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

\(x+\frac{x^2}{2}+\frac{x^3}{3}-\log|1-x|+c\) \(x+\frac{x^2}{2}-\frac{x^3}{3}-\log|1-x|+c\) \(x-\frac{x^2}{2}+\frac{x^3}{3}-\log|1+x|+c\) None of the above

\(x-\frac{x^2}{2}+\frac{x^3}{3}-\log|1+x|+c\)

\(\begin{aligned}\int \frac{x^3}{x+1}dx&=\int \frac{x^3+1-1}{x+1}dx \\ &=\int \frac{x^3+1}{x+1}dx-\int \frac{1}{x+1}dx\\ &=\int \frac{(x+1)(x^2-x+1)}{x+1}dx-\int \frac{1}{x+1}dx\\ &=\frac{x^3}{3}-\frac{x^2}{2}+x-\log|1+x|+c\end{aligned}\)