Evaluate:

$\int \frac{(1+\tan x)}{(1-\tan x)}dx$

Evaluate:

$\int \frac{(1-\cot x)}{(1+\cot x)}dx$

Evaluate:

$\int \frac{(1+\cot x)}{(x+\mathrm{logsin}x)}dx$

Evaluate:

$\int \frac{(1-\sin 2x)}{\left(x+{\cos }^{2}x\right)}dx$

Evaluate:

$\int \frac{{\sec }^2\left(\log x\right)}{x}dx$

Evaluate:

$\int \frac{\sin \left(2{\tan }^{-1}x\right)}{\left(1+x^2\right)}dx$

Evaluate:

$\int \frac{\tan x {\sec }^{2}x}{\left(1-{\tan }^{2}x\right)}dx$

Evaluate:

$\int \frac{\left(x^4+1\right)}{\left(x^2+1\right)}dx$

Evaluate:

$\int {\tan }^{-1}\sqrt{\frac{1-\sin x}{1+\sin x}}dx$