Integrals — Class 12 Maths Solution

: Let $I = \int {\cfrac{{{{\sin }^3}x + {{\cos }^3}x}}{{{{\sin }^2}x{{\cos }^2}x}}} dx$

$= \int {\left( {\cfrac{{{{\sin }^3}x}}{{{{\sin }^2}x{{\cos }^2}x}} + \cfrac{{{{\cos }^3}x}}{{{{\sin }^2}x{{\cos }^2}x}}} \right)} dx$

$= \int {\left( {\sec x\tan x + \cos ec\,x\cot x} \right)dx} = \sec x - \cos ec\,x + C$