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Evaluate int(2^(x))/(sqrt(1-4^(x)))dx...

Evaluate `int(2^(x))/(sqrt(1-4^(x)))dx`

A

`sin^(-1)(2^(x))+C`

B

`(loge^(2))sin^(-1)(2^(x))+C`

C

`(loge^(2))cos^(-1)(2^(x))+C`

D

`(loge^(2))sin^(-1)(2^(x))+C`

Text Solution

Verified by Experts

The correct Answer is:
D
Put `2^(x)=t and2^(x)(log2)dx+dt`.
`:." "I=int(1)/((log2))*(1)/(sqrt(1-t^(2)))dt=(1)/((log_(e)2))sin^(-1)(t)+C`
`=(log_(2)e)sin^(-1)(2^(x))+C`.
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