Question

Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]

Answer 1

Let I=\[\int\]tan x . sec³x dx

      =\[\int\]sec² x . sec x tan x dx

Let sec x = t
⇒ sec x tan x dx = dt

\[\therefore I =  ∫ t^2 dt      \]

\[= \frac{t^3}{3} + C\]

\[ = \frac{\sec^3 x}{3} + C \left( \because x = \sec x \right)\]