$\int \frac{\left\{f\left(x\right)\cdot {\varphi }^{\mathrm{\prime }}\left(x\right)-f^{\mathrm{\prime }}\left(x\right)\cdot \varphi \left(x\right)\right\}}{f\left(x\right)\cdot \varphi \left(x\right)}\{\log \varphi (x)-\log f(x\left)\right\}dx\text{ is =}$

• A

  $\log \frac{\varphi \left(x\right)}{f\left(x\right)}+k$

• B

  $\frac{1}{2}{\left\{\log \frac{\varphi \left(x\right)}{f\left(x\right)}\right\}}^2+k$

• C

  $\frac{\varphi \left(x\right)}{f\left(x\right)}\log \frac{\varphi \left(x\right)}{f\left(x\right)}+k$

• D

  $\text{ None of these }$