Find the limit of $x^{2x}$ as $x$ approaches 0

Find the integral

$\int\left(dx\div x^2\sqrt{9-x^2}\right)$

Find the integral

$\int\frac{x^2dx}{\left(9-x^2\right)^{\frac{3}{2}}}$

Find the integral

$\int\frac{dx}{x\sqrt{x^{2}+36}}$

Find the integral

$\int\frac{\left(x^2-16\right)^{\frac{3}{2}}}{x^3}dx$

Find the integral

$\int\frac{dx}{\sqrt{25-9x^2}}$

Find the integral

$\int\:\frac{x}{\sqrt{2x-5}}dx$

Find the integral

$\int\frac{x+6}{\sqrt{x}}dx$