$$ \int_0^1 \log \left(\frac{1}{x}-1\right) d x= $$

If the foot of the perpendicular drawn from the origin to a plane is $\mathrm{P}(2,-1,4)$, then the equation of the plane is

$$ \int \frac{(5 \sin \theta-2) \cos \theta}{\left(5-\cos ^2 \theta-4 \sin \theta\right)} d \theta= $$

Number of switches in alternative equivalent simple circuit for the circuit is (are)