$x^5\left[\frac{1}{5}(\log x)^3-\frac{4}{25}(\log x)^2-\frac{9}{125} \log x-\frac{8}{125}\right]+C$

$x^5\left[\frac{1}{5}(\log x)^3+\frac{3}{25}(\log x)^2-\frac{6}{125} \log x-\frac{6}{125}\right]+C$

$2 \log \left|\frac{\cos x-2}{\cos x-1}\right|+C$

$\log \left(\frac{(\cos x-2)^2}{(\cos x-1)^4}\right)+C$

$\log \left(\frac{(\cos x-2)^2}{|\cos x-1|}\right)+C$

$\log \left(\frac{(\cos x-2)^4}{(\cos x-1)^2}\right)+C$

$(3 \sqrt{2}, \sin x-\cos x)$

$(2 \sqrt{2}, \sin x-\cos x)$

$\left(\frac{\sqrt{2}}{3}, \sin x-\cos x\right)$

$\left(\frac{3}{\sqrt{2}}, \sin x+\cos x\right)$