高等数学积分表公式推导

《高等数学积分表公式推导》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、高等数学积分表公式推导目录（一）含有axb的积分（1~9）·······················································1（二）含有axb的积分（10~18）···················································522（三）含有xa的积分（19~21）····················································92（四）含有axb(a0)的积分（22~28）······································

2、······112（五）含有axbxc(a0)的积分（29~30）········································1422（六）含有xa(a0)的积分（31~44）·········································1522（七）含有xa(a0)的积分（45~58）·········································2422（八）含有ax(a0)的积分（59~72）·········································372（九）含有abx

3、c(a0)的积分（73~78）····································48xa（十）含有或(xa)(bx)的积分（79~82）···························51xb（十一）含有三角函数的积分（83~112）···········································55（十二）含有反三角函数的积分（其中a0)（113~121）·······················68（十三）含有指数函数的积分（122~131）·································

4、·········73（十四）含有对数函数的积分（132~136）··········································78（十五）含有双曲函数的积分（137~141）··········································80（十六）定积分（142~147）····························································81附录：常数和基本初等函数导数公式·········································85说明···········

5、··········································································86团队人员··············································································87（一）含有axb的积分（1~9）dx11.lnaxbCaxba1b证明：被积函数f(x)的定义域为{x

6、x}axba1令axbt(t0)，则dtadx,dxdtadx11dtaxbat1lntCadx1将taxb

7、代入上式得：lnaxbCaxbaμ1μ12.(axb)dx(axb)C(μ1)a(μ1)1证明：令axbt,则dtadx,dxdtaμ1μ(axb)dxtdta1μ1tCa(μ1)μ1μ1将taxb代入上式得：(axb)dx(axb)Ca(μ1)x13.dxaxbblnaxbC2axbaxb证明：被积函数f(x)的定义域为{x

8、x}axba11令axbt(t0),则xtb,dxdtaa1tbxa11bdx·dt1dt2axbt

9、aat11bdtdt22aattblntC22aa1tblntC2ax1将taxb代入上式得：dxaxbblnaxbC2axba-1-2x11224.dx(axb)2b(axb)blnaxbC3axba2222x1(axb)2abxb)证明：dxdx2axbaaxb2112abx1b(axb)dxdxdx222aaaxbaaxb112(axb)dx(ax