The value of the definite integral $\int_0^{\pi}\dfrac{1}{5 + 4\cos x}\, dx$ is equal to ...

Let $f(x) = x - [x]$ for every real number $x$, where $[x]$ is integral part of $x$. then $\int\limits_{-1}^{1} f(x)\, dx$ is

The area of the region bounded by curves $y = \sin x, y = \cos x$ and the lines $x = 0$, $x = \dfrac{\pi}{4}$ is

The general solution of the differential equation $\sec y + (x - e^{\sin y})\dfrac{dy}{dx} = 0$ is...