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 $A^3 =$

If $\displaystyle\int_0^a \dfrac{dx}{1 + 4x^2} = \dfrac{\pi}{8}$, then $a =$

The value of the integral $\displaystyle\int_{-\sqrt{3}}^{\sqrt{3}} \dfrac{(2x^9 + 3x^8 - 5x^7 + 9x^6 + 4x^3 - x + 3)}{x^2 + 3} \, dx$ is