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Question
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Solution
Let I = `int "e"^x (tan x + log sec x) "d"x`
Take f(x) = log sec x
f'(x) = `1/sec x sec x tan x`
f'(x) = tan x
`[int"e"^x ["f"(x) + "f"(x)] "d"x = "e"^x"f"(x) + "c"]`
∴ I = ex log |sec x| + c
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