Calculus: Early Transcendentals, Chapter 5, 5.4, Section 5.4, Problem 31

You need to evaluate the definite integral, such that:
int_0^1 x(root(3) x + root(4) x)dx = int_0^1 (x^(1+1/3) + x^(1+1/4))dx
int_0^1 x(root(3) x + root(4) x)dx = ((x^(2+1/3))/(2+1/3) + (x^(2+1/4))/(2+1/4))|_0^1
int_0^1 x(root(3) x + root(4) x)dx = ((3/7)x^2root(3)x + (4/9)x^2root(4)x)|_0^1
int_0^1 x(root(3) x + root(4) x)dx = 3/7 + 4/9
int_0^1 x(root(3) x + root(4) x)dx = 55/63
Hence, evaluating the definite integral yields
int_0^1 x(root(3) x + root(4) x)dx = 55/63.