C

Evaluate the following integral on the interval $(0;+\mathrm{\infty })$. $$\int x\ln x\mathrm{d}x$$

The sides of a right triangle form three consecutive terms of an arithmetic sequence. The perimeter of the triangle is $60\mathrm{cm}$. Find the hypotenuse of the triangle (the longest side).

The sides of a box form three consecutive terms of an arithmetic sequence. The volume of the box is $665{\mathrm{cm}}^3$. The shortest side is $5\mathrm{cm}$. Find the surface area of the box.

The sum of the first eight terms of an arithmetic sequence is $44$. The sum of the next four terms is bigger than this value by $50$. Find the thirteenth term $a_{13}$.