Question

18. sec x (sec x + tan x) a

Answer 1

The integral is,

y=  ∫ sec x( sec x + tan x ) dx

Here, y is the solution of integral.

Use the formulas of ∫ sec 2 xdx=tan x +Aand ∫ secx tanxdx=secx+E, where A and E are constants.

y=  ∫ secx( secx + tanx ) dx = ∫ ( sec 2 x + secx tanx ) dx = ∫ sec 2 xdx+ ∫ ( secx tanx ) dx =tanx+secx+D

Here, D is constant.

Thus, the solution of integral is tanx+secx+D.