Write a value of `inte^(a x)\ {a\ f\ (x)+f^(prime)(x)}\ dx`

Write a value of int e^(ax){af(x)+f'(x)}dx

If intg(x)dx=g(x) , then evaluate intg(x){f(x)+f^(prime)(x)}dx

If intg(x)dx=g(x) , then evaluate intg(x){f(x)+f^(prime)(x)}dx

Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C

Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C

Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C

If f(x) attains a local minimum at x=c , then write the values of f^(prime)(c) and f^(prime)prime(c) .

Write the value of int({f(x)phi(x)+f(x)phi(x)}{logphi(x)+iogf(x)})/(f(x)phi(x))dx.

Suppose that f,f^prime and f prime prime are continuous on [0, ln 2] and that f (0) = 0, f prime(0) = 3, f(In 2) = 6,f prime(ln 2) = 4 and int_0^(ln 2) e^(-2x)*f(x)dx=3. Find the value of int_0^(ln2) e^(-2x)*f prime prime(x)dx.

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