Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

$\int \frac{\pi}{x^{n+1}-x} d x=$

Options:

$\frac{\pi}{n} \log _e\left|\frac{x^n-1}{x^n}\right|+C$

$\log _e\left|\frac{x^n+1}{x^n-1}\right|+C$

$\frac{\pi}{n} \log _e\left|\frac{x^n+1}{x^n}\right|+C$

$\pi \log _e\left|\frac{x^n}{x^n-1}\right|+C$

Correct Answer:

$\frac{\pi}{n} \log _e\left|\frac{x^n-1}{x^n}\right|+C$

Explanation:

The correct answer is Option (1) → $\frac{\pi}{n} \log _e\left|\frac{x^n-1}{x^n}\right|+C$