$2 \tan x+\log (1+\tan x)+c$

$\tan x-2 \log (1+\tan x)+c$

$2 \log (1+\tan x)+\tan x+c$

$2 \log (1+\tan x)-\tan x+c$

$\frac{x \operatorname{cosec} x}{x \cos x-\sin x}+\cot x+c$

$\frac{x \operatorname{cosec} x}{x \cos x-\sin x}-\cot x+c$

$\frac{x \operatorname{cosec} x}{x \cos +\sin x}+\cot x+c$

$\frac{x}{x \cos x-\sin x}-\cot x+c$

$\frac{4}{\sqrt{x^5+1}}+c$

$4 x^4\left(x^5+1\right)^{4 / 3}+0$

$=\frac{\left(x^3+1\right)^{4 / 3}}{4 x^4}+c$

$-\frac{\left(x^5+1\right)^{45}}{4 x^5}+c$

$\frac{1}{2} \sqrt{x^2+x+1}+\frac{1}{2} \cosh ^{-1}\left(\frac{x+2}{\sqrt{3}}\right)+c$

$\frac{1}{2} \sqrt{x^2+x+1}+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$

$\sqrt{x^2+x+1}+\frac{2}{\sqrt{3}} \log \left|x^2+x+1\right|+c$

$\sqrt{x^2+x+1}+\frac{1}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$