大神帮满看看这道求极限题

原式=lim(x→0) 2∫[0,x] sintdt*sinx/[2x*ln(1+x^2)]
=lim(x→0) 2∫[0,x] sintdt*x/[2x*x^2]
=lim(x→0) 2∫[0,x] sintdt/[2x^2]
=lim(x→0) 2sinx/(4x)
=1/2