Calculus: Early Transcendentals, Chapter 4, 4.9, Section 4.9, Problem 8

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 (x^(3.4) - 2x^(sqrt2 - 1))dx = int (x^(3.4))dx - int (2x^(sqrt2 - 1))dx
You need to use the following formula:
int x^n dx = (x^(n+1))/(n+1)
int (x^(3.4))dx = (x^(3.4+1))/(3.4+1) + c = (x^(4.4))/(4.4) + c
int (2x^(sqrt2 - 1))dx = 2*(x^(sqrt2 - 1+1))/(sqrt2 - 1+1) + c
int (2x^(sqrt2 - 1))dx = sqrt2*(x^(sqrt2)) + c
Gathering all the results yields:
int (x^(3.4) - 2x^(sqrt2 - 1))dx =(x^(4.4))/(4.4) + sqrt2*(x^(sqrt2)) + c
Hence, evaluating the most general antiderivative of the function yields F(x) = (x^(4.4))/(4.4) + sqrt2*(x^(sqrt2)) + c.