$\int\dfrac{1}{\sqrt{2x - x^2}}dx =$

$\int(x^{21} + x^6 + x^3)(2x^{18} + 7x^3 + 14)^{\frac{1}{3}}\ dx =$

If $f(x) = \int \dfrac{x}{(x^2 + 4)(x^2 + 9)}\, dx$ and $f(0) = \dfrac{1}{5}\log\left(\dfrac{2}{3}\right)$, then $f(1) = $

$\int \dfrac{x^4(x^{10} - 1)}{x^{20} + 3x^{10} + 1}\, dx = \cdots$