$\int \frac{x}{x + 2} dx$ is equal to

The antiderivative of $\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)$ equals

If $\frac{3 \pi}{4} < x < \frac{7 \pi}{4}$, then $\int \left(2^x - \sqrt{1 + \sin 2x} + \frac{1}{x^2} - \frac{1}{x}\right) dx = $

If $\int \sqrt{2} \sqrt{1 + \sin x} \, dx = -4 \cos(ax + b) + c$,then the value of $(a, b)$ is

$\int {\frac{{1 + {{\cos }^2}x}}{{{{\sin }^2}x}}} \,dx = $

The velocity of a particle at time $t$ is given by the relation $v = 6t - \frac{t^2}{6}$. The distance traveled in $3 \ s$ is,if $s = 0$ at $t = 0$.