Mathematics

Solve:-
$$\int {\dfrac{{{e^x}}}{x}} \left( {1 + x.\ln x} \right)dx$$


SOLUTION
$$\displaystyle\int \dfrac{e^{x}}{x}(1+x\ln x)\ dx$$

$$=\displaystyle\int e^{x}\left(\dfrac{1}{x}+\ln x\right)\ dx$$

We know that $$\displaystyle\int e^{x}(f(x)+f(x))\ dx=e^{x}f(x)+c$$

$$=\dfrac{e^{x}}{x}+c$$  because   $$\dfrac{d(\ln x)}{dx}=\dfrac{1}{x}$$
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Subjective Medium Published on 17th 09, 2020
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