Statement 1: `int({f(x)varphi^(prime)(x)-f^(prime)(x)varphi(x)})/(f(x)varphi(x))` `-logf(x)dx=1/2{(varphi(x))/(f(x))}^2+c` Statement 2 : `int(h(x))^n h^(prime)(x)dx=((h(x))^(n+1))/(n+1)+c`

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

Let int e^(x){f(x)-f'(x)}dx=varphi(x) .Then int e^(x)f(x)dx is varphi(x)=

If y+x(dy)/(dx)=x(varphi(xy))/(varphi'(xy)) then varphi(xy) is equal to

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))

If int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a and int_(0)^(1)x^(2)f(x)dx=a^(2) , then : int_(0)^(1)(a-x)^(2)f(x)dx=

int_(n)^(n+1)f(x)dx=n^(2)+n then int_(-1)^(1)f(x)dx=

If int(sqrt(1+root(3)(x)))/(x^(2/3))dx=K(f(x))^(n/k)+C then

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

Let g^(prime)(x)>0a n df^(prime)(x)<0AAx in Rdot Then (f(x+1))>g(f(x-1)) f(g(x-1))>f(g(x+1)) g(f(x+1))