$\int \dfrac{x^4(x^{10} - 1)}{x^{20} + 3x^{10} + 1}\, dx = \cdots$

$\int \left(e^{\log(\sin x)} + \cos x\right) x\, dx = $

The value of $\int \sin 4x \cos 3x\, dx$ is

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