1x+dx.[(1--xdx.Dex(1+ 2lnx)e3vxdxdxcos* x(1+ tan x)VxIntanxarctan x练习dxdxsinx cos x/x(1+x)
. (1 2ln ) 1 dx x x + 1 2 1 (1 ) . x x e dx x + − arctan ln tan (1 ) sin cos x x dx dx x x + x x 练习 3 d x e x x 2 d cos (1 tan ) x x x +
求例5ar22aX-解dxdx222+axa1+ax=+C.arctanaaX1+Q
例5 求 . 1 2 2dx a x + 解 dx a x + 2 2 1 dx a a x + = 2 2 2 1 1 1 + = a x d a a x 2 1 1 1 arctan . 1 C a x a = +
dx例6 求(a > 0)a?-x?dxdx解：21-(-)ad(-)()ax=arcsin=+C(a>0)a作恒等变形是向着我们常用的积分公式努力！
例6 求 2 2 ( 0) dx a a x − 解： − 2 2 a x dx − = 2 1 ( ) 1 a x dx a − = 2 1 ( ) ( ) a x a x d arcsin ( 0) x C a a = + 作恒等变形是向着我们常用的积分公式努力!
dx例7 求a?-x?dx解：dx2aXa+xXdxdx-2aJ2aJaa+x1-x1In|a-x|+CIn+x2a2a1a+x+CIn(a> 0)2aa-xdx1X-0类似地可推出+Cin(a> 0)222aarx+a
例7 求 − 2 2 a x dx 解： − 2 2 a x dx dx a a x a x ) 1 1 ( 2 1 − = + − = + a x dx a x a dx a 2 1 2 1 1 1 ln | | ln | | 2 2 a x a x C a a = + − − + 1 ln | | ( 0) 2 a x C a a a x + = + − 类似地可推出 2 2 1 ln | | ( 0) 2 dx x a C a x a a x a − = + − +
4x-练习dx.=+C.arctan一x2-8x+2533-dx2x-1+C.二arcsinV5.21+x-x2xdx2-x-2r?x-2x+1
2 1 . 8 25 dx x x − + 练习 . 3 4 arctan 3 1 C x + − = 2 d 1 + x x x − 2 1 = arcsin + 5 x C. − 2 2 xdx x x − − 1 2 1 = 3 2 1 + . x x − +