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

1.	Evaluate `int(2^(x))/(sqrt(1-4^(x)))dx`
Answer» Putting `2^(x)=t and(2^(x)log2)dx=dt` , we get `int(2^(x))/(sqrt(1-4^(x)))dx=(1)/((log2))int(dt)/(sqrt(1-t^(2)))` `=(1)/((log2))sin^(-1)t+C=(1)/((log2))*sin^(-1)(2^(x))+C`.

Discussion

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