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当前位置:首页 > 建筑/环境 > 工程监理 > 复旦大学出版社,高等数学,第四版,教材习题答案详细解析
第1页/共8页高等数学上(复旦大学出版社,第四版)教材习题答案第四章,一元函数积分学。第三节不定积分与原函数求法,习题4-3,答案5.0用分部积分,求下列不定积分。东风冷雪1.0222222xsinxdxxdcosx(xcosx2xcosxdx)(xcosx2xdsinx)xcosx2xsinx2sinxdxxcosx2xsinx2cosxc2.0第2页/共8页xxxxxxxedxxde(xeedx)xeec3.022222111lnxdx(xlnxx*dx)22x11xlnxxc24xlnxdx4.023332232322322xarctanxdx111xarctanxdxxarctanx3331x11x(1x)xxarctanxdx331x1111xarctanx(xln|1x|)3322111xarctanxxln|1x|c3665.02222arccosxdxxd(1x)x*arccosxx*arccosx1x1xx*arccosx1xc第3页/共8页6.0222222xtanxdx1x(secx1)dxxdtanxx21dcosx1xtanxtanxdxxxtanxx2cosx21xtanxln|cosx|xc27.0xxxxxxxxxxxxecosxdxedsinxesinxedcosxesinxecosxcosxedx2ecosxdxesinxecosx1ecosxdxe(sinxcosx)c28.0xsinxcosxdx11xsin2xdxxdcos2x24111(xcos2xcos2xdx)xcos2xsin2xc448第4页/共8页9.0323233223232232232(lnx)dxx1lnx3lnxlnx1lnxd()(3lnxd)xxxxxlnx3lnx6lnxlnx3lnx1dx6lnxdxxxxxxlnx3lnx6lnx6dxxxxx1(lnx3lnx6lnx6)cx10.02222222222222222222axdx,xatant,asectdtantasecttantatantsectdta(secttant(sect1)sectdta(secttantln|secttant|sectdtant)1a(secttantln|secttant|)21xaxxaxa(*ln||2aaa1xxaln|xax2|c6.0求下列不定积分;1.0第5页/共8页222222222222x1dx(x1)(x1)x1abcx1x1(x1)(x1)(x1)a(x1)b(x1)c(x2x1)x111a,b1,c2211x1122dx()dxx1x1(x1)(x1)(x1)11ln|x1|c2x12.032222222223dxx13abxcx1(x1)(xx1)xx1a(xx1)(bxc)(x1)3a1,b1,c23dx1x2dx()dxx1(x1)(xx1)xx112x13ln|x1|2xx1131ln|x1|ln|xx1|1322(x)24x12x1ln|3ractan(3xx12)c3.0(这道题,有些坑人,没有意思)第6页/共8页5423332332233323222xx8x(xx)x(xx)xxxx8dxdxxxxx123xx33(xx1)dxxxxx23x1113xxxln|xx|dx323x(x1)(x1)23xabc3x(x1)(x1)xx1x123xa(x1)b(xx)c(xx)323101a,b,c33543323323x12310133dx()x(x1)(x1)3xx1x1231013ln|x|ln|x1|ln|x1|3331(ln|x|ln|x1|ln|x1|23ln|x|10ln|x1|13ln|x1|31ln(24ln|x|9ln|x1|12ln|x1|)3xx8dxxx11xxx8ln|x|3ln|x1|324ln|x1|c4.0263332xdxx11dx1arctanxc33(x)1第7页/共8页5.0222sinxdx1sinxsinx(1sinx)dx(tanxsecxtanx)dxcosxsecx(secx1)dxsecxtanxxc6.0222222222cotxdxsinxcosx1x2ttan,dxdt21t1t21t1t22t*dt**dt2t22t2t1t1t1t11t1t11t1111()dt(1)dtlntt2t2t221x1xln|tan|tanc22227.021dx,1xsectx(1x)12secttantdt2sectdtsecttantx1x2ln|secttant|2ln|1xx|c第8页/共8页8.0x11x1122dxdx(1)dxx11x11x11x1t,dx2tdt12(1)2t2ln|1t|2x12ln|1x1|t11tx11x11dxx4x14ln|1x1|cx11记住口诀,反,对,幂,指,三。积化和差,与万能公式,在三角函数积分中非常有用。答案提供人,东风冷雪。还有一个图片版本,自己查看
本文标题:复旦大学出版社,高等数学,第四版,教材习题答案详细解析
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