$\int(x^{21} + x^6 + x^3)(2x^{18} + 7x^3 + 14)^{\frac{1}{3}}\ dx =$

The value of the integral $\int\limits_{1/e}^{e}\dfrac{|\log x|}{x^2}dx$ is

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