta n x dx =:ln |sec x | + Ctan-1(-x)=-ta n-1 xcot x =2 -csc xf cot x dx =ln |sin x | + Ccot-1(-x)=兀-cot-1 xsec x =sec x tan xfsecx dx :=ln |sec x + tan x | +

2、 Csec-1(-x)=-1 兀-sec xcsc x =-cscx cot xfcscx dx =In |csc x -cot x | + Ccsc-1(-x)=-1 -csc xDx22Dx sin-1 (x)=a12 2a -xsin-1 x dx = x sin-1 x+ J - x2 +Cx- 1-x2 +Ccos-1 x dx = x cos-1sinh-1 ( )= ln (x+ Ja2 + x2 ) x R atan-1 (x)=a二 aa2x22x-?ln (1+x2)+C x+?ln (1+x2)+Cr -1-1/2tan-1 x dx = x tan-1cot-1 x d

3、x = x cot-1cosh-1tanh-1cot-1 (x)=a-i sec（a）()=ln (x+ Jx2 _a2 ) x = 1 a(x)=2_|n()|x| 1 a2ax - a1 - x.2 )0 - x = 1secbi1 ( )=ln(二 + a xcsc-1(x/a)=sinh x =cosh xcosh x=sinh xtanh x =secF xcoth x =-csch2 xsech x=-sech x tanh xcsch x :=-csch x coth xDxsi nh x dx = cosh x + C cosh x dx = sinh x + C tanh x

4、 dx = ln | cosh x |+ C coth x dx = ln | si nh x | + C sech x dx = -2tar-1 (e-x) + C/csch x dx = 2 ln | 十| + CJ1-e3 / x、i / 1 M + x2 x ,小 csch ()=ln( +. 2) |x| 0a x H xduv = udv + vduduv = uv = udv + vdu t udv = uv - vdu2 2cos 0 -sin 0 =cos2 02 2cos 0 + sin 0 =122cosh 0 -sinh 0 =122cosh 0 +sinh 0 =co

5、sh2 0Dx si nh-1(x)= acosh-1 (x)=atan h-1(x)= a12 2a x1.2 2 x -a-aT-xcoth-1 (x)= asechl x)= a_af22x a - x-1csch (x/a)=-ax、a2 +x2si nh-1x dxcosh-1x dxtanh-1x dxcoth-1x dxsech1x dxcsch-1x dx=x sinh-1 x- d x2 + C=x cosh-1 x- x2 -1 + C-12=x tanh x+ ? In | 1-x |+ C-12=x coth x- ? In | 1-x |+ C-1 -1=x sech

6、 x- sin x + C3sin 3 0 =3sin 0 -4sin 03cos30 =4cos 0 -3cos03tsin 0 = ? (3sin 0 -sin3 0)0 =?(3cos 0 +cos3 0)ejx -2jx-xe - eT cos3sin x =sinh x =ejx +e莎cos x =2cosh x =x-xe eb sin P 余弦定理：a2=b2+c2-2bc cosa2 2 2b =a +c -2ac cosB2 2 2c =a +b -2ab cos丫正弦定理：asin a=2R sin名师推荐精心整理学习必备sin ( c B )=sin cos (2 si

7、n2 cos2 cos2 sin B )=cos a cos a sina cos a sina co cg)s a sin B a cos sip a sin B =sin ( a +-B)+ sin (=si n-(sin (a-B)=cos + coa (a + B)=cosmos a a + B)sinsincoscostan (a + sin B =?2 ainn B ) cos a B) -sin B = 2 eg a + B ) si?( - B) a + cos B = 2(cos+ B ) eg - B)-cos B -2 sin ?( a + B ) s?i( - B)ta

8、na + tan P,+ cotot cot P B )=, cot ( B )=斗 tana tan Bcota cot P23nxxx+ + +2!3!n!357xxx+3!5!7!246xxx+ -+2!4!6!234x xx=x-+234357x x-x -+ 一x -+sin x = x-+cos x = 1+In (1+x)ex=1+x+(_1)nx2n1+ .(2n1)!n 2n(二 0 x + (2n)!丄(-1)nxn1+ + (n +1)!.+虽二357(2n +1)“、r “ r(r 一1) 2 r(r 1)(r -2) 3 彳 彳(1+x) =1+rx+ x + x +

9、 -1xXmP1 P2 .pmnPinp心讪)三项/ t1(p1e +t2、np2e + p3)Geometricpqx11p旦2 ptpe1 - qetHypergeometric0JN -J 2X丿a “IN丿N - n、kn 1IN -1 .丿 In 丿Poiss one祝x!入入尹(_1)Normal1昇号； e GJ2ircr2CT4tWt2e 2Betax3(1 x)BgP)Cta + PaP(a + P +1)(a + P)2Gamma-(gEe 仝 Wakan 2A甘a -1丿Exp onent丸e1X1n 2 A扎 kt2Chi-Squared%=f( %2)12 2兰= r

10、V(2)2 e22；E(% 2)=nV( % 2)=2nn(1-2沪Weibull1 VJ_e a aeP +a Er +1 1* 丿2込忖纟+丄厂2(丄+1卩1匕)匕丿1 000 000 000 000 000 000 000 000 1024 yotta Y1 000000000 000 000000 000 1021zettaZ1 000000000 000 000000 1018 exaE1 000000000 000 0001015 peta P1 000000000 000 1012 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 nanon 奈，十亿分之一0.000 000 000 001 10 -12 pico p 皮，兆分之一0.000 000 000