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Question
Integrate the following with respect to x.
`("e"^(3x) +"e"^(5x))/("e"^x + "e"^-x)`
Solution
`int ("e"^(3x) +"e"^(5x))/("e"^x + "e"^-x) "d"x = int ("e"^(3x) (1 + "e"^(2x)))/("e"^x + (1/"e"^x)) "d"x`
= `int ("e"^(3x) (1 + "e"^(2x)))/((("e"^(2x) + 1))/"e"^x) "d"x`
= `int "e"^(3x) x "e"^x "d"x`
= `int "e"^(4x) "d"x`
= `"e"^(4x)/4 + "c"`
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