微积分基本公式

1、微积分公式Dxsinx=cosxcosx=-sinxtanx=sec2xcotx=-csc2xsecx=secxtanxcscx=-cscxcotx?sinxdx=-cosx+C?cosxdx=sinx+C?tanxdx=In|secx|+C?cotxdx=ln|sinx|+C?secxdx=ln|secx+tanx|+C?cscxdx=ln|cscx-cotx|+Csin-1(-x)=-sin-1xcos-1(-x)=?-cos-1xtan-1(-x)=-tan-1xcot-1(-x)=?-cot-1xsec-1(-x)=?-sec-1xcsc-1(-x)=-csc一1xDxsin-1(x)

2、=cos-1(x)=atan-1(x)=acot-1(x)=asec-1(x)=1r22Vax1r227axa22axa22axa?sin-1xdx=xsin-1x+Jix2+C?cos-1xdx=xcos-1x-41x2+C?tan-1xdx=xtan-1x-?ln(1+x2)+C?cot-1xdx=xcot-1x+?ln(1+x2)+C?sec-1xdx=xsec-1x-ln|x+Mx21|+C?csc-1xdx=xcsc-1x+lnsinh(-)=ln(x+Ja2x2)axRcosh-1(-)=ln(x+vx2a2)xa三1-1x1aaxtanh()=一ln()|x|1acsc(a)=.

3、x/22Vxaa|x+Mx21|+Ca2axa-1/x/1,J1x2s一sech(-)=ln(一+)0=xaxxx/22vxa三1csch-1(x)=ln(1+Jx_)|x|csch()ln(2)|x|axx0Dxsinhx=coshxcoshx=sinhxtanhx=sech2xcothx=-csch2xsechx=-sechxtanhxcschx=-cschxcothx?sinhxdx=coshx+C?coshxdx=sinhx+C?tanhxdx=ln|coshx|+C?cothxdx=ln|sinhx|+C?sechxdx=-2tan-1(e-x)+C1ax?cschxdx=2ln|/

4、|+C1e2xduv=udv+vdu?duv=uv=?udv+?vduf?udv=uv-?vducos20-sin20=cos20cos20+sin20=1cosh20-sinh20=1cosh20+sinh20=cosh20Dxsinh-1(x)=cosh-1(x)=tanh-1(x)=?sinh-1-1?cosh?tanh-11-x2|+C?coth-1xdx=xsinhxdx=xcoshxdx=xtanhxdx=xcoth-1x-1x-1-11x23sin30=3sin0-4sin0x+?In|x-?In|coth-1(x)=1-x2|+C?sech-1xdx=xsechsech-1(x

5、)=acsch-1(x)=aax、a2x2+C?csch-1xdx=-1-1x-sinxsin(aB)=sinacosBcosasincos(aB)=cosacosssinasin2sinacosB=sin(a+B)+sin(a-f2cosasinB=sin(a+B)-sin(a-f2cosacosB=cos(a-B)+cos(a+f2sinasinB=cos(a-B)-cos(a+fBB)sinacos?(sinasin?(cosacos?(cosasin?(tan(+sin23nex=1+x+-+2!sinx=x-cosx=1-3!35x+x-a5!24x+x-n!7x,一+7!6x,+2

6、!4!6!+(小2n1+.(2n1)!+.(2n)!cos303fsin3fcossinx=jxee2=4cos30-3cos09=?(3sin9-sin39)0=?(3cos0+cos30)ejxejx2jcosx=jxsinhx=coshx=正弦定理:=2Rsinsinsin余弦定理:a2=b2+c2-2bccosb2=a2+c2-2accosc2=a2+b2-2abcos=2sin?(+B)a-B)-sinBa-B)+cosBa-B)-cosBa-B)=2cos?(=2cos?(=-2sin?(+B)+B)工、tantanB)=,cot(a土tantancotcotcotcot1=ni=

7、?n(n+1)i2=1n(n+1)(2n+1)6234/、nn1ln(1+x)=x-+-+(1)x+234(n1)!357/人n2n1tan-1x=x-x_+:x_-+(_)_x+357(2n1)(1+x)r=1+rx+rll_1)x2+r(r-1)(r-2)x3+-2!3!-1x1ni3=?n(n+1)2i1/x-1-tIXc2x-1t2IX1x-1r(x)=tedt=2tedt=(in-)000tdtB(mn)=1xm-1(1-x)n-1dx=22sin2m-1xcos=00m1,x,dx=dxn/m、mn0(1x)大写小写、卡卡映日大写小写、卡卡映日大写小写、卡卡映日AaalphaIii

8、otaPPrhoBBbetaK降kappaN*？sigmar丫gammaA入lambdaTTtauAsdeltaMmu丫UupsilonEepsilonNVnuphiZzetaS工xiXXkhiH刀etaO0omicronW6psiO0thetan兀piQ3omega倒数关系：sin0csc0=1;tan0cot0=1;cos0sec0=1希腊字母(GreekAlphabets)商数关系：tan平方关系：cos0=4；cot9=理cossin20+sin20=1;tan20+1=sec20;1+cot20=csc200*?=-*?=0*-=-顺位一:对数；反三角(反双曲)00顺位二:多项函数；

9、募函数00=e0();0_e0;1=e0顺位三:指数；三角(双曲)JIH位高JIH位低;?顺位高d顺位低；算术平均数(Arithmeticmean)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(Geometricmean)调和平均数(Harmonicmean)平均差(AverageDeviatoin)变异数(Variance)n(XiX)2Jornn2(XiX)1n1标准差(StandardDeviation)1t1n(XiX)2Jorn1n-21(XiX)1in1分配机率函数f(x)期望值E(x)变异数V(x)动差母函数mt)DiscreteUni

10、form-(n+1)2(n2+1)12ContinuousUniform1.(a+b)-1(b-a)212Bernoullipxq1-x(x=0,1)ppqtq+peBinomialnxn-xpqxnpnpq(q+tnpe)NegativeBinomialkx1kxpqxMultinomialf(Xi,x2,，Xh-i)=n!XiX2Xm一P1p2.pmx1!x2!xm!npnp(1-pi)三项(pe、p2et2+p3)nGeometricx-1pqHypergeometricnKNNnknN1NPoisson入入Normal2aBetaGammaExponent2Chi-Squared/.2

11、=f(X)212-1二(-e2n2万2E(x2)=nV(x2)=2nWeibull10000000000000000000000001024yottaY10000000000000000000001021zettaZ10000000000000000001018exaE10000000000000001015petaP10000000000001012teraT兆1000000000109gigaG十亿1000000106megaM百万1000103kiloK千100102hectoH百10101decaD十10-1decid分，十分之一10-2centic厘(或写作厘)，百分之一10-3millim毫，千分之一00110-6micro?微