यदि `int (2^(x))/(sqrt(1-4^(x)))dx=k sin^(-1)2^(x)` है, तो K का मान है

Options

A. `log 2`
B. `(1)/(2)log2`
C. `(1)/(2)`
D. `(1)/(log2)`

Answer

D

Explanation

दिया है,
`int (2^(x))/(sqrt(1-4x^(2)))dx=int=(2x^(2))/(sqrt(1-(2^(x))^(2)))dx`
माना `2^(x)=t rArr x log 2 log=t`
`:. (dt)/(dx)xx(1)/(t)= log 2 rArr t dx=(dt)/(log 2)`
`:. int (dt)/(log2sqrt((1-t^(2))))=(1)/(log2)int(1)/(sqrt(1-t^(2)))`
`rArr k sin^(-1)2^(x)+C=(1)/(log2)sin^(-1)2^(x)+C`
`:. k=(1)/(log2)` [तुलना करने पर]