dua tich phan thanh$\int\limits_{\frac{\pi }{6}}^{\frac{\pi }{4}}\frac{\sqrt{2} cos^{2}x}{sin^{3}x(sinx-cosx)}dx=\sqrt{2} \int\limits_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{cot^{2}x}{sin^{2}x(1-cotx)}dx$$dat t= cotx thi tich phan thanh$$\int\limits_{\sqrt{3} }^{1}\frac{-t^{2}}{1-t}dt = \int\limits_{\sqrt{3} }^{1}(\frac{t^{2}-1}{t-1}+\frac{1}{t-1})dt=\int\limits_{\sqrt{3} }^{1}(t+1)dt+\int\limits_{\sqrt{3} }^{1}\frac{dt}{t+1}$den day la co ban roi thay can nua thoi

dua tich phan thanh$\int\limits_{\frac{\pi }{6}}^{\frac{\pi }{4}}\frac{\sqrt{2} cos^{2}x}{sin^{3}x(sinx-cosx)}dx=\sqrt{2} \int\limits_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{cot^{2}x}{sin^{2}x(1-cotx)}dx$$dat t= cotx thi tich phan thanh$$\sqrt{2} \int\limits_{\sqrt{3} }^{1}\frac{-t^{2}}{1-t}dt = \sqrt{2} \int\limits_{\sqrt{3} }^{1}(\frac{t^{2}-1}{t-1}+\frac{1}{t-1})dt=\sqrt{2} \int\limits_{\sqrt{3} }^{1}(t+1)dt+\sqrt{2} \int\limits_{\sqrt{3} }^{1}\frac{dt}{t+1}$den day la co ban roi thay can nua thoi