Indefinite integration of Rational functions Questions and solutions

Two functions in rational form involve in indefinite integral calculus. The following problems are the list of indefinite integral problems with solutions in different methods to learn how to find the indefinite integration of the rational functions.

Evaluate $\displaystyle \int{\dfrac{x^2+1}{x^4+1}\,}dx$

Evaluate $\displaystyle \int{\dfrac{x^3+x}{x^4-9}}\,dx$

Evaluate $\displaystyle \int{\dfrac{x^2-1}{x^4+1}}\,dx$