Question

$\tt Integrate : \int {x}^{x} \:ln(ex) \:dx$ ​

Answer 1

$\tt \int {x}^{x} \:ln(ex) \:dx \\\\\tt</p><p>\int {x}^{x} \:(1+lnx) \:dx \\\\\tt</p><p>Let \: x^x=v \\\\\tt</p><p>log \: v= x log x \\\\\tt</p><p>\frac{1}{v}=1+ logx \\\\\tt</p><p>\frac{dv}{dx}=X^x (1+logx) \\\\\tt</p><p>\int dt = v+c \\\\\tt</p><p>=X^x+C</p><p>$

Answer 2

Answer:

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