Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Determinants

Question:

The value of the integral $\int e^x\left(\frac{1}{x}-\frac{1}{x^2}\right) d x$ is :

Options:

$\frac{e^x}{x}+C$, where C is a constant

$\frac{e^{-x}}{x}+C$, where C is a constant

$e^x+C$, where C is a constant

$e^{-x}+C$, where C is a constant

Correct Answer:

$\frac{e^x}{x}+C$, where C is a constant

Explanation:

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

this of the type

$\int e^x (f(x) + f'(x)) dx = e^x f(x) + C$

here $f(x) = \frac{1}{x}~~~~~~f'(x) = \frac{1}{x^2}$

$I = \frac{e^x}{x}+C$