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please solve it ∫[x^(x/2) +e^(xlnx) +(((Π+(√x)ln(x))^2 )/(2ln2(√(x−e^x sin x))))]^2 dx=?

$${please}\:{solve}\:{it} \\ $$$$\int\left[{x}^{\frac{{x}}{\mathrm{2}}} +{e}^{{xlnx}} +\frac{\left(\Pi+\sqrt{{x}}{ln}\left({x}\right)\right)^{\mathrm{2}} }{\mathrm{2}{ln}\mathrm{2}\sqrt{{x}−{e}^{{x}} \mathrm{sin}\:{x}}}\right]^{\mathrm{2}} {dx}=? \\ $$

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if p=(x^2 /(x−2))−(x/(1+(2/x)))−(4/(1+(4/x^2 ))) and x−(4/x)=2 then show that (((32)/p))^2 =80

$${if}\:{p}=\frac{{x}^{\mathrm{2}} }{{x}−\mathrm{2}}−\frac{{x}}{\mathrm{1}+\frac{\mathrm{2}}{{x}}}−\frac{\mathrm{4}}{\mathrm{1}+\frac{\mathrm{4}}{{x}^{\mathrm{2}} }}\:\:\:{and}\:{x}−\frac{\mathrm{4}}{{x}}=\mathrm{2} \\ $$$${then}\:{show}\:{that}\:\:\left(\frac{\mathrm{32}}{{p}}\right)^{\mathrm{2}} =\mathrm{80} \\ $$

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14∫(1/(x[ln(x)]^3 )) d(x)

$$\mathrm{14}\int\frac{\mathrm{1}}{\mathrm{x}\left[\mathrm{ln}\left(\mathrm{x}\right)\right]^{\mathrm{3}} \:}\:\:\mathrm{d}\left(\mathrm{x}\right) \\ $$

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A two digit number (AB)_(10) (AB)_(10) −A^B =(BA)_(10) Find the number. There is a poem. Having arrived at the age of (BA)_(10) .

$${A}\:{two}\:{digit}\:{number}\:\:\left({AB}\right)_{\mathrm{10}} \\ $$$$\left({AB}\right)_{\mathrm{10}} −{A}^{{B}} =\left({BA}\right)_{\mathrm{10}} \\ $$$${Find}\:{the}\:{number}.\:{There}\:{is}\:{a}\:{poem}. \\ $$$${Having}\:{arrived}\:{at}\:{the}\:{age}\:{of}\:\left({BA}\right)_{\mathrm{10}} . \\ $$

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very old q Q.2

$${very}\:{old}\:{q}\:{Q}.\mathrm{2} \\ $$

Question Number 203035 Answers: 0 Comments: 3

e=2 Proof: Let x=((e+2)/2) 2x=e+2 2x(e−2)=(e+2)(e−2) 2ex−4x=e^2 −4 −4x+4=−2ex+e^2 x^2 −4x+4=x^2 −2ex+e^2 (x−2)^2 =(x−e)^2 (√((x−2)^2 ))=(√((x−e)^2 )) x−2=x−e −2=−e e=2

$$\mathrm{e}=\mathrm{2} \\ $$$$\mathrm{Proof}: \\ $$$$\mathrm{Let}\:{x}=\frac{\mathrm{e}+\mathrm{2}}{\mathrm{2}} \\ $$$$\mathrm{2}{x}=\mathrm{e}+\mathrm{2} \\ $$$$\mathrm{2}{x}\left(\mathrm{e}−\mathrm{2}\right)=\left(\mathrm{e}+\mathrm{2}\right)\left(\mathrm{e}−\mathrm{2}\right) \\ $$$$\mathrm{2e}{x}−\mathrm{4}{x}=\mathrm{e}^{\mathrm{2}} −\mathrm{4} \\ $$$$−\mathrm{4}{x}+\mathrm{4}=−\mathrm{2e}{x}+\mathrm{e}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}={x}^{\mathrm{2}} −\mathrm{2e}{x}+\mathrm{e}^{\mathrm{2}} \\ $$$$\left({x}−\mathrm{2}\right)^{\mathrm{2}} =\left({x}−\mathrm{e}\right)^{\mathrm{2}} \\ $$$$\sqrt{\left({x}−\mathrm{2}\right)^{\mathrm{2}} }=\sqrt{\left({x}−\mathrm{e}\right)^{\mathrm{2}} } \\ $$$${x}−\mathrm{2}={x}−\mathrm{e} \\ $$$$−\mathrm{2}=−\mathrm{e} \\ $$$$\mathrm{e}=\mathrm{2} \\ $$

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∫(u/du)=? Is this question correct?

$$\int\frac{{u}}{{du}}=? \\ $$$${Is}\:{this}\:{question}\:{correct}? \\ $$

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