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int (e^(x)+e^(-x))^(2)*(e^(x)-e^(-x))dx ...

`int (e^(x)+e^(-x))^(2)*(e^(x)-e^(-x))dx` is equal to

A

`e^(x)+C`

B

`(1)/(2)(e^(x)-e^(-x))^(2)+C`

C

`(1)/(2)(e^(x)+e^(-x))^(2)+C`

D

`(1)/(3)(e^(x)+e^(-x))^(3)+C`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l=int(e^(x)+e^(-x))^(2).(e^(x)-e^(-x))dx`
Put `e^(x)+e^(-x)=t rArr (e^(x)-e^(-x))dx=dt`
`therefore" "l=int t^(2)dt=(t^(3))/(3)+C=((e^(x)+e^(-x))^(3))/(3)+C`
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