Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 339: 71

$$ \frac{x^{3}}{3}+x+\tan ^{-1} x+C$$

Given $$\int\left(x^{2}+1+\frac{1}{x^{2}+1}\right) d x=\frac{x^{3}}{3}+x+\tan ^{-1} x+C$$ Since \begin{aligned}\int\left(x^{2}+1+\frac{1}{x^{2}+1}\right) d x&=\int x^2dx+\int dx+\int \frac{1}{x^{2}+1}dx\\ &= \frac{x^{3}}{3}+x+\tan ^{-1} x+C \end{aligned}