Methods of Integration by Substitution

Evaluate: $\int \frac{e^{{\tan }^{-1}x}}{1+x^2}dx$

 ${\displaystyle \int \frac{dx}{\sqrt{5-4x-2x^2}}}$  is equal to:

 ${\displaystyle \int \frac{\cos \sqrt{x}}{\sqrt{x}}}dx$ is equal to:

 ${\displaystyle \int \frac{\sin \sqrt{x}}{\sqrt{x}}dx}$  is equal to

The value of  ${\displaystyle \int \sqrt{\frac{1-x}{1+x}}dx}$ would be

Evaluate  ${\displaystyle \int \frac{x^2}{x^2+6x+12}}dx.$

Evaluate the following integral $\int \frac{x^2}{\sqrt{1-x}}dx$

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

The value of  ${\displaystyle \int \left(\sqrt{\tan x}+\sqrt{\cot x}\right)dx}$ is