Question Number 226936 by Estevao last updated on 19/Dec/25
Answered by Ghisom_ last updated on 19/Dec/25
$$\int\mathrm{2}^{\mathrm{ln}\:{x}} {dx}=\int{x}^{\mathrm{ln}\:\mathrm{2}} {dx}=\frac{{x}^{\mathrm{1}+\mathrm{ln}\:\mathrm{2}} }{\mathrm{1}+\mathrm{ln}\:\mathrm{2}}+{C} \\ $$
Commented by Estevao last updated on 19/Dec/25
$${Good}.\:{Demonstre} \\ $$
Commented by Ghisom_ last updated on 19/Dec/25
$${a}^{\mathrm{ln}\:{b}} =\left(\mathrm{e}^{\mathrm{ln}\:{a}} \right)^{\mathrm{ln}\:{b}} =\mathrm{e}^{\mathrm{ln}\:{a}\:\mathrm{ln}\:{b}} =\left(\mathrm{e}^{\mathrm{ln}\:{b}} \right)^{\mathrm{ln}\:{a}} ={b}^{\mathrm{ln}\:{a}} \\ $$