What is the function y if dy/dx=13x^14+4x^5-2x ?

To determine a function, when knowing it's derivative,
we'll have to determine te indefinite integral of the expression of
derivative.

We'll determine the indefinite integral of
f'(x)=13x^14+4x^5-2x.

Int f'(x)dx = f(x) +
C

Int (13x^14+4x^5-2x)dx

Int (13x^14+4x^5-2x)dx = Int (13x^14)dx + Int
(4x^5)dx - Int (2x)dx

Int (13x^14)dx = 13*x^(14+1)/(14+1)
+ C

Int (13x^14)dx = 13x^15/15 + C
(1)

Int (4x^5)dx = 4*x^(5+1)/(5+1) +
C

Int (4x^5)dx = 4*x^6/6 + C
(2)

Int 2xdx = 2*x^2/2 + C

Int
2xdx = x^2 + C (3)

We'll add:
(1)+(2)-(3)

Int (13x^14+4x^5-2x)dx = 13x^15/15 + 4*x^6/6 -
x^2 + C

So, the function
is:

y = 13x^15/15 + 4*x^6/6 -
x^2

Notes