`int\ {f(x) g^(prime prime)(x)-f^(prime prime) g(x)} \ dx` equals

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

Suppose that f(x) isa quadratic expresson positive for all real xdot If g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x), then for any real x

Suppose that f(x) isa quadratic expresson positive for all real xdot If g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x), then for any real x

A nonzero polynomial with real coefficient has the property that f(x)=f^(prime)(x)dot f^(prime prime)(x)dot If a is the leading coefficient of f(x), then the value of 1/(2a) is____

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

Suppose that f(x) is a quadratic expresson positive for all real x If g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x), then for any real x (where f^(prime)(x) and f^(primeprime)(x) represent 1st and 2nd derivative, respectively). (a) g(x) 0 (c). g(x)=0 (d). g(x)geq0

Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f^(prime_ prime)(x)-2f^(prime)(x)-15f(x)=0 for all xdot Then the value of (|a b|)/3 is ___

Let the function f satisfies f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) foe all x and f(0)=3 The value of f(x).f^(prime)(-x)=f(-x).f^(prime)(x) for all x, is

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,