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Integrate the following functions (e^(2x...

Integrate the following functions `(e^(2x) -e^(-2x))/(e^(2x) + e^(-2x)`

Text Solution

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Let t = `e^(2x)+e^(2x)`. Then
dt = `(2e^(2x)-2e^(-2x))dx`
=`2(e^(2x)-e^(-2x)) dx`
`gt (e^(2x)-e^(-2x)) dx = (dt)/2`
therefore `int (e^(2x)-e^(-2x))/(e^(2x)+e^(-2x)) dx = int 1/t (dt)/2 = 1/2 log|t|+c`
=`1/2 log|e^(2x)+e^(-2x)|+c`
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