Mathematics

$$\int {{x^x}\ln \left( {x} \right)dx}  = $$


ANSWER

$${x^x} + c$$


SOLUTION
Put $$t=x^{x}\implies \ln t =x\ln x\implies \dfrac{d{t}}{t}=(1+\ln x)d{x}\implies d{t}=x^{x}(1+\ln x)d{x}$$
$$\displaystyle\int x^{x}(\ln x+1)d{x}=\int d{t}=t+c=x^{x}+c$$
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Single Correct Medium Published on 17th 09, 2020
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