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Question
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
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Solution
Let `I = int (sec^2 x)/sqrt(tan^2 x + 4) dx`
Put tan x = t
sec2 x dx = dt
Hence, `I = int dt/sqrt(t^2 + 4) dt`
`= log abs ((t + sqrt(t^2 + 4))+ C` `....[∵ int dx/sqrt (a^2 + x^2) = log |x + sqrt(x^2 + a^2)| + C]`
`= log abs (tan x + sqrt(tan^2 x + 4)) + C`
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