Evaluate the definite integral accurate to three decimal places:

∫-1
((x-x^2)/(2*x^1/3))dx
-8

That should be x^(1/3) since x^1/3 is simply x^1, then all divided by 3,
i.e. x^1/3 = (x^1)/3 = x/3 = (1/3) x

∫₋₈⁻¹ (x − x²) / (2x^(1/3)) dx = 1/2 ∫₋₈⁻¹ (x − x²) x^(−1/3) dx
. . . . . . . . . . . . . . . . . . . . . . = 1/2 ∫₋₈⁻¹ (x^(2/3) − x^(5/3)) dx
. . . . . . . . . . . . . . . . . . . . . . = 1/2 (3/5 x^(5/3) − 3/8 x^(8/3)) |₋₈⁻¹
. . . . . . . . . . . . . . . . . . . . . . = (3/10 x^(5/3) − 3/16 x^(8/3)) |₋₈⁻¹
. . . . . . . . . . . . . . . . . . . . . . = (3/10 (−1) − 3/16 (1)) − (3/10 (−32) − 3/16 (256))
. . . . . . . . . . . . . . . . . . . . . . = −3/10 − 3/16 (1) + 48/5 + 48
. . . . . . . . . . . . . . . . . . . . . . = 4569/80
. . . . . . . . . . . . . . . . . . . . . . = 57.1125