The correct option is D sin(59x)sin59x59+C
I=∫sin(60x)sin58x dx
=∫sin(59x+x)sin58x dx
=∫(sin(59x)cosx+cos(59x)sinx)sin58x dx
=∫[sin(59x)sin58xcosx+sin59xcos(59x)]dx
Integrate sin(59x)sin58xcosx by parts, we get
=sin(59x)sin59x59−∫cos(59x)sin59x dx+∫cos(59x)sin59x dx
=sin(59x)sin59x59+C