Integrate with respect to $x:$$\int \left(\frac{x}{x^2+1}\right)dx$

Integrate with respect to $x:$$\int {\sec }^{2}x\tan xdx$

Integrate with respect to $x:$$\int \left(\frac{1-\sin x}{x+\cos x}\right)dx$.

Integrate with respect to $x:$$\int \left(\frac{e^{2x}}{e^{2x}-2}\right)dx$

Integrate with respect to $x:$$\int \left\{\frac{\sec x}{\ln \left(\sec x+\tan x\right)}\right\}dx$.

Integrate with respect to $x:$$\int \left(\frac{x}{\sqrt{x+2}}\right)dx$.

Integrate with respect to $x:$$\int {\left(e^x+\frac{1}{e^x}\right)}^{2}dx$