If a spherical balloon has a variable diameter $3x + \dfrac{9}{2}$ units, then the rate of change of its volume with respect to $x$ is

$\displaystyle\int \dfrac{30x^{14} + 15^x \log 225}{x^{15} + 15^x} \, dx =$

If $\displaystyle\int \dfrac{\sin 2x}{\sin^4 x + \cos^4 x} \, dx = f(x) + c$ where c is constant of integration, then the value of $\tan(f(x))$ is

$\displaystyle\int e^{2x} \dfrac{2(\sin 2x \cos 2x - 1)}{2 \sin^2 2x} \, dx = A \, e^{2x} \cot 2x + c$
(Where c is the constant of integration.), then $A^3 =$