Question

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

• A. $\frac{1}{log2}$
• B. $log2$
• C. ${\left(log2\right)}^2$
• D. $\frac{1}{{\left(log2\right)}^2}$

Answer 1

Answer: (D)

$2^x=z\Rightarrow 2^{x}dx=\frac{dz}{\ell n2}$
$\Rightarrow \frac{1}{\ell n2}\int 2^{z}dz=\frac{1}{{\left(\ell n2\right)}^2}{2}^x+c$