Calculus of a Single Variable, Chapter 4, 4.1, Section 4.1, Problem 14

You need to evaluate the indefinite integral, hence, you need to split the integral, such that:
int (8x^3 - 9x^2 + 4) dx = int 8x^3 dx - int 9x^2 dx + int 4dx
You need to use the following formula int x^n dx = (x^(n+1))/(n+1) + c
int 8x^3 dx = (8x^(3+1))/(3 +1) + c => int 8x^3 dx = (8x^4)/(4) + c => int 8x^3 dx = (2x^4) + c
int 9x^2 dx = (9x^3)/3 + c => int 9x^2 dx = (3x^3) + c
int 4dx = 4x + c
Gathering the results yields:
int (8x^3 - 9x^2 + 4) dx = 2x^4 - 3x^3 + c
Hence, evaluating the indefinite integral, yields int (8x^3 - 9x^2 + 4) dx = 2x^4 - 3x^3 + 4x + c.