`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)).[log g(x)-log f(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=

Let g^(prime)(x)>0a n df^(prime)(x) g(f(x-1)) f(g(x+1))>f(g(x-1)) g(f(x+1))

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real xdot Then g^(f(x)) equals. -(f^(x))/((f^'(x))^3) (b) (f^(prime)(x)f^(x)-(f^(prime)(x))^3)/(f^(prime)(x)) (f^(prime)(x)f^(x)-(f^(prime)(x))^2)/((f^(prime)(x))^2) (d) none of these