\(\begin{array}{l}\rightarrow \frac{dx}{x} = -cosec^2 v dv \end{array} \) now integrating both the sides w.r.t. to x and v respectively, we get \(\begin{array}{l} \int \frac{dx}{x} = \int -cosec^2 v dv \end{array} \) \(\begin{array}{l} ln x = \frac{1}...