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Question
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Options
`e^x - (1)/(3e^(3x)) + c`
`e^x + (1)/(3e^(3x)) + c`
`e^-x + (1)/(3e^(3x)) + c`
`e^-x - (1)/(3e^(3x)) + c`
Solution
`e^x - (1)/(3e^(3x)) + c`
[ Hint : `int (e^(2x) + e^-2x)/e^x*dx`
= `int e^x*dx + int e^(-3x)*dx`
= `e^x + (e^(-3x))/((- 3)) + c`
= `e^x - (1)/(3e^(3x)) + c`].
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