Question

Write a value of $\int e^x\left(\frac{1}{x}-\frac{1}{x^2}\right)dx$.

Answer 1

$$\begin{gathered} \mathrm{Let}I=\int e^x\left(\frac{1}{x}-\frac{1}{x^2}\right)dx \\ \mathrm{As}\mathrm{we}\mathrm{know}\mathrm{that}\int e^x\left\{f\left(x\right)+f\text{'}\left(x\right)\right\}dx=e^{x}f\left(x\right)+C \\ \therefore I=\frac{e^x}{x}+C \end{gathered}$$