例5求积分∫sim(mx)dx 解jsm(mx)x= e sin(n x')-∫xdim(mx) xsin(n x)-xcos (n x). dx x sin(n x)=xcos(n x)+xdlcos(n x)I x[sin(n x)-cos(n x)1-sin(n x)dx ∴「sin(nx)dx=|sin(nx)-cos(nx)+C 2 上页例5 求积分 sin(ln ) .  x d x 解  sin(ln x)d x  = x sin(ln x) − x d[sin(ln x)]  = −  d x x x x x x 1 sin(ln ) cos(ln )  = x sin(ln x) − x cos(ln x) + x d[cos(ln x)]  = x[sin(ln x) − cos(ln x)] − sin(ln x)d x   sin(ln x)d x [sin(ln ) cos(ln )] . 2 x x C x = − +