Question

Write a value of $\int \tan x{\sec }^{3}xdx$.

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
$\therefore I=$ ∫ t² dt
$$\begin{gathered} =\frac{t^3}{3}+C \\ =\frac{{\sec }^{3}x}{3}+C\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\left(\mathit{\because }x=\sec \mathit{}x\right) \end{gathered}$$