Find the most general antiderivative?

Question

Find the most general antiderivative of f(x)=4sqrt(x)-5/x^6. Check your answer by differentiation.

Use C to denote an arbitrary constant.

Answer 1

I = ∫ 4.x^(1/2) - 5.x^(-6) dx
I = [4.x^(3/2)] /(3/2) + x^(-5) + C
I = (8/3).x^(3/2) + 1/x^5 + C

Check
y = (8/3).x^(3/2) + x^(-5) + C
dy/dx = 4.x^(1/2) - 5/x^(6) as required

Answer 2

F(x) = 6√x³ + 1/x^5 + C
where F(x) is the antiderivitive of f(x)