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Evaluate: int1/(e^x+e^(-x))\ dx...

Evaluate: `int1/(e^x+e^(-x))\ dx`

Text Solution

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`int frac{d x}{e^{x}+e^{-x}} `
`=int frac{d x}{e^{x}+frac{1}{e^{x}}} `
`=int frac{e^{x} d x}{e^{2 x}+1} `
`text { let } e^{x}=t `
`Rightarrow e^{x} d x=d t `
Now, `int frac{e^{x} d x}{e^{2 x}+1} `
`=int frac{d t}{1+t^{2}} `
`=tan ^{-1}(t)+c `
...
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