Mathematics

The integral $$\displaystyle  \int (1+x-\displaystyle \frac{1}{x})e^{x+\frac{1}{x}} dx $$ is equal to 


ANSWER

$$ xe^{x+\frac{1}{x}} +c $$


SOLUTION
$$\displaystyle \int (1+x-\displaystyle \frac{1}{x})e^{x+\frac{1}{x}} dx $$

$$\displaystyle =\int e^{(x+\frac{1}{x})}dx + \int x(1-\displaystyle \frac{1}{x^{2}})e^{(x+\frac{1}{x})}dx$$

$$\displaystyle =\int e^{(x+\frac{1}{x})}dx + xe^{(x+\frac{1}{x})}-\int e^{(x+\frac{1}{x})}dx$$

Using integration by parts

$$ =xe^{(x+\frac{1}{x})}+c$$
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Single Correct Hard Published on 17th 09, 2020
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