If $\int\limits_{-\pi/2}^{\pi/2}(\sin^2 x + \sin^3 x)dx = k$, then the value of $k$

If $I_n = \int\limits_0^{\pi/4}\tan^n x\ dx, n \in N$ then $I_{n+2} + I_n$ is equal to

The area in square units of the region bounded by the curve $y = \sqrt{16 - x^2}$ and lines $x = 0, x = 4$ above the X-axis is

The general solution of the differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} = x^2 + 5$ is ....