$\int \frac{\log x}{x^{2}}dx$ is equal

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int \frac{\log x}{x^{2}}dx$ is equal to

Options:

$\frac{1}{2}\left(\log x+1\right)+C$

$-\frac{1}{x}\left(\log x+1\right)+C$

$\frac{1}{x}\left(\log x+1\right)+C$

$\frac{1}{x}\left(\log x-1\right)+C$

Correct Answer:

$-\frac{1}{x}\left(\log x+1\right)+C$

Explanation:

$\int \frac{\log x}{x^{2}}dx=\frac{-\log x}{x}+\int\frac{1}{x^2}dx$

$=\frac{-\log x}{x}-\frac{1}{x}+C$

$=-\frac{1}{x}(\log x+1)+C$