Answer
$\frac{1}{3}$ $x^{3}$$-$ $ln|x+1|$ $+$ $C$
Work Step by Step
Given that,
$\frac {x^{5}+x-1}{x^{3}+1}$
Now,
=$\frac {x^{5}+x-1}{x^{3}+1}$
= $x^{2}$$+$$\frac{-x^{2}+x-1}{x^{3}+1}$
=$x^{2}$$+$$\frac{-x^{2}+x-1}{(x+1)(x^{2}-x+1)}$
=$x^{2}$ $+$ $\frac{-1}{x+1}$
=$x^{2}$ $-$ $\frac{1}{x+1}$
So,
$\int\frac {x^{5}+x-1}{x^{3}+1}dx$
=$\int(x^{2}-\frac {1}{x+1})dx$
=$\frac{1}{3}$ $x^{3}$$-$ $ln|x+1|$ $+$ $c$