Calculus: Early Transcendentals, Chapter 4, 4.9, Section 4.9, Problem 7

The most general antiderivative F(x) of the function f(x) can be found using the following relation:
int f(x)dx = F(x) + c
int (7x^(2/5) + 8x^(-4/5))dx = int (7x^(2/5))dx + int (8x^(-4/5))dx
You need to use the following formulas:
int x^n dx = (x^(n+1))/(n+1)
int x^(-n)dx = (x^(-n+1))/(-n+1)
int (7x^(2/5))dx = (x^(2/5+1))/(2/5+1) = (5/7)*x^(7/5) + c
int (8x^(-4/5))dx = (x^(-4/5+1))/(-4/5+1) = 5*x^(1/5) + c
Gathering all the results yields:
int (7x^(2/5) + 8x^(-4/5))dx = (5/7)*x^(7/5) + 5*x^(1/5) + c
Hence, evaluating the most general antiderivative of the function yields F(x) = (5/7)*x^(7/5) + 5*x^(1/5) + c.