sin2nx=sin(2n-1)xcosx+cos(2n-1)xsinx
=1/2(sin2nx+sin(2n-2)x)+cos(2n-1)xsinx
∴∫(sin2nx/sinx)dx=1/2∫(sin2nx+sin(2n-2)x)/sinxdx+∫cos(2n-1)xdx
∴1/2∫(sin2nx/sinx)dx=1/2∫(sin(2n-2)x)/sinxdx+∫cos(2n-1)xdx
∴∫(sin2nx/sinx)dx=∫(sin(2n-2)x)/sinxdx+2∫cos(2n-1)xdx
=∫(sin(2n-4)x)/sinxdx+2∫cos(2n-3)xdx+2∫cos(2n-1)xdx
=∫(sin2x)/sinxdx+2∑(1~n)∫cos(2n-1)xdx
=-2sinx+2∑(1~n)[sin(2n-1)/(2n-1)]
