`int \ {f(x)*g^(prime)(x)-f^(prime)(x)g(x))/(f(x)*g(x)){logg(x)-logf(x)} \ dx`

int(f(x)*g'(x)-f'(x)g(x))/(f(x)*g(x)){log g(x)-log f(x)}dx

int(f(x)*g\'(x)-f\'(x)g(x))/(f(x)*g(x))*{logg(x)-logf(x)}dx= (A) log (g(x)/f(x))+c (B) log (f(x)/g(x))+c (C) 1/2log (g(x)/f(x))^2+c (D) none of these

int_( is )((f(x)g'(x)-f'(x)g(x))/(f(x)g(x)))*(log(g(x))-log(f(x))dx

If int(f^(prime)(x)g(x)-g^(prime)(x)f(x))/((f(x)+g(x))sqrt(f(x)g(x)-g^2(x)))d x=sqrt(m)tan^(- 1)(sqrt((f(x)-g(x))/(ng(x))+C) where m,n in N and 'C' is constant of integration (g(x) > 0). Find the value

int(f(x)g'(x)+g(x)f'(x))/(f(x)g(x))[logf(x)+logg(x)]dx=

Evaluate int[f(x)g^(n)(x)-f^(n)(x)g(x)]dx

int[f(x).phi'(x)-f'(x).phi(x)]/[f(x).phi(x)]{logphi(x)-logf(x)}.dx is equal to

int(f'(x))/(f(x).logf(x))dx=

int x{f(x^(2))g'(x^(2))-f'(x^(2))g(x^(2))}dx

Suppose fa n dg are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all xa n df^(prime)a n dg' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x))e q u a l (a)(-2f^(prime)(x))/f (b) (2g^(prime)(x))/(g(x)) (c)(-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))