原式=lim(x->0)3x²ln(1+2sinx³)/[3(∫(0,x)ln(1+2sint)dt)²×ln(1+2sinx)]
=lim(x->0)x²ln(1+2sinx³)/[(∫(0,x)ln(1+2sint)dt)²×ln(1+2sinx)]
=lim(x->0)x²(2sinx³)/[(∫(0,x)ln(1+2sint)dt)²×(2sinx)]
=lim(x->0)x²(x³)/[(∫(0,x)ln(1+2sint)dt)²×(x)]
=lim(x->0)(x^4)/[(∫(0,x)ln(1+2sint)dt)²]
=lim(x->0)(4x³)/2[(∫(0,x)ln(1+2sint)dt)]ln(1+2sinx)
=lim(x->0)(x³)/[(∫(0,x)ln(1+2sint)dt)](sinx)
=lim(x->0)(x³)/[(∫(0,x)ln(1+2sint)dt)]x
=lim(x->0)(x²)/[(∫(0,x)ln(1+2sint)dt)]
=lim(x->0)(2x)/(ln(1+2sinx))
=lim(x->0)(2x)/(2sinx)
=lim(x->0)(2x)/(2x)
=1