高等数学高等数学课件 (69).pdf

一、第一类换元积分法设设)(uf具有原函数，具有原函数，=dxxxf)()(=)()(xuduuf)(xu=可导，可导，则有换元公式则有换元公式122sec1tanxx=+=+2tan secxx =sec sectanxxx =22tansec1xx=1.sec6 xdx xdx6sec42secsecxxdx=22(tan1)tanxdx=+=+42(tan2tan1)tanxxdx=+=+53tan2tantan.53xxxC=+=+246tansec.xxdx 46tansecxx 422tan(1tan)tanxx dx=+=+442tansecsecxxxdx=864(tan2tantan)(tan)xxx dx=+=+975121tantantan975xxxC=+=+2tansecnkxx(N)k 22sec1tan,xx=+=+tanux=353tansec.xxdx 53tansecxx 222(sec1)secsecxx dx=42tansecsec tanxxxxdx=642(sec2secsec)(sec)xxx dx=+=+753121secsecsec753xxxC=+=+21tansecknxx (N)k+22tansec1,xx=secux=43tan.xdx 3tan xdx 2tantanxxdx=2tan(sec1)xxdx=2tansectanxxdxxdx=tantanln|cos|xdxx=+=+21tanln|cos|.2xxC=+=+1sin cossin()sin()2ababab=+=+1cos coscos()cos()2ababab=+=+1sin sincos()sin()2ababab=+=+5.2cos3cos xdxx1coscoscos()cos(),2ABABAB=+=+=dxxxxdxx)5cos(cos212cos3cos.5sin101sin21Cxx+=6.cos11+dxx+dxxcos11()()1cos1cos1cosxdxxx=+=dxxx2cos1cos1 =dxxx2sincos1 =)(sinsin1sin122xdxdxx.sin1cotCxx+=