The value of $\int \frac{\sin x}{\cos^2 x} \, dx$ is

If $\int(1-\cos x) \operatorname{cosec}^2 x \, dx = f(x) + c$,then $f(x)$ is equal to

$\int {\frac{{dx}}{{\sin x - \cos x + \sqrt 2 }}} $ equals

Find an anti-derivative for the following function using the method of inspection:
$\cos 2x$

The velocity of a particle at time $t$ is given by the relation $v = 6t - \frac{t^2}{6}$. Its displacement $S$ is zero at $t = 0$,then the distance travelled in $3 \text{ s}$ is

$\int e^{-x \log 2} 2^x dx =$