GIVEN integration is of the form \(\smallint {\rm{g}}\left( {{\rm{f}}\left( {\rm{x}} \right)} \right){\rm{f'}}\left( {\rm{x}} \right){\rm{dx}}\) where g(x) and f(x) are both differentiable functions then we substitute f(x) = u which implies that f’ (x)dx = DU.Therefore, the integral becomes \(\smallint {\rm{g}}\left( {\rm{u}} \right){\rm{du}}\) which can be solved by GENERAL FORMULAS. SOLUTION:In the given integral substitute \(\sin {\rm{x}} = {\rm{u}}\) therefore \(\cos {\rm{x\;dx}} = {\rm{du}}\).Therefore, the given integral becomes,\(\smallint {{\rm{e}}^{\rm{u}}}{\rm{du}} = {{\rm{e}}^{\rm{u}}} + {\rm{C}}\)Now resubstitute \({\rm{u}} = \sin {\rm{x}}\).Therefore, \(\smallint \cos {\rm{x}}{{\rm{e}}^{\sin {\rm{x}}}}{\rm{dx}} = {{\rm{e}}^{\sin {\rm{x}}}} + {\rm{C}}\).