Question

What is the result? ∫([1/x].dx/x^3) D=[1/2, 1]

Answer 1

$\displaystyle\int_{.5}^1\frac{1}x\frac{dx}{x^3}=\int_{.5}^1\frac{dx}{x^4}=\left[\frac{-1}{3x^3}\right]_{.5}^1=\frac{7}3$

[Your notation is not 100% clear since you're not using the math tool, so if that's not what you meant, leave a comment and I'll correct the answer.]