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[高数164]隐函数的不定积分问题(1)
高等数学习题讲解 第164题
高等数学(上)习题集146/264
![[高数163]被积函数带绝对值的不定积分问题](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/1e7bd3e72231482eb40ce7bc023a884c~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=YHYsC2tA2CXo4Hil9Pvv8rtlu%2FU%3D)
App03:49![[高数164]隐函数的不定积分问题(1)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/16d57214be694c16b18ddcb17ab232b5~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=10AQoe%2BsaBMBuWW8t2l3V2%2BINN4%3D)
App04:54![[高数165]隐函数的不定积分问题(2)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/bfeb34fd42b245c2b43bf283fabaac14~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=%2Fjis45qmEe79IlOCMO7O4ZDJbGc%3D)
App04:31![[高数166]未知函数的不定积分](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/ddd321a2c39a446cb223b4153af9aa4a~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=dMwOE%2B67NKh%2BZn3v7aCl1ayapco%3D)
App03:09![[高数167]这种凑微分的方法也是少见](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/6420bd1330fd4bb280024435e2b370ab~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=JjftCl3aYE5qVByhJTS27jHXHjY%3D)
App04:48![[高数168]有道不难但复杂的题](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/94e15bf1e7884823982cd17080a8ec4b~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=HK6cpuf6dnybuf4T7gsD02bHhck%3D)
App08:08![[高数169]先倒代换后根式代换](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/76d32cdc203244d4bfe117ab240d0cf6~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=CQZMtaAD4AGhPCs4Id9PBEt%2FtGE%3D)
App07:09![[高数170]题目简洁但解答过程复杂](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/0e5398a781cf4715ae99c4bdb49de1b2~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=yVfgcaFmS%2BST69yrYEOGGvqYn64%3D)
App11:20![[高数171]注意观察被积函数的特点](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8376261b53c44289aa4bb0bbf724d157~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=sYGWXxYzLDmLJU%2FqWPcNSuc98mE%3D)
App02:39![[高数172]见招拆招|遇水搭桥|逢山开路](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8afdf78dcc004f0686158fab4374e3b1~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=QtdkkplQSjddOgnebpG0bqjzt1s%3D)
App05:34![[高数173]这样子的被积函数可以使用根式代换](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/9c1d68c58ab84829834200c0a438e2aa~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=yyF6gEnguqIPb09SH8v9LFMtx3A%3D)
App08:42![[高数174]三角函数的不定积分|三角公式很重要 (1)](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/008446c617d34ec7a4c7a1e5055448e0~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=xczYjBiD%2Be9V9ivkjjMVNfPAqsY%3D)
App02:20![[高数175]三角函数的不定积分|三角公式很重要 (2)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/5af14b80a1114bb4a196fdc8d4aba75d~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=RAxG1VBQV9SsGD%2F8joAvQy3cpBU%3D)
App01:57![[高数176]三角函数的不定积分|三角公式很重要 (3)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/07dde814583b433bbfcd623611082387~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=yLireGaZgUaEITT7zLTMbCnqxTQ%3D)
App03:06![[高数177]三角函数的不定积分|三角公式很重要 (4)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/6c2323be51094d69b65c6573a83c6e33~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=Cjtg0lA4AHAJxvz%2F7%2FlggCQGkc0%3D)
App04:16![[高数178]三角函数的不定积分|三角公式很重要 (5)](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/7299bb1d65a147968201d509883b6d4e~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=4RJssoVpO9pNRcUv3myHtTw%2Bs%2FM%3D)
App05:22![[高数179]三角函数的不定积分|三角公式很重要 (6)](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/0921484550ba48ba980761c07fa2861b~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=zPHaiguelHkifN2QsXmMSwnpWAU%3D)
App04:38![[高数180]不看答案我得想很久](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/c54177f0ac484b668b99c9704c9d92b6~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=20250310061020004EF72F28E342C44D5A&requestFrom=704&version_code=80402&x-expires=1773094220&x-signature=vsw%2BkyDL8A7JTKJZPeUIGPEtnfo%3D)
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