Consider the function f(x)=x^4+2sqrt x. Let F(x) be the anti-derivative of f(x) with F(1)=-9.

Question

Then F(x)= ?

Answer 1

This is just like your other problem.
f(x) = x^4 + 2√x
F(x) = 1/5 x^5 + 2/3 x^(3/2) + C
Now use F(1) = -9 to find C
1/5 * 1 + 2/3 * 1 + C = -9
and finish it off.

Answer 2

oops.
F(x) = 1/5 x^5 + 2 * 2/3 x^(3/2) + C
1/5 * 1 + 2 * 2/3 * 1 + C = -9

Answer 3

F(x)=-10/x+2/5x^5+48/5