微分积分公式浓缩免费版

高等数学微分和积分数学公式（集锦）一、基本导数公式0c1xxxxeelnxxaaa1lnxx1loglnxaxasincosxxcossinxx2tansecxx2cotcscxxsecsectanxxxcsccsccotxxx21arcsin1xx21arccos1xx21arctan1xx21arccot1xx二、n阶导数公式!nnxnnaxbnaxbeaelnnxxnaaa11!1nnnnanaxbaxb11!ln1nnnnanaxbaxbsinsin2nnaxbaaxbncoscos2nnaxbaaxbn三、导数的四则运算法则uvuvuvuvuv2uuvuvvv四、高阶导数的运算法则nnnuxvxuxvxnncuxcuxnnnuaxbauaxb()0nnnkkknkuxvxcuxvx五、基本积分公式kdxkxc11xxdxclndxxcxlnxxaadxcaxxedxec21arctan1dxxcx21arcsin1dxxcx2211arctanxdxcaxaa2211ln2xadxcxaaxa221arcsinxdxcaax22221lndxxxacxacossinxdxxcsincosxdxxc221sectancosdxxdxxcx221csccotsinxdxxcxtanlncosxdxxccotlnsinxdxxcseclnsectanxdxxxccsclncsccotxdxxxc六、分部积分法公式⑴形如naxxedx，令nux，axdvedx形如sinnxxdx令nux，sindvxdx形如cosnxxdx令nux，cosdvxdx⑵形如arctannxxdx，令arctanux，ndvxdx形如lnnxxdx，令lnux，ndvxdx⑶形如sinaxexdx，cosaxexdx令,sin,cosaxuexx均可。七、常用凑微分公式积分型换元公式1faxbdxfaxbdaxbauaxb11fxxdxfxdxux1lnlnlnfxdxfxdxxlnuxxxxxfeedxfedexue1lnxxxxfaadxfadaaxuasincossinsinfxxdxfxdxsinuxcossincoscosfxxdxfxdxcosux2tansectantanfxxdxfxdxtanux2cotcsccotcotfxxdxfxdxcotux21arctanarcnarcn1fxdxftaxdtaxxarctanux21arcsinarcsinarcsin1fxdxfxdxxarcsinux八、重要公式xxx1lnlim010lim1xxxexexx)1(lim0axaxxln1lim0xxx11lim0lim()1nnaaolim1nnnlim0xxelimxxe0lim1xxxxxxsinlim0xxxtanlim0xxxarcsinlim0xxxarctanlim02021cos1limxxx0sinlim1xxxlimarctan2xxlimtan2xarcxlimarccot0xxlimarccotxx九、几种常见的微分方程1.可分离变量的微分方程：dyfxgydx，11220fxgydxfxgydy2.齐次微分方程：dyyfdxx3.一阶线性非齐次微分方程：dypxyQxdx解为：pxdxpxdxyeQxedxc