Mathematics

Solve: $$\displaystyle \int { \dfrac {dx  }{ e^x+e^{-x} }  } $$


SOLUTION
$$ \displaystyle \int \frac{dx}{e^{x}+e^{-x}} $$

$$ \displaystyle \Rightarrow \int \frac{e^{x}}{e^{2x}+1}dx\Rightarrow \int \frac{d(e^{x})}{(e^{x})^{2}+1} $$

$$ \displaystyle \Rightarrow \int \frac{dz}{z^{2}+1}$$   [let z = $$ e^{x} $$ ]

$$ \displaystyle \Rightarrow tan^{-1}(z)+c $$    [c is arbitrary constant]

$$ \displaystyle \Rightarrow tan^{-1}(e^{x})+c $$ 

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Subjective Medium Published on 17th 09, 2020
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