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

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

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

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

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

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

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

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

$\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x+5}{\sqrt{7}}\right) + c$

$-\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x-5}{\sqrt{7}}\right) + c$

$\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x-5}{\sqrt{7}}\right) + c$

$-\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x+5}{\sqrt{7}}\right) + c$

$\dfrac{8}{5}\log|4 + x| - \dfrac{2}{5}\log|1 - x| + c$

$2\log|4 + x| + \dfrac{2}{5}\log|1 - x| + c$

$-\log|4 + x| + \dfrac{2}{5}\log|1 - x| + c$

$-\dfrac{8}{5}\log|4 + x| - \dfrac{2}{5}\log|1 - x| + c$