求积分 cos2x/cos^xsin^2x dx求积分cos2x/cos^xsin^2x dx
问题描述:
求积分 cos2x/cos^xsin^2x dx
求积分
cos2x/cos^xsin^2x dx
答
∫ cos2x / (sinx * cosx) dx= ∫ cos2x / (1/2 * sin2x) dx= 4∫ cos2x / (sin2x) dx= 4∫ csc2x * cot2x dx= -2∫ csc2x * cot2x d(2x)= -2csc2x + C= -2/(sin2x) + C= -secx*cscx + C