Question

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

• A. \(\frac{1}{4} \log_{e}\left|\frac{x^4}{1 + x^{4}}\right| + C\)
• B. \(\frac{1}{5} \log_{e}\left|\frac{x}{1 + x^{4}}\right| + C\)
• C. \(\frac{1}{4} \log_{e}\left|\frac{x}{1 + x^{4}}\right| + C\)
• D. \(\frac{1}{2} \log_{e}\left|\frac{x^2}{1 + x^{4}}\right| + C\)
• E. \(\log_{e}\left|\frac{x}{1 + x^{4}}\right| + C\)

Hint:

For integrals of the form \(\int \frac{dx}{x(1+x^n)}\), use substitution \(t = x^n\).

Answer 1

The Correct Option is A