# Determine the function f(x) if f'(x)=15x^14+36x^5-2x^3?

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The derivative of f(x) is given, f'(x) = 15x^14+36x^5-2x^3

To find f(x) we integrate f'(x)

Int[f'(x) dx]

=> Int [ 15x^14+36x^5-2x^3 dx]

=> 15*x^15 / 15 + 36*x^6 / 6 - 2*x^4 / 4

=> x^15 + 6x^6 - (x^4)/2 + C

The function f(x) = x^15 + 6x^6 - (x^4)/2 + C

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the primitive of the original function, we'll have to determine te indefinite integral of the expression of derivative.

We'll determine the indefinite integral of

f'(x)=15x^14+36x^5-2x^3

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

Int (15x^14+36x^5-2x^3)dx

We'll apply the property of the indefinite integral, to be additive:

Int (15x^14+36x^5-2x^3)dx = Int (15x^14)dx + Int (36x^5)dx - Int (2x^3)dx

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

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

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

Int (36x^5)dx = 36*x^(5+1)/(5+1) + C

Int (36x^5)dx = 36*x^6/6 + C

Int (36x^5)dx = 6*x^6 + C (2)

Int 2x^3dx = 2*x^4/4 + C

Int 2xdx = x^4/2 + C (3)