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Question
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Solution
`I = int sec^2 x /sqrt(tan^2 x+4) dx.`
`"Let" tan x = t`
`sec^2 xdx = dt`
So, `I = int dt/sqrt(t^2 + 4)`
or, `I = int dt/sqrt(t^2 + 2^2)`
Since, we Know
`int dx/sqrt(x^2 + a^2) = "In" |x + sqrt(a^2 + x^2)| + "C"`
`I = "In" |t + sqrt(t^2 + 4)| + "C"`
`i.e`
`I = "In"|tanx + sqrt(tan^2 x + 4)| + "C"`
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