Statement 1: $I =$

$\begin{array}{l}\int \frac{f\left(x\right)g^{\mathrm{\prime }}\left(x\right)-f^{\mathrm{\prime }}\left(x\right)g\left(x\right)}{f\left(x\right)g\left(x\right)}\{\log g(x)-\log f(x\left)\right\}dx\\ =\frac{1}{2}{\left\{\log \frac{g\left(x\right)}{f\left(x\right)}\right\}}^2+C\end{array}$

Statement 2: $\int \left(\varphi \right(x\left){)}^n{\varphi }^{\mathrm{\prime }}\right(x)dx=\frac{\left(\varphi \right(x){)}^{n+1}}{n+1}+C$

STATEMENT-1 is False, STATEMENT-2 is True

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False