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[高数163]被积函数带绝对值的不定积分问题
高等数学习题讲解 第163题
高等数学(上)习题集145/264
![[高数162]被积函数是分段函数的不定积分问题](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/36c2dcd42eb54ed6b3947e1e3cb82a71~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=q0M5POELK1AvfZksHdi4T90WTMc%3D)
App04:09![[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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=XaJjZU3QGKZpVA31BS717kH2bEc%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=6OtLNIaOtgSXykV5mQYk5GiwRSY%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=%2BBA2uvYkXu9QCWA%2FH22vANBzANM%3D)
App04:31![[高数166]未知函数的不定积分](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/ddd321a2c39a446cb223b4153af9aa4a~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=ybWK%2BDP%2FZQEe2MwymUu%2BgbCDe98%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=IulVmhQB4gUhXvdQkZX2GAiIvwU%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=DoN%2BnRB%2B24T%2FkQRlfwiF5G8Rh7E%3D)
App08:08![[高数169]先倒代换后根式代换](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/76d32cdc203244d4bfe117ab240d0cf6~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=k%2FWq%2BD33TmIlwG4KLTPY6EJRVW8%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=j9x7%2FZO2jU9YNnyVvSG%2BEks9XtA%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=UnMg0VSYfo%2Fr9PH3g4nsEMVRRq4%3D)
App02:39![[高数172]见招拆招|遇水搭桥|逢山开路](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/8afdf78dcc004f0686158fab4374e3b1~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=MOn8ZCAiPHMVVXoWV24Ls26%2FGB0%3D)
App05:34![[高数173]这样子的被积函数可以使用根式代换](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/9c1d68c58ab84829834200c0a438e2aa~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=cUUT2BFFdTEgZXh%2FrR2O0e8mX7o%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=2acQ9GdjU%2FMpDHezDknwQWfKyGo%3D)
App02:20![[高数175]三角函数的不定积分|三角公式很重要 (2)](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/5af14b80a1114bb4a196fdc8d4aba75d~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=1UFiiSMUxOvuEZd%2Fa3RkrFcyrCk%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=1OH5guti%2Bc%2B%2B6fN3yYXvJpyf5Jo%3D)
App03:06![[高数177]三角函数的不定积分|三角公式很重要 (4)](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/6c2323be51094d69b65c6573a83c6e33~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=c4ZppQD1E%2FkJPp1JJ4mW%2FCXgm7U%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=g%2F42Jbe3x6ZfNZ%2BRInkb%2FipXiW8%3D)
App05:22![[高数179]三角函数的不定积分|三角公式很重要 (6)](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/0921484550ba48ba980761c07fa2861b~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=LdFqg1Ci3a8Zkm0t3K5aeVE9Idw%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&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2024110613590163A7921097BFD275F950&requestFrom=704&version_code=80402&x-expires=1762408741&x-signature=TP%2B0i3IcjyFRjcWwG7nnvT6N7oQ%3D)
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