The derivative of a function f with respect to x is given by \(f'(x) = 3x^{2} - \frac{4}{x^{5}}\). If \(f(1) = 4\), find f(x).
Simplify \((216)^{-\frac{2}{3}} \times (0.16)^{-\frac{3}{2}}\)
Given that \(\log_{3}(x - y) = 1\) and \(\log_{3}(2x + y) = 2\), find the value of x.
If \(\frac{^{8}P_{x}}{^{8}C_{x}} = 6\), find the value of x.
Evaluate \(\int_{1}^{2} [\frac{x^{3} - 1}{x^{2}}] \mathrm {d} x\).
