例8 ∫lnx+Ⅵ+x2)dx=xmx+√+x)-∫ =xln(x+√1+x2)-√1+x2+c 例9、「e2 cose dx= e sine " sine-sine'de' =e sine cose +c b5110,x'sin'xdx=x25(1-cos2x)dx xdsin2, xsin2x += xsin 2x d 64 Sin 2X xd cosa X SIn2X XcOS2X+-sin 2x+c例 8、   + + + + = + + − c 1 x dx ln(x 1 x )dx xln(x 1 x ) 2 2 2 xln(x 1 x ) 1 x c 2 2 = + + − + + 例 9、  =  2x x x x e cose dx e dsine = −  x x x x e sine sine de e sine cose c x x x = + + 例 10、  =  (1− cos2x)dx 2 1 x sin xdx x 2 2 2 = −  x dsin2x 4 1 6 x 2 3 = − +  xsin 2x dx 2 1 x sin2x 4 1 6 x 2 3 = − −  xd cos2x 4 1 sin 2x 4 x 6 x 3 2 sin 2x c 8 1 x cos2x 4 1 x sin2x 4 1 6 x 2 3 = − − + +