dx dx d(=) 1g=cO d(te hn 所以 ncsc x-ctox+c sin x d(x In/csc(x+o)-ctg(x 2 sin(x+ 例10 (a>0) 解:设x=asnt,则ax= acosta, f= arcsin a≤X≤a, a- sin t acos tdt =a2∫ cost costa= a']@tdr (1+cos 2n)dt (t+=Sn21)+c13 解：  x dx sin =  2 cos 2 2sin x x dx =  2 cos 2 ) 2 ( x 2 x tg x d =  2 ) 2 ( x tg x d tg = c x tg + 2 ln x ctgx x x x x x x x tg = − − = = = csc sin 1 cos sin 2 2sin 2 cos 2 sin 2 2 所以  x dx sin = ln csc x − ctgx + c  x dx cos =  + + ) 2 sin( ) 2 (   x d x = x + − ctg x + ) + c 2 ) ( 2 ln csc(   = ln sec x + tgx + c 例 10．  a − x dx 2 2 (a  0) 解： 设 x = asin t ， 则 dx = acostdt ， a x t = arcsin ， − a  x  a ， 2 2   −  t   a − x dx 2 2 =  a − a sin t acostdt 2 2 2 = a cost costdt 2  =  a tdt 2 2 cos =  + t dt a (1 cos 2 ) 2 2 = ( cos 2 ) 2 2   dt + tdt a = t t c a + sin 2 ) + 2 1 ( 2 2 = t c a t a + sin 2 + 2 4 2 2 = a x c x a a x + − + 2 2 2 2 arcsin 2