例1计算 arcsin xar. 解令W= arcsinx,巾=d 2 d rdx arcsin ra =lxarcsinx 2 0 0 1 (1-x2) 262 3 十 122解 arcsin . 2 1 0 xdx 令 u = arcsin x, dv = dx, 则 , 1 2 x dx du − = v = x,  2 1 0 arcsin xdx   2 1 = xarcsin x 0  − − 2 1 0 2 1 x xdx 2 6 1  =  (1 ) 1 1 2 1 2 0 2 2 1 d x x − − +  12  =   2 1 0 2 + 1− x 1. 2 3 12 = + −  例1 计算