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inte^(x)sqrt(e^(2x)+4)dx=?...

`inte^(x)sqrt(e^(2x)+4)dx=?`

A

`(1)/(2)e^(x)sqrt(e^(2x)+4)-2log |e^(x)+sqrt(e^(2x)+4)|+C`

B

`(1)/(2)e^(x)sqrt(e^(2x)+4)+2log |e^(x)+sqrt(e^(2x)+4)|+C`

C

` e^(x)sqrt(e^(2x)+4)+(1)/(2)log |e^(x)+sqrt(e^(2x)+4)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `e^(x)=t and e^(x)dx=dt.`then ,
`I=int sqrt(t^(2)+4)dt=int sqrt(t^(2)+2^(2))dt =(t)/(2)sqrt(t^(2)+4)+(4)/(2)log |t+sqrt(t^(2)+4)|+C`
`=(1)/(2) e^(x)sqrt(e^(2x)+4)+2log |e^(x)+sqrt(e^(2x)+4)|+C.`
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