∫tanxdx/(3sinx^2+cosx^2)
=∫tanxdx/(3-2cosx^2)
=∫tanxdx/cosx^2(3/cosx^2-2)
=∫tanxdtanx/(3/cosx^2-2)
=(1/2)∫dtanx^2/(3tanx^2+1)
=(1/6)ln(3tanx^2+1)+C
求不定积分∫TANX/(3SINX^2+COSX^2)DX
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∫sinx/(cosx)^3 dx= 1/2 （tanx)^2+C