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

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

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'g(x)}dx equals

int [f(x)g"(x) - f"(x)g(x)]dx is

int((f'(x)g(x)+f(x)g'(x)))/((1+(f(x)g(x))^(2)))dx is where C is constant of integration

int_(ln lambda)^(ln (1/lambda)) (f(x^2/3)(f(x)+f(-x)))/(g(3x^2)(g(x)-g(-x))) dx=

int_(ln lambda)^(ln(1/lambda))(f(x^(2)/3)(f(x)+f(-x)))/(g(3x^(2))(g(x)-g(-x)))dx=

The derivative of (log x) ^(x) w.r.t x is (log x)^(x-1) [1+ log x log (log x)] R : (d)/(dx) {f (x) ^(g(x))[g (x) (f'(x))/(f (x)) + g'(x) log (f(x) ]