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Question
Integrate the following with respect to x:
`sec^2 x/5 + 18 cos2x + 10sec(5x + 3) tan(5x + 3)`
Solution
`int [sec^2 x/5 + 18 cos2x + 10sec(5x + 3) tan(5x + 3)] "d"x`
= `int sec^2 x/5 "d"x + 18 int cos 2x "d"x + 10 int sec(5x + 3) tan(5x + 3) "d"x`
= `(tan x/5)/(1/5) + 18 ((sin 2x)/2) + 10 (sec(5x + 3))/5 + "c"`
= `5 tan (x/5)/5 + 9 sin 2x + 2sec (5x + 3) + "c"`
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