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2-x-1-x-dx-2ln-3-ln-2-please-help-me-to-solve-for-x-




Question Number 63378 by minh2001 last updated on 03/Jul/19
∫_2 ^x (1/x)dx=2ln(3)−ln(2)  please help me to solve for x
$$\underset{\mathrm{2}} {\overset{{x}} {\int}}\frac{\mathrm{1}}{{x}}{dx}=\mathrm{2}{ln}\left(\mathrm{3}\right)−{ln}\left(\mathrm{2}\right) \\ $$$${please}\:{help}\:{me}\:{to}\:{solve}\:{for}\:{x} \\ $$
Answered by MJS last updated on 03/Jul/19
the borders must be independent of the integral variable  ∫_2 ^x (dt/t)=ln x −ln 2  ⇒ ln x =2ln 3 ⇒ x=9
$$\mathrm{the}\:\mathrm{borders}\:\mathrm{must}\:\mathrm{be}\:\mathrm{independent}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{variable} \\ $$$$\underset{\mathrm{2}} {\overset{{x}} {\int}}\frac{{dt}}{{t}}=\mathrm{ln}\:{x}\:−\mathrm{ln}\:\mathrm{2} \\ $$$$\Rightarrow\:\mathrm{ln}\:{x}\:=\mathrm{2ln}\:\mathrm{3}\:\Rightarrow\:{x}=\mathrm{9} \\ $$

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