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`int {(1+2 tan x(tan x + sec x))^(1//2)` dx is equal toA. `log (sec x + tan x)+c`B. `log (sec x + tanx)^(1//2) + c`C. `log sec x (sec x + tanx) + c`D. None of these |
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Answer» Correct Answer - C Let ` I = int{1 +2 tan x (tan x + sec x)}^(1//2) dx` ` = int{(1+2 tan^(2) x + 2 tan x sec x}^(1//2) dx` ` = int{sec^(2) x + tan^(2) x + 2 tan x secx}^(1//2) dx` `= int (sec x tan x) dx ` `log ( sec x + tan x) + log sec x + c` `log sec x (sec x + tan x) + c` |
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