bài này bạn đặt [tex]t=\frac{\pi }{2}-x=>dt=-dx[/tex]
khi đó: [tex]\int_{0}^{\frac{\pi }{2}}\frac{sin^7x}{sin^7x+cos^7x}dx=\int_{\frac{\pi }{2}}^{0}\frac{-cos^7t}{cos^7t+sin^7t}dt=\int_{0}^{\frac{\pi }{2}}\frac{cos^7t}{cos^7t+sin^7t}dt=\int_{0}^{\frac{\pi }{2}}\frac{cos^7x}{sin^7x+cos^7x}dx[/tex]
khi đó, [tex]2I=\int_{0}^{\frac{\pi }{2}}\frac{sin^7x}{sin^7x+cos^7x}dx+\int_{0}^{\frac{\pi }{2}}\frac{cos^7x}{sin^7x+cos^7x}dx=\int_{0}^{\frac{\pi }{2}}1dx=\pi/2 =>I=\pi /4[/tex]
bạn nhớ các quan hệ lượng giác: [tex]sin(x)=cos(\frac{\pi }{2}-x)[/tex]