It is given that d dt ( tlog ⁡t-t )= log ⁡t then exp ⁡ ( _0^12 xlog ⁡(1+x^2) dx )=

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Correct answer: C. (c) Given d dt ( tlog ⁡t-t )= log ⁡t Take, exp ⁡ ( _0^12 xlog ⁡(1+x^2) dx ) Let 1+x^2=t ⇒2 xdx= dt Then, exp ⁡( _1^2 log ⁡t- dt)=( exp ⁡ ( tlog ⁡t-t ))_1^2 = exp ⁡ (2 log ⁡2-2- log ⁡1+1 )= exp ⁡ ( log ⁡4-1 )=e^ ln ⁡4e^-1= 4e

$It is given that \frac{d}{dt} (tlog t - t) = log t then exp (\int_{0}^{1} 2 xlog (1 + x^{2}) dx) =$

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