Question

The integral \( \int \frac{2+x^4}{1+x^2} dx \) is equal to

• A. \(\frac{1}{3}x^3 + 3 \tan^{-1}x - x + C\)
• B. \(\frac{1}{3}x^3 + 3 \tan^{-1}x + x + C\)
• C. \(\frac{1}{3}x^3 - 3 \tan^{-1}x - x + C\)
• D. \(\frac{1}{3}x^3 - 3 \tan^{-1}x + x + C\)

Hint:

When integrating rational functions where the numerator's degree is greater than or equal to the denominator's degree, always perform algebraic division (or manipulation) first. This breaks the complex fraction into simpler terms (a polynomial and a proper rational fraction) that are easier to integrate.

Answer 1

The Correct Option is A