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

If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int_0^2 x^2[x]\, dx$ is equal to

If $\int_0^1 \dfrac{dx}{\sqrt{x + 1} - \sqrt{x}} = \sqrt{2}k$, then the value of $k$ is...