Question

∫（cos2x／sin^2x）dx

Answer 1

cos2x=cos*2x-sin*2x cot*2x=csc*2x-1 cotx的导数=-csc*2x ∫（cos2x／sin^2x）dx=∫cos*2x-sin*2x／sin^2xdx 经过化简得 =∫cot*2xdx-∫1dx =∫csc*2xdx-∫1dx-∫1dx =-cotx-2x+c∫（cos2x／sin^2x）dx

Answer 2

cos2x=cos*2x-sin*2x cot*2x=csc*2x-1 cotx的导数=-csc*2x
∫（cos2x／sin^2x）dx=∫cos*2x-sin*2x／sin^2xdx 经过化简得 =∫cot*2xdx-∫1dx =∫csc*2xdx-∫1dx-∫1dx =-cotx-2x+c

Answer 3

∫ cos2x / (sin²x * cos²x) dx
= ∫ cos2x / (1/2 * sin2x)² dx
= 4∫ cos2x / (sin²2x) dx
= 4∫ csc2x * cot2x dx
= -2∫ csc2x * cot2x d(2x)
= -2csc2x + C
= -2/(sin2x) + C
= -secx*cscx + C