Write a value of `inte^x\ (1/x-1/(x^2))\ dx`

Explanation

Solution:

`I=\int e^{x}\(\frac{1}{x}-\frac{1}{x^{2}}\right) d x `

=`\int e^{x} \frac{1}{x} d x-\int e^{x} \frac{1}{x^{2}} d x`

Let `\{u}=\{e}^{\{x}} \Rightarrow d \{u}=\{e}^{\{x}} \{dx}`

`d v=\frac{1}{x^{2}} d x \Rightarrow v=\frac{-1}{x}`

`\int u \cdot v d x=u \int v d x-\int\[\int v d x \cdot \frac{d u}{d x} \cdot d x] \ldots \ldots `. by parts formula.

Integrating by parts, we get

=`\int e^{x} \frac{1}{x} d x+\frac{1}{x} e^{x}-\int e^{x} \frac{1}{x} d x+c`

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