Mathematics

If $$\displaystyle\int 2^{2x}\cdot 2^xdx=A\cdot 2^{2^x}+c$$, then $$A=?$$


ANSWER

$$\dfrac{1}{(log 2)^2}$$


SOLUTION
$$2^x=z\Rightarrow 2^xdx=\dfrac{dz}{ln 2}$$

$$\Rightarrow \dfrac{1}{ln 2}\displaystyle\int 2^zdz=\dfrac{1}{(ln 2)^2}2^{2^x}+c$$.
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Single Correct Medium Published on 17th 09, 2020
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