Question

$\int_{}^{}\frac{\{ f(x).\varphi'(x)–f'(x)\varphi(x)\}}{f(x).\varphi(x)}${logf(x)–logf(x)}dx =

• A. log$\frac{\varphi(x)}{f(x)}$ + K
• B. $\frac { 1 } { 2 }$ $\left\{ \log\frac{\varphi(x)}{f(x)} \right\}^{2}$+ K
• C. $\frac{\varphi(x)}{f(x)}$.log$\frac{\varphi(x)}{f(x)}$+K
• D. None of these

Answer 1

Answer: (B)

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

Answer 2

Sol. I = $\frac{1}{2\pi fC}$d$\left\{ \log\frac{\varphi(x)}{f(x)} \right\}$

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