The value of $\int \frac{\mathrm{d} x}{7+6 x-x^2}$ is equal to

If $\int \frac{\mathrm{d} x}{1+3 \sin ^2 x}=\frac{1}{2} \tan ^{-1}(\mathrm{f}(x))+\mathrm{c}$, where c is a constant of integration, then $\mathrm{f}(x)$ is equal to

The value of $\int \frac{\sec x \cdot \tan x}{9-16 \tan ^2 x} \mathrm{dx}$ is equal to

The value of $\int \frac{d x}{5+4 \sin x}$ is equal to