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int(e^x)/(e^(2x)+4)dx...

`int(e^x)/(e^(2x)+4)dx`

A

`3+2pi`

B

`4-pi`

C

`2+pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Putting `e^(x)-1=t^(2)` in the given integral, we have
`int_(0)^(log5) (e^(x)sqrt(e^(x)-1))/(e^(x)+3) dx=2 int_(0)^(2) (t^(2))/(t^(2)+4) dt =2 (int_(0)^(2) 1 dt -4int_(0)^(2) (dt)/(t^(2)+4))`
`=2[(t-2 tan^(-1)(t/2))_(0)^(2)]`
`=2[(2-2xxpi//4)]=4-pi`
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