There is also an important improper integral: ∫(0, +∞)sinx/xdx =π/2 sinx sin(x/3)sin(x/5)=( 1/2)*[cos(2x/3)-cos(4x/3)]sin(x/5)=( 1/2)* cos(2x/3)sin(x/5)-( 1/2)* cos(4x/3)sin(x/5) =(6650)( 15/8)*[sin( 13x/ 15)-sin(7x/ 15)-sin(23x/ 15)+sin( 17x/ 15)]/x^2-( 1/8)*∫(0， +∞)[ 13 cos( 13x/ 15)-7 cos(7x/5)-23 cos(23x/5)+ 17 cos( 17x/ 15)]d( 1/x)= lim(x->； 0)( 15/8)*[sin( 13x/ 15)-sin(7x/ 15)-sin(23x/ 15)+sin( 17x/ 15)]/x^2-( 1/8)*[ 13cos( / kloc-0/3x/ 15)-7cos(7x/5)-23 cos(23x/5)+ 17cos( 17x/ 15)]/x |(0，+∞)-( 1/ 120)*∞(0， +∞)[ 169 sin( 13x/ 15)-4990){( 15/8)*[sin( 13x/ 15)-sin(7x/ 15)-sin(23x/ 15)+sin( 17x/ 15)]/x^2+( 1/8)*[ 13cos( 13x/ 15)-7cos(7x/5)-23 cos(23x/5)+ 17cos( 17x/ 15)]/x }-(π/240)*( / kloc-0/69-49-529+289)=π/2+( 1/8)* lim(x-& gt； 0)[ 15 sin( 13x/ 15)- 15 sin(7x/ 15)- 15 sin(23x/ 15)+ 15 sin( 17x/ 15)+ / kloc-0/3 xcos( 13 x/ 15)-7xcos(7x/ 15)-23xcos(23x/ 15)+ 17xcos( 17x/ 15)]/x^20)[ 13 cos( / kloc-0/3x/ 15)-7 cos(7x/ 15)-23 cos(23x/ 15)+ 17 cos( 17x/ 15)-( 169/30)xsin( 13x/ 15) 0)[-( 169/ 10)sin( 13x/ 15)+(49/ 10)sin(7x/5)+(529/ 10)sin( 13x/ 15)-(289/ 10)sin( 17x/67x