Question

If \(\int 2^{2^{x}} \cdot 2^{x} d x=A \cdot 2^{2^{x}}+c\), then \(A=\)
(A) \(\frac{1}{\log 2}\)
(B) \(\log 2\)
(C) \((\log 2)^{2}\)
(D) \(\frac{1}{(\log 2)^{2}}\)

Answer 1

Ans: (D)
Hint \(: 2^{x}=z \Rightarrow 2^{x} d x=\frac{d z}{\ln 2}\)
$$
\Rightarrow \frac{1}{\ln 2} \int 2^{z} d z=\frac{1}{(\ln 2)^{2}} 2^{2^{x}}+c
$$

Answer 2

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Answer 3

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