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求积分技巧: 通过配方法,转化为基本积分表中的积分形式[084]
在这个视频中, 我们利用配方法对被积函数进行变换, 从而得到易于求解的积分形式. 分别是以下四种形式: 1/(x^2+a^2); 1/sqrt(x^2+a^2) 1/sqrt(x^2-a^2) 1/sqrt(a^2-x^2)
高等数学(上)习题集74/264
App04:40![求积分技巧: 通过配方法,转化为基本积分表中的积分形式[084]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/6d55da2b3be24bd19f56eaf69df5b898~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=2wpIhh2egSOrf1ljqQMBP3NKc3g%3D)
App10:05![求积分技巧之裂项求积,通过裂项转化为若干个积分公式的积分[085]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/1388b6ea9efc470bbd77cf0b2bd20309~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=0uIqL0Ecjr9iF3AjAGS8qBaIzL8%3D)
App14:06![求积分技巧之凑微分法(1), 最基础也是最重要的求积分方法[086]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8d8cdf6f5547400291dd60547e32a911~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=JgWmtJjJtbpu3Zi%2Fk1RhhJYnyrM%3D)
App08:43![求积分技巧之凑微分法(2), 最基础也是最重要的求积分方法[087]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/9de6447729cb4290a20668a0693a96a6~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=QSgu65Yg87nwVfChhzkwf8x2tQ8%3D)
App07:58![求积分技巧之分部积分法; 三指幂对反, 顺序不能忘[088]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/b2cd6ade410a4c14b8075e354d01110c~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=pLSMAjYsYzWUHhlA66RCoj2HCQY%3D)
App08:18![三角代换使用说明, sec^2t = 1 + tan^2t [090]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/799c75786a0044b5958adf7d2ba7ff48~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=keGeb7zo2hMx2mXPcCJrIlBZhb0%3D)
App09:27![三角代换使用说明, cos^2t = 1 - sin^2t [091]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/fc4b46ea8d6741a594ac5c46373d5fc3~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=KYoG0uFvtcdReFWg2lKcZquhbDA%3D)
App11:49![根号? 根号! 换掉它! 根式代换 [092]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/911fb0cbd92441f5a7134c6854171552~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=hyju6b7fusaMy3rGDzOL9ROfyIw%3D)
App09:58![根式代换就是替换掉不易求解的根号部分 [093]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2f5944aa6d734c3d96a519c34f127c88~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=HDJOUR8jalyg98O6e0eYpPzAw4w%3D)
App09:06![两道解题思路不拐弯的积分题|第二类换元法|裂项求积 [094]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/51fe2817a9f14283b33219e7901dc016~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=YqS5WHtv5uZS72m%2FnNK%2FB0adQTM%3D)
App08:35![根式代换与三角代换都可以求解的两道题 [095]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/f040bca229ed4f94a33f87c1f89d2ceb~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=%2BGxeSmauD0znS3FdRtElELF7unc%3D)
App06:08![三角代换能解的题, 我根式代换也想试一试[096]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/200afc81ad974f40be25d1e14e04a8c2~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=aVQVg79fAqPnqdrvtHoz4Q7gO7I%3D)
App05:21![好吧, 这里居然是用分部积分[097]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8a61e746eb044856b425d15b515eb765~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=5lzDJSNQFi06AWmo1NzjCHl7pXI%3D)
App06:05![凑微分嘛! 没有就构造[098]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/34bbb99701004974983f85acc5b98194~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=6jwSAgfVdf4tTK7vMxj8UtrfmOw%3D)
App04:23![一种常见的凑微分方式: 硬凑! 积分嘛, 不寒碜[099]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/9008b820b68e44d5b6217aebbee651bd~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=Jo4V%2FaZBvIVGILLl5YSnX3rgqb8%3D)
App04:58![[100]两种方法求解, 难度差很大](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/7d2f088e942848438d530894bda7571d~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=Un8yC%2FVZQM4%2BDE8r%2BXiFckHt9y4%3D)
App14:01![[101]有趣的换元方式; 拆项后将某一部分积分转化为所求积分](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/4f81bf6fb9ba4d1f8280c04bf57c2b7c~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=Rnj%2FbJjg9dl0jdtLzlf%2BtDLL5UY%3D)
App03:51![[102]不用费曼积分法也能求.](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/edac18a3965a4d478b0fa1d4a22d656f~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=6fI9zR%2BTf9xge7s9n3nGJFZImCw%3D)
App05:18![[103]两种方法求解这道不定积分. 万能代换|三角变换](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/eda1c5848484405d92f9ac9a0840fe06~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=82noNMQOiIM8FB53ylCk6nOyO%2Fg%3D)
App08:13![[104]两种方法半角代换|三角变换; 技巧性比较强的两种解法](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/d8a21c8c4e6d4dde8728b5ed7e93dae6~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=XH5QC7I%2FoS7efvBSWss6QTKEezA%3D)
App11:09![[105] 想凑微分? 得先熟悉函数的导数.](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8e2d23f4de434840a1b67605879ffc0e~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=OUJ4gADzHmK5uDCIMUs%2FUVGEQxs%3D)
App03:35![[106] 分部积分法 | 少见的凑微分方式](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/392b1829fd2f49f098ebf285347a9554~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=U%2BYHHaF8phMIkakXgAxnyDxFwKA%3D)
App02:49![[107] 利用已知函数的导数凑微分](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/4918ebba85414bc086c4fc1ee73c0f0c~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=opNCB3BXAd7KxcVGxxWGxe%2BQ7Ls%3D)
App02:16![[108] 构造式地凑微分, 然后利用分部积分法求解](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/276ceae24da64de99525427550fda7d7~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=XJYEMS9bvHg3aoyJOlQjU5l7KeU%3D)
App03:17![[109] 半角代换求不定积分](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/0292a09e40964315adb611437e1d68cd~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=8m5g8OuAiyJvdaKdddQ9kWGfQec%3D)
App02:59![[111] 分部积分法+三角恒等式](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/f3caaa4dce0c43deb5b550bbad82b1b9~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=nTTsuAYtc6gCVtylkHWCYaLhRMU%3D)
App03:07![[115] 三角变换多种多样. 这里先凑微分,后换元, 再拆项求积](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/0eb6421bf94e49c4ba50dc4260af525b~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=swFO4QomKoMAPI8dxLPA9%2Be2dnk%3D)
App02:47![[117] 积化和差公式用于求积分](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/d47db3a5891e4005b8d083659df96c63~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=GLP5%2B5lQcZqWqc%2BFgWR35O8wERI%3D)
App02:20![[119] 不用万能代换, 构造式地凑微分](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/bff57a998ab343bf9e80015a32eef678~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=Al5uXdfrEp51d6HvXvR7aW2O%2FQ0%3D)
App03:46![[高数121] 三角代换求不定积分 | 思路直接且清晰](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/363005e55cf7440f96cd9ddf11a22efa~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=202503131938332380665AAD09559299B7&requestFrom=704&version_code=80402&x-expires=1773401915&x-signature=Z6hjWGBi7Dp5whSzGQnOIY4qpxI%3D)
App04:51
