# Integrate: x^4 /x+1

Solution:

$I=\int \frac{x^{4}}{x+1}dx\\ \\ \Rightarrow \hspace{1cm}I=\int\frac{x^{4}-1+1}{x+1}dx \\ \\ \Rightarrow \hspace{1cm}I=\int \frac{(x^{2}-1)(x^{2}+1)+1}{x+1}dx \\ \\ \Rightarrow \hspace{1cm} I=\int (x-1)(x^{2}+1)dx+\int \frac{1}{x+1}dx \\ \\ \Rightarrow \hspace{1cm}I=\frac{x{4}}{4}+\frac{x{2}}{2}-\frac{x{3}}{3}-x+ln \left | x+1 \right |+c$

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