Question

Integrate the following with respect to x:

x sec x tan x

Answer 1

`int x sec x tan x  "d"x`

u = x

u’ = 1 

u” = 0

dv = sec x tan x dx 

v = `int sec x tan x  "d"x` = sec x

v₁ = `int "v"  "d"x`

= `int sec x  "d"x`

= `log |sec x + tan x|`

v₂ = `int "v"_1  "d"x`

= `int log |sec x + tan x|  "d"x`

`int "u"  "dv"` = uv – u’v₁ + u”v₂ – u”’v₃ + ………….

`int x sec x tan x  "d"x = x sec x – 1 × log |sec x + tan x| + 0 xx int  log |x sec x tan x| + "c"`

`int x sec x tan x  "d"x = x sec x – log |sec x + tan x| + "c"`