Assertion(A): $\int \frac{\left\{f\left(x\right)\varphi \text{'}\left(x\right)-f\text{'}\left(x\right)\varphi \left(x\right)\right\}}{f\left(x\right)\varphi \left(x\right)}\left\{\log \varphi \left(x\right)-\log f\left(x\right)\right\}dx=\frac{1}{2}{\left\{\log \frac{\varphi \left(x\right)}{f\left(x\right)}\right\}}^2+C$
Reason (R) : $\int {\left(g\right(x\left)\right)}^{n}g\text{'}\left(x\right)dx=\frac{{\left(g\right(x\left)\right)}^{n+1}}{n+1}+C$

Both A and R are true and R is the correct explanation of A

A is true, but R is false

A is false but R is true

Both A and R are true and R is not the correct explanation of A