1.

`int(2)/((e^(x)+e^(-x))^(2))dx` is equal toA. `(-e^(-x))/(e^(x)+e^(-x))+C`B. `-(1)/(e^(x)+e^(-x))+C`C. `-(1)/((e^(x)+1)^(2))+C`D. `(1)/(e^(x)-e^(-x))+C`

Answer» Correct Answer - a
We have `I= int(2)/((e^(x)+e^(-x))^(2))dx`
`=int (2e^(2x))/((e^(2x)+1)^(2))dx= int(1)/((e^(2x)+1)^(2))d(e^(2x)+1)`
`rArr I=-(1)/(e^(2x)+1)+C=(-e^(-x))/(e^(x)+e^(-x))+C`


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