1.

The value of the integral `int(dx)/((e^(x)+e^(-x))^2)` isA. `(1)/(2)(e^(2x)+1)+C`B. `(1)/(2)(e^(-2x)+1)+C`C. `-(1)/(2)(e^(2x)+1)^(-1)+C`D. `(1)/(4)(e^(2x)-1)+C`

Answer» Correct Answer - C
Let `l=int(dx)/((e^(x)+e^(-x))^(2))=int(e^(2x)dx)/((e^(2x)+1)^(2))`
Put `e^(2x)+1-z rArr 2e^(2x)dx=dz`
`therefore" "i=(1)/(2)int(dz)/(z^(2))=-(1)/(2z)+C`
`=-(1)/(2(e^(2x)+1))+C`
`=-(1)/(2)(e^(2x)+1)^(-1)+C`


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