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Question
Evaluate : `int (sec^2 x)/(tan^2 x + 4)` dx
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Solution
Let I = `int (sec^2 x)/(tan^2 x + 4)` dx
Put tan x = t
`sec^2 x dx = dt`
I = `int dt/[ t^2 + 2^2 ]`
I = `1/2 tan^-1 (t/2) + c`
`( ∴ int 1/[ x^2 + a^2] dx = 1/a tan^-1 x/a + c)`
I = `1/2 tan^-1(tan x/2) + c`
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