1.5 посмотрите пожалуйста

[latex]\int\limits_0^\frac\pi2\frac{\cos x}{1+\cos x}dx\\\cos x=\cos^2\frac x2-\sin^2\frac x2\\1=\sin^2\frac x2+\cos^2\frac x2\\\int\limits_0^\frac\pi2\frac{\cos x}{1+\cos x}dx=\int\limits_0^\frac\pi2\frac{\cos^2\frac x2-\sin^2\frac x2}{\sin^2\frac x2+\cos^2\frac x2+\cos^2\frac x2-\sin^2\frac x2}dx=\int\limits_0^{\frac\pi2}\frac{\cos^2\frac x2-\sin^2\frac x2}{2\cos^2\frac x2}dx=[/latex] [latex]=\int\limits_0^{\frac\pi2}\frac{\cos^2\frac x2-1+\cos^2\frac x2}{2\cos^2\frac x2}dx=\int\limits_0^{\frac\pi2}\frac{2\cos^2\frac x2-1}{2\cos^2\frac x2}dx=\int\limits_0^{\frac\pi2}\left(1-\frac1{2\cos^2\frac x2}\right)dx=\\=\int\limits_0^{\frac\pi2}dx-\frac12\int\limits_0^{\frac\pi2}\frac{dx}{\cos^2\frac x2}=\left.x\right|\limits_0^{\frac\pi2}-\left.\frac12(2tg\frac x2)\right|\limits_0^{\frac\pi2}=\frac\pi2-0-(1-0)=\frac\pi2-1[/latex]