If f(x) = 5x^4 - 4x - 3/x. F(x) = integral f(x), find F(1)= 0 find f(x)

f(x) = 5x^4-4x-3/x.

To find
F(1) = 0

Solution:

F(x) =
Intf(x) dx = Int {5x^4-4x-3/x} dx.

We use Int x^n dx =
(x^(n+1))/n. And Int dx/x = lnx

F(x) = (5x^5)/5 -(4x^2)/2
-3lnx + C, where C  is constant

F(x) = x^5 -2x^2 -3lnx +
1.

Put  x =1

Put F(1) =  1^5
-2*1^2 - 3ln(1) + C

0 = 1-2-3*0 +C, as  F(1) = 0 by data . 
ln(1) = 0.

0 = -1+C

C=
1.

Therefore F(x) = x^5-2x^2-3/nx