同济大学数学系《高等数学》第7版笔记和课后习题含考研真题详解(4-6章)【圣才出品】

圣才电子书十万种考研考证电子书、题库视频学习平台www.100xuexi.com（1）?1x2?1dx?ln?x?x2?1??C

（2）?1x2x2?1dx?x2?1x?C（3）??2x

1

x

2?1??x?1?2dx?arctanx?x?1?C（4）?secxdx?lntanx?secx?C（5）?

xcosxdx?xsinx?cosx?C（6）?exsinxdx?1x2e?sinx?cosx??C解：（1）ddx???ln?x?x2?1??C???1???1?x?

??1?x?x2?1?x2?1?x2?1x（2）d?x?x2?11dx?

x2?1??C???x2?1??x??

x2?x2x2?1（3）d?1?

112xdx??arctanx?x?1?C???x2?1??x?1?2??x2?1??x?1?2（4）ddx?lntanx?secx?C??1

tanx?secx??sec2x?secxtanx??secx（5）d

dx?xsinx?cosx?C??sinx?xcosx?sinx?xcosx

（6d?1dx??2ex?sinx?cosx??C????1x1xx

2e?sinx?cosx??2e?cosx?sinx??esinx2．求下列不定积分：（1）?dxx2；（2）?xxdx；6/159）