1 =√1+x2 arctan x d 2 令x=tant -dx 1+x 2 a sec tdt=sec tdt 1+ tan t In(sec t+ tant)+C=In(x+v1+x2)+C rarctan x 2 2 1+x arctan x-In(x+v1+x)+C 上页d x x x x  + = + − 2 2 1 1 1 arctan 令 x = tant dx x  + 2 1 1  + = tdt t 2 2 sec 1 tan 1  = sec tdt = ln(sec t + tan t) + C = ln( x + 1 + x ) + C 2  +  d x x x x 2 1 arctan 1 x arctan x 2 = + ln( 1 ) . 2 − x + + x + C