\(\int \frac{x^3}{x^4 +1}dx\) is equal to

\(\log (x^2+1)+c\) \(\frac{1}{4}\log (x^4+1)+c\) \(-\log (x^4+1)+c\) None of these

\(\frac{1}{4}\log (x^4+1)+c\)

\(\begin{aligned}\int \frac{x^3}{x^4+1}dx&=\frac{1}{4}\int \frac{4x^3}{x^4+1}dx \\ &=\frac{1}{4}\int \frac{1}{t}dt \text{ where }x^{4}+1=t\end{aligned}\)