$\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

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