Question

\( \int \frac{x^{n-1}}{x^n + a^n} dx = \)

• A. \( \frac{1}{n} \tan^{-1}\left(\frac{x^n}{a^n}\right) + C \)
• B. \( \frac{1}{n} \tan^{-1}\left(\frac{x}{a}\right) + C \)
• C. \( \frac{1}{n} \sin^{-1}\left(\frac{x}{a}\right) + C \)
• D. \( \frac{n}{a} \cos^{-1}\left(\frac{x}{a}\right) + C \)
• E. \( \frac{1}{na} \cot^{-1}\left(\frac{x}{a}\right) + C \)

Hint:

When numerator is derivative of denominator, use \( \log \) directly.

Answer 1

The Correct Option is B