Manu Chauhan

We will be applying Integration by Parts,

Consider ∫ logx dx = ∫ logx.1 dx where f(x) = logx , g(x) = 1 we know, ∫ f(x) g(x) dx =  f(x) ∫ g(x) dx - ∫f'(x) (∫ g(x) dx) dx Applying the above formula we get, ∫ logx.1 dx = logx .x - ∫ 1/x (x) dx +c = xlogx - ∫ dx +c = xlogx - x +c = x(logx -1) +c, Where c is the constanct of Integration.

Ions are the atoms or molecules having a charge on it, which is due to the gain or loss of electrons to form an ionic bond. The ions with opposite charges suffer opposite charge attraction, i.e. the electrostatic attraction and form the compound based on ionic bond. The ions are of two types: Cation: Positively charged atom, i.e. formed by loss of extra electron in the outermost shell of an atom which is loosely bound or have a least nuclear charge. E.g. Na+, Ca2+, Mg2+, etc.. Anion: Negatively charged atom, i.e. formed by the gain of one or more electron to complete the octet of the outermost shell of the atom. e.g. Cl-, Br-, SO2-, etc.

Position vector specifies the position of a with object respect to an origin ( chosen as a reference point ). At the same time, the displacement vector is the change in the position vector of two points and is ideally not dependent on the origin.