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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large\frac {e^{2x}+e^{-2x}}{e^{2x}-e^{-2x}}$$dx$

\[\begin {array} {1 1} (a)\;\log (e^{2x}-e^{-2x})+c \\ (b)\;\log (e^{2x}+e^{-2x})+c \\ (c)\;\log (e^{2x}-e^{-2x})^{1/2}+c \\ (d)\;None \end {array}\]
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1 Answer

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$e^{2x}-e^{-2x}=t$
=> $ 2[e^{2x}+e^{-2x}]dx=dt$
=> $\int \large\frac{dt}{2t}$
$\large\frac{1}{2} $$\log (e^{2x}-e^{-2x})+c$
Hence c is the correct answer.
answered Dec 19, 2013 by meena.p
 
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