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int(2^x)/(sqrt(1-4^x))dx=ksin^(- 1)2^x+c...

`int(2^x)/(sqrt(1-4^x))dx=ksin^(- 1)2^x+c`, then k =

A

`sin^(-1)(2^(x))log2+C`

B

`(sin^(-1)(2^(x)))/(log2)+C`

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `2^(x)=t and 2^(x) log 2dx=dt.`
`therefore I=(1)/(log2)int(dt)/(sqrt(1-t^(2)))=(1)/(log2)sin^(-1)t+C=(1)/((log2))sin^(-1)(2^(x))+C.`
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