例5求积分sm(mnx) 解:原式- csin(n x)-「 xdsin(nx) xsin(n x)x cos(In x) dx xsin(n x)-Icos(n x dx xsin(n x)-xcos( x)+xd[cos(n x) x[sin(n x)-cos (n x)]sin(n xdx 原式=sin(nx)-cos(nx)+C例5 求积分 x dx  sin(ln ) 解: 原式= xsin(ln x) xd[sin(ln x)]  − dx x x x x x  = −  1 sin(ln ) cos(ln ) x x x dx  = sin(ln )− cos(ln ) xsin(ln x) xcos(ln x) xd[cos(ln x)]  = − + x x x x dx  = [sin(ln )−cos(ln )]− sin(ln ) ∴原式= x x C x [sin(ln ) − cos(ln )]+ 2