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Question
`int dx/(e^x + e^(-x))` is equal to ______.
Options
tan-1(ex) + C
tan-1(e-x) + C
log (ex – e-x) + C
log (ex + e-x) + C
Solution
`int dx/(e^x + e^(-x))` is equal to tan-1(ex) + C.
Explanation:
Let I = `int dx/(e^x + e^(- x))`
`= int dx/(e^x + 1/e^x)`
`= int (e^x dx)/(e^(2x) + 1)`
Put ex = t
ex dx = dt
`therefore I = int dt/(t^2 + 1) = tan^-1 t + C`
`= tan^-1 (e^x) + C`
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