Question

If $\int 2^{2^x}.2^{x} dx = A.2^{2^x} + c, $ then A =

• A. $\frac{1}{log\,2}$
• B. $log\,2$
• C. $\left(log\,2\right)^{2}$
• D. $\frac{1}{\left(log\,2\right)^{2}}$

Answer 1

Answer: (D)

$2^{x} = z \Rightarrow 2^{x} dx = \frac{dz}{\ell n\,2}$
$\Rightarrow \frac{1}{\ell n\,2}\int2^{z} dz = \frac{1}{\left(\ell n\,2\right)^{2}}2^{x} + c$