Mathematics

$$\displaystyle \int x^{x}\left ( 1+\log x \right )dx$$ is equal to


ANSWER

$$\displaystyle x^{x}+k$$


SOLUTION
Let $$I=\int  x^{ x }\left( 1+\log  x \right) dx$$
Substitute $$t={ x }^{ 2 }+1\Rightarrow dt=x^{ x }\left( 1+\log  x \right) dx$$
$$\therefore I=\int { dt } =t+k={ x }^{ x }+k$$
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Single Correct Medium Published on 17th 09, 2020
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