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int sec^(3) x dx...

`int sec^(3) x dx`

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`"Let I "= int sec^(3) d dx`
`= int sec^(2) x.sec x dx`
` =sec ^(2) x dx - int {(d)/(dx) sec. x int sec^(2) x dx } dx`
`"(Tanking sec x as 1st function)"`
`= "sec x . tan x "- int " sec x tan x . tan x dx "`
`= " sec x tan x . -" int " sec x . "(sec^(2) x - 1) dx`
`=" sec x tan x - " int sec^(3) " x dx + " int "sec + dx "`
` rArr " " I = sec x tan x - I + log | sec x + tan x | " C_(1)`
` rarr " "2I =sec x tan x + log | sec x + tan x| +"c_(1)`
` rArr I =(1)/(2) "[sec x tan x + log | sec x + tan x |]"+c`
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