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Question
Integrate the following with respect to x:
x sec x tan x
Solution
`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"`
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