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Examples: int sec^2x / sqrt ( 16 + tan^...

Examples: ` int sec^2x / sqrt ( 16 + tan^2x) dx`

A

`log|tanx+sqrt(tan^(2)x+16)|+C`

B

`log|x+sqrt(tan^(2)x+16)|+C`

C

`log|tan x-sqrt(tan^(2)x+16)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Put `tan x=t and sec^(2)x dx =dt . `then ,
`I=int (dt)/(sqrt(t^(2)+4^(2)))=log |t+sqrt(t^(2)+16)|=log |tan x+sqrt(tan^(2)x+16)|+C.`
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