If $\int\frac{2^{1/x}}{x^2}dx=K.2^{1/x}$

CUET Preparation Today

Start Free Mocks

Home Questions F5S6CCFJEE

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

If $\int\frac{2^{1/x}}{x^2}dx=K.2^{1/x}$, then K is equal to:

Options:

$\frac{-1}{\log 2}$

- log 2

-1

$\frac{1}{2}$

Correct Answer:

$\frac{-1}{\log 2}$

Explanation:

We have, $\int\frac{2^{1/x}}{x^2}dx=K.2^{1/x}$

Differentiating both sides w.r.t. x, we get $\frac{2^{1/x}}{x^2}=K.2^{1/x}.(\frac{-1}{x^2}).\log 2⇒K=\frac{-1}{\log 2}$