Question

$\int \left(e^x\right)\left[\frac{(x-1)}{x^2}\right]dx=$

• A. $\frac{e^x}{x^2}+c$
• B. $\frac{-e^x}{x^2}+c$
• C. $\frac{e^x}{x}+c$
• D. $\frac{-e^x}{x}+c$

Answer 1

The correct option is C

$\frac{e^x}{x}+c$

Explanation for the correct option:

Given, $\int \left(e^x\right)\left[\frac{(x-1)}{x^2}\right]dx$

$=\int \left(e^x\right)\left[\frac{1}{x}-\frac{1}{x^2}\right]dx$

$=\frac{e^x}{x}+c$ $\left[\because \int e^x\left[f\left(x\right)+f\text{'}\left(x\right)\right]dx=e^{x}f\left(x\right)+C\right]$

Hence, Option ‘C’ is Correct.