Help with some basic calc questions

Find the general antiderivative of the given function. f(y) = sin (5y) + cos (8y) The general antiderivative is F(y) = COS (5x) + sin (8x) + C.Find the general antiderivative of the given function. fly) = sec 4y The antiderivative of fly ) = sec - dy is F(y)= - tan 4x + CAssume that a is a positive constant. Find the general antiderivative of the given function. (a + 1)x f(x) = a p(a + 1jx The antiderivative of f(x) = a is F(x) =Find the general solution of the differential equation. dy = de ,120 dt The general solution is y =3 dy X dx 3 , for x 2 0 with y (0) = 2 The solution to the initial-value problem is y = for x 20