$y = 0$

$y = \pm\sqrt{3}$

$y = \dfrac{1}{2}$

$y = \pm 3$

$k < 1$

$k > 1$

$k < \sqrt{2}$

$k > \sqrt{2}$

$\dfrac{1}{4\sqrt{2}}\log\left|\dfrac{1 + \sqrt{2}\sin x}{1 - \sqrt{2}\sin x}\right| + \dfrac{1}{4}\log|\sec x + \tan x| + c$

$\dfrac{1}{4\sqrt{2}}\log\left|\dfrac{1 + \sqrt{2}\sin x}{1 - \sqrt{2}\sin x}\right| - \dfrac{1}{4}\log|\sec x + \tan x| + c$

$\dfrac{1}{4\sqrt{2}}\log\left|\dfrac{1 - \sqrt{2}\sin x}{1 + \sqrt{2}\sin x}\right| + \dfrac{1}{4}\log|\sec x + \tan x| + c$

$\dfrac{1}{4\sqrt{2}}\log\left|\dfrac{1 - \sqrt{2}\sin x}{1 + \sqrt{2}\sin x}\right| - \dfrac{1}{4}\log|\sec x + \tan x| + c$

$\dfrac{1}{\log 2}\left[\dfrac{2^x}{2}\sqrt{4^x + 4} + 2\log|2^x + \sqrt{4^x + 4}|\right] + c$

$\dfrac{2^x}{2}\sqrt{4^x + 4} + 2\log|2^x + \sqrt{4^x + 4}| + c$

$\dfrac{1}{\log 2}\left[\dfrac{2^x}{2}\sqrt{4^x + 4} + \log|2^x + \sqrt{4^x + 4}|\right] + c$

$\left[\dfrac{2^x}{\log 4}\sqrt{4^x + 4} + \log|2^x + \sqrt{4^x + 4}|\right] + c$