For a real number ' $a$ ', if a real valued function $f(x)=4 x^3+a x^2+3 x-2$ is monotonic in its domain, then the range of ' $a$ ' is

If the point $P\left(x_1, y_1\right)$ lying on the curve $y=x^2-x+1$ is the closest point to the line $y=x-3$, then the perpendicular distance from $P$ to the line $3 x+4 y-2=0$ is

$$ \int \frac{3^x(x \log 3-1)}{x^2} d x= $$

If $\frac{5 \pi}{4} < x < \frac{7 \pi}{4}$, then $\int \sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}} d x=$