$\int_0^{2 \pi} \sin ^3 x \cos ^2 x \, dx = $ . . . . . . .

$\int_{-1}^3 \left(\tan^{-1}\left(\frac{x}{x^2+1}\right) + \tan^{-1}\left(\frac{x^2+1}{x}\right)\right) dx =$

The value of $ \int_{-3}^{3} (ax^5 + bx^3 + cx + k) dx $,where $a, b, c, k$ are constants,depends only on . . . . . .

The value of the integral $\int_{\frac{1}{n}}^{\frac{an - 1}{n}} \frac{\sqrt{x}}{\sqrt{a - x} + \sqrt{x}} dx$ is

The value of the integral $\int_0^\pi(1-|\sin 8 x|) d x$ is

For $U_n = \int\limits_0^1 x^n (2 - x)^n \, dx$ and $V_n = \int\limits_0^1 x^n (1 - x)^n \, dx$,where $n \in N$,which of the following statements is true?