$(5$ points$)$ Some integrals cannot be solved algetraically. The integrals

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{cos(x)}{x}dx,$ and $,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xln(x)cos(x)dx$

are two such integrals $-$ it can be proven that no closed$-$form solution exists in terms of elementary functions for either. However, their sum can be eqpessed in terms of elementary functions. Vere interention by purts on

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xln(x)cos(x)dx$

to obtain a closed$-$form expression for the sum:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xln(x)cos(x)dx{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{cos(x)}{x}dx$