The value of $\int_{0}^{1} \left( \prod_{r=1}^{n} (x+r) \right) \left( \sum_{k=1}^{n} \frac{1}{x+k} \right) dx$ equals

Soil erosion can be prevented by

Two identical vessels $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The masses of gas in $A$ and $B$ are $m_A$ and $m_B$,respectively. The gases are allowed to expand isothermally to the same final volume $2V$. The changes in pressures of the gas in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$,respectively. Then:

When the angle of inclination of an inclined plane is $\theta$, an object slides down with uniform velocity. If the same object is pushed up with an initial velocity $u$ on the same inclined plane, it goes up the plane and stops at a certain distance on the plane. Thereafter, the body:

In which of the following pairs of categories is it more difficult to determine the relationship to other taxa at the same level, thus making the problem of classification more complex?

The set of solutions of the equation $(\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2$ is